added japanese translation of arnoldi module. 75/14475/2
Rui Hirokawa [Tue, 29 Apr 2014 09:33:32 +0000 (18:33 +0900)]
Change-Id: I48f05a8a43d18a342cc4d4ba3b9884e281a44c92

scilab/modules/arnoldi/help/ja_JP/dnaupd.xml [new file with mode: 0644]
scilab/modules/arnoldi/help/ja_JP/dneupd.xml [new file with mode: 0644]
scilab/modules/arnoldi/help/ja_JP/dsaupd.xml [new file with mode: 0644]
scilab/modules/arnoldi/help/ja_JP/dseupd.xml [new file with mode: 0644]
scilab/modules/arnoldi/help/ja_JP/eigs.xml
scilab/modules/arnoldi/help/ja_JP/znaupd.xml [new file with mode: 0644]
scilab/modules/arnoldi/help/ja_JP/zneupd.xml [new file with mode: 0644]

diff --git a/scilab/modules/arnoldi/help/ja_JP/dnaupd.xml b/scilab/modules/arnoldi/help/ja_JP/dnaupd.xml
new file mode 100644 (file)
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--- /dev/null
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+<?xml version="1.0" encoding="UTF-8"?>
+
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="dnaupd" xml:lang="ja">
+    
+    <refnamediv>
+        
+        <refname>dnaupd</refname>
+        
+        <refpurpose>
+            
+            暗黙のうちに再開されるArnoldi反復へのインターフェイスで,
+            
+            実線形演算子の小数の固有値/ベクトルの組を近似的に計算します.
+            
+            <emphasis role="bold">
+                
+                この関数は廃止されました. <link linkend="eigs">eigs</link>を使用してください
+                
+            </emphasis>
+            
+        </refpurpose>
+        
+    </refnamediv>
+    
+    <refsynopsisdiv>
+        
+        <title>Calling Sequence</title>
+        
+        <synopsis>[IDO, RESID, V, IPARAM, IPNTR, WORKD, WORKL, INFO] = dnaupd(ID0, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, IPARAM, IPNTR, WORKD, WORKL, INFO)</synopsis>
+        
+    </refsynopsisdiv>
+    
+    <refsection>
+        
+        <title>Arguments</title>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>ID0</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        Integer. (INPUT/OUTPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Reverse communication flag. IDO must
+                        
+                        be zero on the first call to dnaupd. IDO will be set internally to
+                        
+                        indicate the type of operation to be performed. Control is then
+                        
+                        given back to the calling routine which has the responsibility to
+                        
+                        carry out the requested operation and call dnaupd with the result.
+                        
+                        The operand is given in WORKD(IPNTR(1)), the result must be put in
+                        
+                        WORKD(IPNTR(2)).
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 0: first call to the reverse communication
+                                
+                                interface.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = -1: compute Y = OP * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for Y. This
+                                
+                                is for the initialization phase to force the starting vector
+                                
+                                into the range of OP.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 1: compute Y = OP * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for Y. In
+                                
+                                mode 3 and 4, the vector B * X is already available in
+                                
+                                WORKD(ipntr(3)). It does not need to be recomputed in forming OP
+                                
+                                * X.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 2: compute Y = B * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for
+                                
+                                Y.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 3: compute the IPARAM(8) real and imaginary parts of
+                                
+                                the shifts where INPTR(14) is the pointer into WORKL for placing
+                                
+                                the shifts. See Remark 5 below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>IDO = 99: done.</para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>BMAT</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        Character. (INPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        specifies the type of the matrix B that defines the
+                        
+                        semi-inner product for the operator OP.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>'I' - standard eigenvalue problem A * x = lambda * x</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'G' - generalized eigenvalue problem A * x =
+                                
+                                lambda * B * x
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>N</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT)</para>
+                    
+                    <para>dimension of the eigenproblem.</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>WHICH</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        string of length 2. (INPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Specifies which of the Ritz values of OP to
+                        
+                        compute.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'LM' - want the NEV eigenvalues of largest
+                                
+                                magnitude.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'SM' - want the NEV eigenvalues of smallest
+                                
+                                magnitude.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'LR' - want the NEV eigenvalues of largest real
+                                
+                                part.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'SR' - want the NEV eigenvalues of smallest real
+                                
+                                part.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'LI' - want the NEV eigenvalues of largest imaginary
+                                
+                                part.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'SI' - want the NEV eigenvalues of smallest imaginary
+                                
+                                part.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>NEV</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        Integer. (INPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        number of eigenvalues of OP to be computed. 0 &lt;
+                        
+                        NEV &lt; N-1.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>TOL</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        scalar. (INPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Stopping criterion: the relative accuracy of the Ritz
+                        
+                        value is considered acceptable if BOUNDS(I) &lt;= TOL*ABS(RITZ(I)).
+                        
+                        If TOL &lt;= 0. is passed the machine precision is set.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>RESID</term>
+                
+                <listitem>
+                    
+                    <para>array of length N. (INPUT/OUTPUT)</para>
+                    
+                    <para>
+                        
+                        On INPUT: If INFO = 0, a random initial residual vector is
+                        
+                        used, else RESID contains the initial residual vector, possibly from
+                        
+                        a previous run.
+                        
+                    </para>
+                    
+                    <para>On OUTPUT: RESID contains the final residual vector.</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>NCV</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        Integer. (INPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        number of columns of the matrix V. NCV must satisfy
+                        
+                        the two inequalities 2 &lt;= NCV - NEV and NCV &lt;= N.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        This will indicate how many Arnoldi vectors are generated at
+                        
+                        each iteration.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        After the startup phase in which NEV Arnoldi vectors are
+                        
+                        generated, the algorithm generates approximately NCV - NEV Arnoldi
+                        
+                        vectors at each subsequent update iteration. Most of the cost in
+                        
+                        generating each Arnoldi vector is in the matrix-vector operation
+                        
+                        OP * x.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        NOTE: 2 &lt;= NCV - NEV in order that complex conjugate pairs of
+                        
+                        Ritz values are kept together. (See remark 4 below)
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>V</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        N by NCV array. (OUTPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Contains the final set of Arnoldi basis
+                        
+                        vectors.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>IPARAM</term>
+                
+                <listitem>
+                    
+                    <para>array of length 11. (INPUT/OUTPUT)</para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(1) = ISHIFT: method for selecting the implicit
+                                
+                                shifts. The shifts selected at each iteration are used to
+                                
+                                restart the Arnoldi iteration in an implicit fashion.
+                                
+                            </para>
+                            
+                            <itemizedlist>
+                                
+                                <listitem>
+                                    
+                                    <para>
+                                        
+                                        ISHIFT = 0: the shifts are provided by the user via
+                                        
+                                        reverse communication. The real and imaginary parts of the
+                                        
+                                        NCV eigenvalues of the Hessenberg matrix H are returned in
+                                        
+                                        the part of the WORKL array corresponding to RITZR and
+                                        
+                                        RITZI. See remark 5 below.
+                                        
+                                    </para>
+                                    
+                                </listitem>
+                                
+                                <listitem>
+                                    
+                                    <para>
+                                        
+                                        ISHIFT = 1: exact shifts with respect to the current
+                                        
+                                        Hessenberg matrix H. This is equivalent to restarting the
+                                        
+                                        iteration with a starting vector that is a linear
+                                        
+                                        combination of approximate Schur vectors associated with the
+                                        
+                                        "wanted" Ritz values.
+                                        
+                                    </para>
+                                    
+                                </listitem>
+                                
+                            </itemizedlist>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>IPARAM(2) = LEVEC. No longer referenced.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>IPARAM(3) = MXITER </para>
+                            
+                            <para>
+                                
+                                On INPUT: maximum number of Arnoldi update iterations
+                                
+                                allowed.
+                                
+                            </para>
+                            
+                            <para>
+                                
+                                On OUTPUT: actual number of Arnoldi update iterations
+                                
+                                taken.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(4) = NB: blocksize to be used in the recurrence.
+                                
+                                The code currently works only for NB = 1.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(5) = NCONV: number of "converged" Ritz values. This
+                                
+                                represents the number of Ritz values that satisfy the
+                                
+                                convergence criterion.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(6) = IUPD No longer referenced. Implicit restarting
+                                
+                                is ALWAYS used.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(7) = MODE On INPUT determines what type of
+                                
+                                eigenproblem is being solved. Must be 1,2,3,4; See under
+                                
+                                Description of dnaupd for the five modes available.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(8) = NP When ido = 3 and the user provides shifts
+                                
+                                through reverse communication (IPARAM(1)=0), dnaupd returns NP,
+                                
+                                the number of shifts the user is to provide.
+                                
+                            </para>
+                            
+                            <para>0 &lt; NP &lt;= NCV-NEV. See Remark 5 below.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>IPARAM(9) = NUMOP, </para>
+                            
+                            <para>IPARAM(10) = NUMOPB, </para>
+                            
+                            <para>IPARAM(11) = NUMREO, </para>
+                            
+                            <para>
+                                
+                                On OUTPUT: NUMOP = total number of OP*x operations, NUMOPB
+                                
+                                = total number of B*x operations if BMAT='G', NUMREO = total
+                                
+                                number of steps of re-orthogonalization.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>IPNTR</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        array of length 14. (OUTPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Pointer to mark the starting locations in
+                        
+                        the WORKD and WORKL arrays for matrices/vectors used by the Arnoldi
+                        
+                        iteration.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(1): pointer to the current operand vector X in
+                                
+                                WORKD.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(2): pointer to the current result vector Y in
+                                
+                                WORKD.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(3): pointer to the vector B * X in WORKD when used
+                                
+                                in the shift-and-invert mode.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(4): pointer to the next available location in WORKL
+                                
+                                that is untouched by the program.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(5): pointer to the NCV by NCV upper Hessenberg
+                                
+                                matrix H in WORKL.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(6): pointer to the real part of the ritz value array
+                                
+                                RITZR in WORKL.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(7): pointer to the imaginary part of the ritz value
+                                
+                                array RITZI in WORKL.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(8): pointer to the Ritz estimates in array WORKL
+                                
+                                associated with the Ritz values located in RITZR and RITZI in
+                                
+                                WORKL.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5
+                                
+                                below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                    <para>
+                        
+                        Note: IPNTR(9:13) is only referenced by dneupd . See Remark
+                        
+                        2.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(9): pointer to the real part of the NCV RITZ values
+                                
+                                of the original system.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(10): pointer to the imaginary part of the NCV RITZ
+                                
+                                values of the original system.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(11): pointer to the NCV corresponding error
+                                
+                                bounds.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(12):pointer to the NCV by NCV upper quasi-triangular
+                                
+                                Schur matrix for H.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(13): pointer to the NCV by NCV matrix of
+                                
+                                eigenvectors of the upper Hessenberg matrix H. Only referenced
+                                
+                                by dneupd if RVEC = 1 See Remark 2 below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>WORKD</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        Double precision work array of length 3 * N. (REVERSE
+                        
+                        COMMUNICATION)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Distributed array to be used in the basic Arnoldi iteration
+                        
+                        for reverse communication. The user should not use WORKD as
+                        
+                        temporary workspace during the iteration. Upon termination
+                        
+                        WORKD(1:N) contains B*RESID(1:N). If an invariant subspace
+                        
+                        associated with the converged Ritz values is desired, see remark 2
+                        
+                        below, subroutine dneupd uses this output. See Data Distribution
+                        
+                        Note below.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>WORKL</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        work array of length at least 3 * NCV ** 2 + 6 * NCV.
+                        
+                        (OUTPUT/WORKSPACE)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Private (replicated) array on each PE or array
+                        
+                        allocated on the front end. See Data Distribution Note below.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>INFO</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT/OUTPUT)</para>
+                    
+                    <para>
+                        
+                        If INFO == 0, a randomly initial residual vector is used, else
+                        
+                        RESID contains the initial residual vector, possibly from a previous
+                        
+                        run.
+                        
+                    </para>
+                    
+                    <para>Error flag on output.</para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>0: Normal exit.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                1: Maximum number of iterations taken. All possible
+                                
+                                eigenvalues of OP has been found. IPARAM(5) returns the number
+                                
+                                of wanted converged Ritz values.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                2: No longer an informational error. Deprecated starting
+                                
+                                with release 2 of ARPACK.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                3: No shifts could be applied during a cycle of the
+                                
+                                Implicitly restarted Arnoldi iteration. One possibility is to
+                                
+                                increase the size of NCV relative to NEV. See remark 4
+                                
+                                below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-1: N must be positive.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-2: NEV must be positive.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-3: NCV-NEV &gt;= 2 and less than or equal to N.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -4: The maximum number of Arnoldi update iterations
+                                
+                                allowed must be greater than zero.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI',
+                                
+                                'SI'.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-6: BMAT must be one of 'I' or 'G'.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -7: Length of private work array WORKL is not
+                                
+                                sufficient.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -8: Error return from LAPACK eigenvalue
+                                
+                                calculation.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-9: Starting vector is zero.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-10: IPARAM(7) must be 1, 2, 3, 4.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-11: IPARAM(7) = 1 and BMAT = 'G' are incompatable.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-12: IPARAM(1) must be equal to 0 or 1.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -9999: Could not build an Arnoldi factorization. IPARAM(5)
+                                
+                                returns the size of the current Arnoldi factorization. The user
+                                
+                                is advised to check that enough workspace and array storage has
+                                
+                                been allocated.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+        </variablelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Description</title>
+        
+        <para>
+            
+            Reverse communication interface for the Implicitly Restarted Arnoldi
+            
+            iteration. This subroutine computes approximations to a few eigenpairs of
+            
+            a linear operator "OP" with respect to a semi-inner product defined by a
+            
+            symmetric positive semi-definite real matrix B. B may be the identity
+            
+            matrix. NOTE: If the linear operator "OP" is real and symmetric with
+            
+            respect to the real positive semi-definite symmetric matrix B, i.e. B*OP =
+            
+            (OP`)*B, then subroutine dsaupd should be used instead.
+            
+        </para>
+        
+        <para>
+            
+            The computed approximate eigenvalues are called Ritz values and the
+            
+            corresponding approximate eigenvectors are called Ritz vectors.
+            
+        </para>
+        
+        <para>
+            
+            dnaupd is usually called iteratively to solve one of the following
+            
+            problems:
+            
+        </para>
+        
+        <itemizedlist>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 1: A*x = lambda*x. <literal>
+                        
+                        OP = A , B =
+                        
+                        I
+                        
+                    </literal>
+                    
+                    .
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 2: A*x = lambda*M*x, M symmetric positive definite
+                    
+                    <literal>OP = inv[M]*A, B = M</literal>. (If M can be factored see
+                    
+                    remark 3 below)
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 3: A*x = lambda*M*x, M symmetric positive semi-definite.
+                    
+                    <literal>OP = Real_Part{ inv[A - sigma*M]*M }, B = M</literal>.
+                    
+                    shift-and-invert mode (in real arithmetic)
+                    
+                </para>
+                
+                <para>
+                    
+                    If <literal>OP*x = amu*x</literal>, then
+                    
+                </para>
+                
+                <para>
+                    
+                    <literal>
+                        
+                        amu = 1/2 * [ 1/(lambda-sigma) +
+                        
+                        1/(lambda-conjg(sigma))]
+                        
+                    </literal>
+                    
+                    .
+                    
+                </para>
+                
+                <para>
+                    
+                    Note: If sigma is real, i.e. imaginary part of sigma is zero;
+                    
+                    <literal>
+                        
+                        Real_Part{ inv[A - sigma*M]*M } == inv[A -
+                        
+                        sigma*M]*M
+                        
+                    </literal>
+                    
+                    <literal>
+                        
+                        amu ==
+                        
+                        1/(lambda-sigma)
+                        
+                    </literal>
+                    
+                    .
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 4: A*x = lambda*M*x, M symmetric semi-definite <literal>
+                        
+                        OP
+                        
+                        = Imaginary_Part{ inv[A - sigma*M]*M } , B = M
+                        
+                    </literal>
+                    
+                    .
+                    
+                    shift-and-invert mode (in real arithmetic)
+                    
+                </para>
+                
+                <para>
+                    
+                    If <literal>OP*x = amu*x</literal>, then <literal>
+                        
+                        amu = 1/2i * [
+                        
+                        1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ]
+                        
+                    </literal>
+                    
+                    .
+                    
+                </para>
+                
+            </listitem>
+            
+        </itemizedlist>
+        
+        <para>
+            
+            Both mode 3 and 4 give the same enhancement to eigenvalues close to
+            
+            the (complex) shift sigma. However, as lambda goes to infinity, the
+            
+            operator OP in mode 4 dampens the eigenvalues more strongly than does OP
+            
+            defined in mode 3.
+            
+        </para>
+        
+        <para>
+            
+            NOTE: The action of w &lt;- inv[A - sigma * M] * v or w &lt;- inv[M] * v
+            
+            should be accomplished either by a direct method using a sparse matrix
+            
+            factorization and solving <literal>[A - sigma * M] * w = v</literal> or
+            
+            <literal>M * w = v</literal>, or through an iterative method for solving
+            
+            these systems. If an iterative method is used, the convergence test must
+            
+            be more stringent than the accuracy requirements for the eigenvalue
+            
+            approximations.
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Example</title>
+        
+        <programlisting role="example">
+            
+            <![CDATA[
+// The following sets dimensions for this problem.
+
+nx    = 10;
+
+nev   = 3;
+ncv   = 6;
+bmat  = 'I';
+which = 'LM';
+
+// Local Arrays
+
+iparam  = zeros(11, 1);
+ipntr   = zeros(14, 1);
+_select = zeros(ncv, 1);
+dr       = zeros(nev + 1, 1);
+di      = zeros(nev + 1, 1);
+z       = zeros(nx, nev + 1);
+resid   = zeros(nx, 1);
+v       = zeros(nx, ncv);
+workd   = zeros(3 * nx, 1);
+workev  = zeros(3 * ncv, 1);
+workl   = zeros(3 * ncv * ncv + 6 * ncv, 1);
+
+// Build the test matrix
+
+A            = diag(10 * ones(nx, 1));
+A(1:$-1,2:$) = A(1:$-1,2:$) + diag(6 * ones(nx-1,1));
+A(2:$,1:$-1) = A(2:$,1:$-1) + diag(-6 * ones(nx-1,1));
+
+tol    = 0;
+ido    = 0;
+
+ishfts = 1;
+maxitr = 300;
+mode1  = 1;
+
+iparam(1) = ishfts;
+iparam(3) = maxitr;
+iparam(7) = mode1;
+
+sigmar = 0; // the real part of the shift
+sigmai = 0; // the imaginary part of the shift
+info_dnaupd = 0;
+
+// M A I N   L O O P (Reverse communication)
+
+while(ido <> 99)
+  // Repeatedly call the routine DNAUPD and take actions indicated by parameter IDO until
+  // either convergence is indicated or maxitr has been exceeded.
+
+  [ido, resid, v, iparam, ipntr, workd, workl, info_dnaupd] = dnaupd(ido, bmat, nx, which, nev, tol, resid, ncv, v, iparam, ipntr, workd, workl, info_dnaupd);
+
+  if(info_dnaupd < 0)
+    printf('\nError with dnaupd, info = %d\n',info_dnaupd);
+    printf('Check the documentation of dnaupd\n\n');
+  end
+
+  if(ido == -1 | ido == 1)
+    // Perform matrix vector multiplication
+    workd(ipntr(2):ipntr(2) + nx -1) = A * workd(ipntr(1):ipntr(1) + nx - 1);
+  end
+end
+
+// Post-Process using DNEUPD.
+rvec    = 1;
+howmany = 'A';
+info_dneupd = 0;
+
+[dr, di, z, resid, v, iparam, ipntr, workd, workl, info_dneupd] = dneupd(rvec, howmany, _select, dr, di, z, sigmar, sigmai, workev, ...
+                                                                       bmat, nx, which, nev, tol, resid, ncv, v, ...
+                                                                       iparam, ipntr, workd, workl, info_dneupd);
+
+if(info_dneupd < 0)
+  printf('\nError with dneupd, info = %d\n', info_dneupd);
+  printf('Check the documentation of dneupd.\n\n');
+end
+
+printf('\nDNSIMP\n');
+printf('======\n');
+printf('\n');
+printf('Size of the matrix is %d\n', nx);
+printf('The number of Ritz values requested is %d\n', nev);
+printf('The number of Arnoldi vectors generated (NCV) is %d\n', ncv);
+printf('What portion of the spectrum: %s\n', which);
+printf('The number of Implicit Arnoldi update iterations taken is %d\n', iparam(3));
+printf('The number of OP*x is %d\n', iparam(9));
+printf('The convergence criterion is %d\n', tol);
+
+]]>
+            
+        </programlisting>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Remarks</title>
+        
+        <para>
+            
+            1. The computed Ritz values are approximate eigenvalues of OP. The
+            
+            selection of WHICH should be made with this in mind when Mode = 3 and 4.
+            
+            After convergence, approximate eigenvalues of the original problem may be
+            
+            obtained with the ARPACK subroutine dneupd.
+            
+        </para>
+        
+        <para>
+            
+            2. If a basis for the invariant subspace corresponding to the
+            
+            converged Ritz values is needed, the user must call dneupd immediately
+            
+            following completion of dnaupd. This is new starting with release 2 of
+            
+            ARPACK.
+            
+        </para>
+        
+        <para>
+            
+            3. If M can be factored into a Cholesky factorization M = LL` then
+            
+            Mode = 2 should not be selected. Instead one should use Mode = 1 with OP =
+            
+            inv(L) * A * inv(L`). Appropriate triangular linear systems should be solved
+            
+            with L and L` rather than computing inverses. After convergence, an
+            
+            approximate eigenvector z of the original problem is recovered by solving
+            
+            L`z = x where x is a Ritz vector of OP.
+            
+        </para>
+        
+        <para>
+            
+            4. At present there is no a-priori analysis to guide the selection
+            
+            of NCV relative to NEV. The only formal requirement is that NCV &gt; NEV +
+            
+            2. However, it is recommended that NCV &gt;= 2 * NEV + 1. If many problems of
+            
+            the same type are to be solved, one should experiment with increasing NCV
+            
+            while keeping NEV fixed for a given test problem. This will usually
+            
+            decrease the required number of OP*x operations but it also increases the
+            
+            work and storage required to maintain the orthogonal basis vectors. The
+            
+            optimal "cross-over" with respect to CPU time is problem dependent and
+            
+            must be determined empirically. See Chapter 8 of Reference 2 for further
+            
+            information.
+            
+        </para>
+        
+        <para>
+            
+            5. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the NP
+            
+            = IPARAM(8) real and imaginary parts of the shifts in locations
+            
+        </para>
+        
+        <programlisting>
+            
+            real part                  imaginary part
+            
+            -----------------------    --------------
+            
+            1   WORKL(IPNTR(14))           WORKL(IPNTR(14) + NP)
+            
+            2   WORKL(IPNTR(14) + 1)         WORKL(IPNTR(14) + NP + 1)
+            
+            .                          .
+            
+            .                          .
+            
+            .                          .
+            
+            NP  WORKL(IPNTR(14) + NP - 1)      WORKL(IPNTR(14) + 2 * NP - 1).
+            
+        </programlisting>
+        
+        <para>
+            
+            Only complex conjugate pairs of shifts may be applied and the pairs
+            
+            must be placed in consecutive locations. The real part of the eigenvalues
+            
+            of the current upper Hessenberg matrix are located in WORKL(IPNTR(6))
+            
+            through WORKL(IPNTR(6) + NCV - 1) and the imaginary part in WORKL(IPNTR(7))
+            
+            through WORKL(IPNTR(7) + NCV - 1). They are ordered according to the order
+            
+            defined by WHICH. The complex conjugate pairs are kept together and the
+            
+            associated Ritz estimates are located in WORKL(IPNTR(8)),
+            
+            WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8) + NCV - 1).
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection role="see also">
+        
+        <title>See Also</title>
+        
+        <simplelist type="inline">
+            
+            <member>
+                
+                <link linkend="dsaupd">dsaupd</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="dneupd">dneupd</link>
+                
+            </member>
+            
+        </simplelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Bibliography</title>
+        
+        <para>
+            
+            1. D.C. Sorensen, "Implicit Application of Polynomial Filters in a
+            
+            k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), pp
+            
+            357-385.
+            
+        </para>
+        
+        <para>
+            
+            2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
+            
+            Restarted Arnoldi Iteration", Rice University Technical Report TR95-13,
+            
+            Department of Computational and Applied Mathematics.
+            
+        </para>
+        
+        <para>
+            
+            3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall,
+            
+            1980.
+            
+        </para>
+        
+        <para>
+            
+            4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos
+            
+            Program", Computer Physics Communications, 53 (1989), pp 169-179.
+            
+        </para>
+        
+        <para>
+            
+            5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to
+            
+            Implement the Spectral Transformation", Math. Comp., 48 (1987), pp
+            
+            663-673.
+            
+        </para>
+        
+        <para>
+            
+            6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
+            
+            Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", SIAM J.
+            
+            Matr. Anal. Apps., January (1993).
+            
+        </para>
+        
+        <para>
+            
+            7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines for
+            
+            Updating the QR decomposition", ACM TOMS, December 1990, Volume 16 Number
+            
+            4, pp 369-377.
+            
+        </para>
+        
+        <para>
+            
+            8. R.B. Lehoucq, D.C. Sorensen, "Implementation of Some Spectral
+            
+            Transformations in a k-Step Arnoldi Method". In Preparation.
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Used Functions</title>
+        
+        <para>Based on ARPACK routine dnaupd</para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>履歴</title>
+        
+        <revhistory>
+            
+            <revision>
+                
+                <revnumber>5.4.0</revnumber>
+                
+                <revremark>
+                    
+                    関数は廃止され,<link linkend="eigs">eigs</link>に代替されました.
+                    
+                </revremark>
+                
+            </revision>
+            
+        </revhistory>
+        
+    </refsection>
+    
+</refentry>
+
diff --git a/scilab/modules/arnoldi/help/ja_JP/dneupd.xml b/scilab/modules/arnoldi/help/ja_JP/dneupd.xml
new file mode 100644 (file)
index 0000000..b2ca460
--- /dev/null
@@ -0,0 +1,1194 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="dneupd" xml:lang="ja">
+    
+    <refnamediv>
+        
+        <refname>dneupd</refname>
+        
+        <refpurpose>
+            
+            暗黙のうちに再開されるArnoldi反復へのインターフェイスで,
+            
+            実線形演算子の小数の固有値/ベクトルの組を近似する
+            
+            A * z = lambda * B * z の固有値を収束的近似により計算します.
+            
+            <emphasis role="bold">
+                
+                この関数は廃止されました. <link linkend="eigs">eigs</link>を使用してください
+                
+            </emphasis>
+            
+        </refpurpose>
+        
+    </refnamediv>
+    
+    <refsynopsisdiv>
+        
+        <title>Calling Sequence</title>
+        
+        <synopsis>
+            
+            [Dr, Di, Z, RESID, V, IPARAM, IPNTR, WORKD, WORKL, INFO] = dneupd(RVEC, HOWMANY, SELECT, Dr, Di, Z, SIGMAr, SIGMAi, WORKev,
+            
+            BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, IPARAM, IPNTR, WORKD, WORKL, INFO)
+            
+        </synopsis>
+        
+    </refsynopsisdiv>
+    
+    <refsection>
+        
+        <title>Arguments</title>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>RVEC</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT)</para>
+                    
+                    <para>
+                        
+                        Specifies whether a basis for the invariant subspace
+                        
+                        corresponding to the converged Ritz value approximations for the
+                        
+                        eigenproblem A * z = lambda * B * z is computed.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>RVEC = 0 Compute Ritz values only.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>RVEC = 1 Compute the Ritz vectors or Schur vectors.</para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                    <para>See Remarks below.</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>HOWMANY</term>
+                
+                <listitem>
+                    
+                    <para>Character. (INPUT) </para>
+                    
+                    <para>
+                        
+                        Specifies the form of the basis for the invariant subspace
+                        
+                        corresponding to the converged Ritz values that is to be
+                        
+                        computed.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>'A': Compute NEV Ritz vectors;</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>'P': Compute NEV Schur vectors;</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'S': compute some of the Ritz vectors, specified by the
+                                
+                                integer array SELECT.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>SELECT</term>
+                
+                <listitem>
+                    
+                    <para>Integer array of dimension NCV. (INPUT) </para>
+                    
+                    <para>
+                        
+                        If HOWMANY = 'S', SELECT specifies the Ritz vectors to be
+                        
+                        computed. To select the Ritz vector corresponding to a Ritz value
+                        
+                        (DR(j), DI(j)), SELECT(j) must be set to 1.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        If HOWMANY = 'A' or 'P', SELECT is used as internal
+                        
+                        workspace.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>DR</term>
+                
+                <listitem>
+                    
+                    <para>Double precision array of dimension NEV + 1. (OUTPUT)</para>
+                    
+                    <para>
+                        
+                        If IPARAM(7) = 1, 2 or 3 and SIGMAI = 0.0 then on exit: DR
+                        
+                        contains the real part of the Ritz approximations to the eigenvalues
+                        
+                        of A * z = lambda * B * z.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        If IPARAM(7) = 3, 4 and SIGMAI is not equal to zero, then on
+                        
+                        exit: DR contains the real part of the Ritz values of OP computed by
+                        
+                        DNAUPD.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        A further computation must be performed by the user to
+                        
+                        transform the Ritz values computed for OP by DNAUPD to those of the
+                        
+                        original system A * z = lambda * B * z. See remark 3 below.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>DI</term>
+                
+                <listitem>
+                    
+                    <para>Double precision array of dimension NEV + 1. (OUTPUT) </para>
+                    
+                    <para>
+                        
+                        On exit, DI contains the imaginary part of the Ritz value
+                        
+                        approximations to the eigenvalues of A * z = lambda * B * z associated
+                        
+                        with DR.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        NOTE: When Ritz values are complex, they will come in complex
+                        
+                        conjugate pairs. If eigenvectors are requested, the corresponding
+                        
+                        Ritz vectors will also come in conjugate pairs and the real and
+                        
+                        imaginary parts of these are represented in two consecutive columns
+                        
+                        of the array Z (see below).
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>Z</term>
+                
+                <listitem>
+                    
+                    <para>Double precision N by NEV + 1 array </para>
+                    
+                    <para>if RVEC = 1 and HOWMANY = 'A'. (OUTPUT) </para>
+                    
+                    <para>
+                        
+                        On exit, if RVEC = 1 and HOWMANY = 'A', then the columns of Z
+                        
+                        represent approximate eigenvectors (Ritz vectors) corresponding to
+                        
+                        the NCONV = IPARAM(5) Ritz values for eigensystem A * z = lambda * B * z.
+                        
+                        The complex Ritz vector associated with the Ritz value with positive
+                        
+                        imaginary part is stored in two consecutive columns. The first
+                        
+                        column holds the real part of the Ritz vector and the second column
+                        
+                        holds the imaginary part. The Ritz vector associated with the Ritz
+                        
+                        value with negative imaginary part is simply the complex conjugate
+                        
+                        of the Ritz vector associated with the positive imaginary part.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        If RVEC = 0 or HOWMANY = 'P', then Z is not referenced.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        NOTE: If if RVEC = 1 and a Schur basis is not required, the
+                        
+                        array Z may be set equal to first NEV+1 columns of the Arnoldi basis
+                        
+                        array V computed by DNAUPD . In this case the Arnoldi basis will be
+                        
+                        destroyed and overwritten with the eigenvector basis.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>SIGMAR</term>
+                
+                <listitem>
+                    
+                    <para>Double precision (INPUT) </para>
+                    
+                    <para>
+                        
+                        If IPARAM(7) = 3 or 4, represents the real part of the
+                        
+                        shift.
+                        
+                    </para>
+                    
+                    <para>Not referenced if IPARAM(7) = 1 or 2.</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>SIGMAI</term>
+                
+                <listitem>
+                    
+                    <para>Double precision (INPUT) </para>
+                    
+                    <para>
+                        
+                        If IPARAM(7) = 3 or 4, represents the imaginary part of the
+                        
+                        shift.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Not referenced if IPARAM(7) = 1 or 2. See remark 3
+                        
+                        below.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>WORKEV</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        Double precision work array of dimension 3 * NCV.
+                        
+                        (WORKSPACE)
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+        </variablelist>
+        
+        <para>
+            
+            NOTE: The remaining arguments BMAT, N, WHICH, NEV, TOL, RESID, NCV,
+            
+            V, IPARAM, IPNTR, WORKD, WORKL, LWORKL, INFO must be passed directly to
+            
+            DNEUPD following the last call to DNAUPD .
+            
+        </para>
+        
+        <para>
+            
+            These arguments MUST NOT BE MODIFIED between the last call to
+            
+            DNAUPD and the call to DNEUPD .
+            
+        </para>
+        
+        <para>
+            
+            Three of these parameters (V, WORKL, INFO) are also output
+            
+            parameters.
+            
+        </para>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>V</term>
+                
+                <listitem>
+                    
+                    <para>Double precision N by NCV array. (INPUT/OUTPUT) </para>
+                    
+                    <para>
+                        
+                        Upon INPUT: the NCV columns of V contain the Arnoldi basis
+                        
+                        vectors for OP as constructed by DNAUPD.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Upon OUTPUT: If RVEC = 1 the first NCONV = IPARAM(5) columns
+                        
+                        contain approximate Schur vectors that span the desired invariant
+                        
+                        subspace. See Remark 2 below.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        NOTE: If the array Z has been set equal to first NEV+1 columns
+                        
+                        of the array V and RVEC = 1 and HOWMANY= 'A', then the Arnoldi basis
+                        
+                        held by V has been overwritten by the desired Ritz vectors. If a
+                        
+                        separate array Z has been passed then the first NCONV = IPARAM(5)
+                        
+                        columns of V will contain approximate Schur vectors that span the
+                        
+                        desired invariant subspace.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>WORKL</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        Double precision work array of length LWORKL.
+                        
+                        (OUTPUT/WORKSPACE)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        WORKL(1:ncv*ncv+3*ncv) contains information obtained in dnaupd
+                        
+                        . They are not changed by dneupd .
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        WORKL(ncv*ncv+3*ncv+1:3*ncv*ncv+6*ncv) holds the real and
+                        
+                        imaginary part of the untransformed Ritz values, the upper
+                        
+                        quasi-triangular matrix for H, and the associated matrix
+                        
+                        representation of the invariant subspace for H.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Note: IPNTR(9:13) contains the pointer into WORKL for
+                        
+                        addresses of the above information computed by dneupd .
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(9): pointer to the real part of the NCV RITZ values
+                                
+                                of the original system.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(10): pointer to the imaginary part of the NCV RITZ
+                                
+                                values of the original system.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(11): pointer to the NCV corresponding error
+                                
+                                bounds.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(12): pointer to the NCV by NCV upper
+                                
+                                quasi-triangular Schur matrix for H.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(13): pointer to the NCV by NCV matrix of
+                                
+                                eigenvectors of the upper Hessenberg matrix H. Only referenced
+                                
+                                by dneupd if RVEC = 1 See Remark 2 below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>INFO</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (OUTPUT).</para>
+                    
+                    <para>Error flag on output.</para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>0: Normal exit.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                1: The Schur form computed by LAPACK routine dlahqr could
+                                
+                                not be reordered by LAPACK routine dtrsen . Re-enter subroutine
+                                
+                                dneupd with IPARAM(5)=NCV and increase the size of the arrays DR
+                                
+                                and DI to have dimension at least dimension NCV and allocate at
+                                
+                                least NCV columns for Z.
+                                
+                            </para>
+                            
+                            <para>
+                                
+                                NOTE: Not necessary if Z and V share the same space.
+                                
+                                Please notify the authors if this error occurs.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-1: N must be positive.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-2: NEV must be positive.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-3: NCV-NEV &gt;= 2 and less than or equal to N.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI',
+                                
+                                'SI'.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-6: BMAT must be one of 'I' or 'G'.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -7: Length of private work WORKL array is not
+                                
+                                sufficient.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -8: Error return from calculation of a real Schur form.
+                                
+                                Informational error from LAPACK routine dlahqr.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -9: Error return from calculation of eigenvectors.
+                                
+                                Informational error from LAPACK routine dtrevc.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-10: IPARAM(7) must be 1, 2, 3, 4.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-11: IPARAM(7) = 1 and BMAT = 'G' are incompatible.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-12: HOWMANY = 'S' not yet implemented. </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-13: HOWMANY must be one of 'A' or 'P' if RVEC = 1.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -14: DNAUPD did not find any eigenvalues to sufficient
+                                
+                                accuracy.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -15: DNEUPD got a different count of the number of
+                                
+                                converged Ritz values than DNAUPD got. This indicates the user
+                                
+                                probably made an error in passing data from DNAUPD to DNEUPD or
+                                
+                                that the data was modified before entering DNEUPD.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+        </variablelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Description</title>
+        
+        <para>
+            
+            This subroutine returns the converged approximations to eigenvalues
+            
+            of A * z = lambda * B * z and (optionally):
+            
+        </para>
+        
+        <orderedlist>
+            
+            <listitem>
+                
+                <para>The corresponding approximate eigenvectors;</para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    An orthonormal basis for the associated approximate invariant
+                    
+                    subspace;
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>Both.</para>
+                
+            </listitem>
+            
+        </orderedlist>
+        
+        <para>
+            
+            There is negligible additional cost to obtain eigenvectors. An
+            
+            orthonormal basis is always computed.
+            
+        </para>
+        
+        <para>
+            
+            There is an additional storage cost of n*nev if both are requested
+            
+            (in this case a separate array Z must be supplied).
+            
+        </para>
+        
+        <para>
+            
+            The approximate eigenvalues and eigenvectors of A * z = lambda * B * z are
+            
+            derived from approximate eigenvalues and eigenvectors of of the linear
+            
+            operator OP prescribed by the MODE selection in the call to DNAUPD. DNAUPD
+            
+            must be called before this routine is called.
+            
+        </para>
+        
+        <para>
+            
+            These approximate eigenvalues and vectors are commonly called Ritz
+            
+            values and Ritz vectors respectively. They are referred to as such in the
+            
+            comments that follow.
+            
+        </para>
+        
+        <para>
+            
+            The computed orthonormal basis for the invariant subspace
+            
+            corresponding to these Ritz values is referred to as a Schur basis.
+            
+        </para>
+        
+        <para>
+            
+            See documentation in the header of the subroutine DNAUPD for
+            
+            definition of OP as well as other terms and the relation of computed Ritz
+            
+            values and Ritz vectors of OP with respect to the given problem A * z =
+            
+            lambda * B * z.
+            
+        </para>
+        
+        <para>
+            
+            For a brief description, see definitions of IPARAM(7), MODE and
+            
+            WHICH in the documentation of DNAUPD .
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Remarks</title>
+        
+        <orderedlist>
+            
+            <listitem>
+                
+                <para>Currently only HOWMNY = 'A' and 'P' are implemented. </para>
+                
+                <para>Let trans(X) denote the transpose of X. </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Schur vectors are an orthogonal representation for the basis of
+                    
+                    Ritz vectors. Thus, their numerical properties are often superior. If
+                    
+                    RVEC = 1 then the relationship
+                    
+                </para>
+                
+                <para>
+                    
+                    A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and
+                    
+                    trans(V(:,1:IPARAM(5))) * V(:,1:IPARAM(5)) = I
+                    
+                </para>
+                
+                <para>are approximately satisfied. </para>
+                
+                <para>
+                    
+                    Here T is the leading submatrix of order IPARAM(5) of the real
+                    
+                    upper quasi-triangular matrix stored workl(ipntr(12)). That is, T is
+                    
+                    block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
+                    
+                    2-by-2 diagonal block has its diagonal elements equal and its
+                    
+                    off-diagonal elements of opposite sign. Corresponding to each 2-by-2
+                    
+                    diagonal block is a complex conjugate pair of Ritz values. The real
+                    
+                    Ritz values are stored on the diagonal of T.
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    If IPARAM(7) = 3 or 4 and SIGMAI is not equal zero, then the
+                    
+                    user must form the IPARAM(5) Rayleigh quotients in order to transform
+                    
+                    the Ritz values computed by DNAUPD for OP to those of A * z =
+                    
+                    lambda * B * z. Set RVEC = 1 and HOWMNY = 'A', and compute
+                    
+                </para>
+                
+                <para>trans(Z(:,I)) * A * Z(:,I) if DI(I) = 0. </para>
+                
+                <para>
+                    
+                    If DI(I) is not equal to zero and DI(I+1) = - D(I), then the
+                    
+                    desired real and imaginary parts of the Ritz value are
+                    
+                </para>
+                
+                <para>
+                    
+                    trans(Z(:,I)) * A * Z(:,I) + trans(Z(:,I+1)) * A * Z(:,I+1),
+                    
+                </para>
+                
+                <para>
+                    
+                    trans(Z(:,I)) * A * Z(:,I+1) - trans(Z(:,I+1)) * A * Z(:,I),
+                    
+                </para>
+                
+                <para>respectively. </para>
+                
+                <para>
+                    
+                    Another possibility is to set RVEC = 1 and HOWMANY = 'P' and
+                    
+                    compute
+                    
+                </para>
+                
+                <para>trans(V(:,1:IPARAM(5))) * A * V(:,1:IPARAM(5)) </para>
+                
+                <para>
+                    
+                    and then an upper quasi-triangular matrix of order IPARAM(5) is
+                    
+                    computed. See remark 2 above.
+                    
+                </para>
+                
+            </listitem>
+            
+        </orderedlist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Example</title>
+        
+        <programlisting role="example">
+            
+            <![CDATA[ 
+
+// The following sets dimensions for this problem.
+
+nx    = 10;
+
+nev   = 3;
+ncv   = 6;
+bmat  = 'I';
+which = 'LM';
+
+// Local Arrays
+
+iparam  = zeros(11, 1);
+ipntr   = zeros(14, 1);
+_select = zeros(ncv, 1);
+dr       = zeros(nev + 1, 1);
+di      = zeros(nev + 1, 1);
+z       = zeros(nx, nev + 1);
+resid   = zeros(nx, 1); 
+v       = zeros(nx, ncv);
+workd   = zeros(3 * nx, 1); 
+workev  = zeros(3 * ncv, 1);
+workl   = zeros(3 * ncv * ncv + 6 * ncv, 1);
+
+// Build the test matrix
+
+A            = diag(10 * ones(nx, 1));
+A(1:$-1,2:$) = A(1:$-1,2:$) + diag(6 * ones(nx-1,1));
+A(2:$,1:$-1) = A(2:$,1:$-1) + diag(-6 * ones(nx-1,1));
+
+tol    = 0;
+ido    = 0;
+
+ishfts = 1;
+maxitr = 300;
+mode1  = 1;
+
+iparam(1) = ishfts;
+iparam(3) = maxitr;
+iparam(7) = mode1;
+
+sigmar = 0; // the real part of the shift
+sigmai = 0; // the imaginary part of the shift
+info_dnaupd = 0;
+
+// M A I N   L O O P (Reverse communication)
+
+while(ido <> 99)
+  // Repeatedly call the routine DNAUPD and take actions indicated by parameter IDO until
+  // either convergence is indicated or maxitr has been exceeded.
+
+  [ido, resid, v, iparam, ipntr, workd, workl, info_dnaupd] = dnaupd(ido, bmat, nx, which, nev, tol, resid, ncv, v, iparam, ipntr, workd, workl, info_dnaupd);
+  
+  if(info_dnaupd < 0)
+    printf('\nError with dnaupd, info = %d\n',info_dnaupd);
+    printf('Check the documentation of dnaupd\n\n');
+  end
+  
+  if(ido == -1 | ido == 1)
+    // Perform matrix vector multiplication 
+    workd(ipntr(2):ipntr(2) + nx -1) = A * workd(ipntr(1):ipntr(1) + nx - 1);
+  end
+end
+
+// Post-Process using DNEUPD.
+rvec    = 1;
+howmany = 'A';
+info_dneupd = 0;
+
+[dr, di, z, resid, v, iparam, ipntr, workd, workl, info_dneupd] = dneupd(rvec, howmany, _select, dr, di, z, sigmar, sigmai, workev, ...
+                                                                       bmat, nx, which, nev, tol, resid, ncv, v, ...
+                                                                       iparam, ipntr, workd, workl, info_dneupd);
+                                                                       
+if(info_dneupd < 0)
+  printf('\nError with dneupd, info = %d\n', info_dneupd);
+  printf('Check the documentation of dneupd.\n\n');
+end
+
+printf('\nDNSIMP\n');
+printf('======\n');
+printf('\n');
+printf('Size of the matrix is %d\n', nx);
+printf('The number of Ritz values requested is %d\n', nev);
+printf('The number of Arnoldi vectors generated (NCV) is %d\n', ncv);
+printf('What portion of the spectrum: %s\n', which);
+printf('The number of Implicit Arnoldi update iterations taken is %d\n', iparam(3));
+printf('The number of OP*x is %d\n', iparam(9));
+printf('The convergence criterion is %d\n', tol);
+]]>
+            
+        </programlisting>
+        
+    </refsection>
+    
+    <refsection role="see also">
+        
+        <title>See Also</title>
+        
+        <simplelist type="inline">
+            
+            <member>
+                
+                <link linkend="dsaupd">dsaupd</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="dnaupd">dnaupd</link>
+                
+            </member>
+            
+        </simplelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Bibliography</title>
+        
+        <para>
+            
+            1. D.C. Sorensen, "Implicit Application of Polynomial Filters in a
+            
+            k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), pp
+            
+            357-385.
+            
+        </para>
+        
+        <para>
+            
+            2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
+            
+            Restarted Arnoldi Iteration", Rice University Technical Report TR95-13,
+            
+            Department of Computational and Applied Mathematics.
+            
+        </para>
+        
+        <para>
+            
+            3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall,
+            
+            1980.
+            
+        </para>
+        
+        <para>
+            
+            4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos
+            
+            Program", Computer Physics Communications, 53 (1989), pp 169-179.
+            
+        </para>
+        
+        <para>
+            
+            5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to
+            
+            Implement the Spectral Transformation", Math. Comp., 48 (1987), pp
+            
+            663-673.
+            
+        </para>
+        
+        <para>
+            
+            6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos
+            
+            Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", SIAM J.
+            
+            Matr. Anal. Apps., January (1993).
+            
+        </para>
+        
+        <para>
+            
+            7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines for
+            
+            Updating the QR decomposition", ACM TOMS, December 1990, Volume 16 Number
+            
+            4, pp 369-377.
+            
+        </para>
+        
+        <para>
+            
+            8. R.B. Lehoucq, D.C. Sorensen, "Implementation of Some Spectral
+            
+            Transformations in a k-Step Arnoldi Method". In Preparation.
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Used Functions</title>
+        
+        <para>Based on ARPACK routine dneupd</para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>履歴</title>
+        
+        <revhistory>
+            
+            <revision>
+                
+                <revnumber>5.4.0</revnumber>
+                
+                <revremark>
+                    
+                    関数は廃止され,<link linkend="eigs">eigs</link>に代替されました.
+                    
+                </revremark>
+                
+            </revision>
+            
+        </revhistory>
+        
+    </refsection>
+    
+</refentry>
+
diff --git a/scilab/modules/arnoldi/help/ja_JP/dsaupd.xml b/scilab/modules/arnoldi/help/ja_JP/dsaupd.xml
new file mode 100644 (file)
index 0000000..4cb1553
--- /dev/null
@@ -0,0 +1,1486 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="dsaupd" xml:lang="ja">
+    
+    <refnamediv>
+        
+        <refname>dsaupd</refname>
+        
+        <refpurpose>
+            
+            暗黙のうちに再開されるArnoldi反復へのインターフェイスで,
+            
+            実対称線形演算子の小数の固有値/ベクトルの組を近似的に計算します.
+            
+            <emphasis role="bold">
+                
+                この関数は廃止されました. <link linkend="eigs">eigs</link>を使用してください
+                
+            </emphasis>
+            
+        </refpurpose>
+        
+    </refnamediv>
+    
+    <refsynopsisdiv>
+        
+        <title>Calling Sequence</title>
+        
+        <synopsis>[IDO, RESID, V, IPARAM, IPNTR, WORKD, WORKL, INFO] = dsaupd(ID0, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, IPARAM, IPNTR, WORKD, WORKL, INFO)</synopsis>
+        
+    </refsynopsisdiv>
+    
+    <refsection>
+        
+        <title>Arguments</title>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>ID0</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT/OUTPUT) </para>
+                    
+                    <para>
+                        
+                        Reverse communication flag. IDO must be zero on the first call
+                        
+                        to dsaupd . IDO will be set internally to indicate the type of
+                        
+                        operation to be performed. Control is then given back to the calling
+                        
+                        routine which has the responsibility to carry out the requested
+                        
+                        operation and call dsaupd with the result.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        The operand is given in WORKD(IPNTR(1)), the result must be put
+                        
+                        in WORKD(IPNTR(2)). (If Mode = 2 see remark 5 below)
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 0: first call to the reverse communication
+                                
+                                interface.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = -1: compute Y = OP * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for Y. This
+                                
+                                is for the initialization phase to force the starting vector
+                                
+                                into the range of OP.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 1: compute Y = OP * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for Y. In
+                                
+                                mode 3, 4 and 5, the vector B * X is already available in
+                                
+                                WORKD(ipntr(3)). It does not need to be recomputed in forming OP
+                                
+                                * X.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 2: compute Y = B * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for
+                                
+                                Y.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 3: compute the IPARAM(8) shifts where IPNTR(11) is
+                                
+                                the pointer into WORKL for placing the shifts. See remark 6
+                                
+                                below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>IDO = 99: done</para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>BMAT</term>
+                
+                <listitem>
+                    
+                    <para>Character. (INPUT)</para>
+                    
+                    <para>
+                        
+                        Specifies the type of the matrix B that defines the semi-inner
+                        
+                        product for the operator OP.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>'I': standard eigenvalue problem A * x = lambda * x</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'G': generalized eigenvalue problem A * x =
+                                
+                                lambda * B * x
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>N</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT)</para>
+                    
+                    <para>Dimension of the eigenproblem.</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>WHICH</term>
+                
+                <listitem>
+                    
+                    <para>String of length 2. (INPUT)</para>
+                    
+                    <para>Specifies which of the Ritz values of OP to compute.</para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'LA' - compute the NEV largest (algebraic)
+                                
+                                eigenvalues.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'SA' - compute the NEV smallest (algebraic)
+                                
+                                eigenvalues.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'LM' - compute the NEV largest (in magnitude)
+                                
+                                eigenvalues.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'SM' - compute the NEV smallest (in magnitude)
+                                
+                                eigenvalues.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'BE' - compute NEV eigenvalues, half from each end of the
+                                
+                                spectrum. When NEV is odd, compute one more from the high end
+                                
+                                than from the low end. (see remark 1 below)
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>NEV</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT)</para>
+                    
+                    <para>
+                        
+                        Number of eigenvalues of OP to be computed. 0 &lt; NEV &lt;
+                        
+                        N.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>TOL</term>
+                
+                <listitem>
+                    
+                    <para>scalar. (INPUT)</para>
+                    
+                    <para>
+                        
+                        Stopping criterion: the relative accuracy of the Ritz value is
+                        
+                        considered acceptable if BOUNDS(I) &lt;= TOL * ABS(RITZ(I)). If TOL
+                        
+                        &lt;= 0. is passed the machine precision is set.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>RESID</term>
+                
+                <listitem>
+                    
+                    <para>Array of length N. (INPUT/OUTPUT)</para>
+                    
+                    <para>
+                        
+                        On INPUT: If INFO = 0, a random initial residual vector is
+                        
+                        used, else RESID contains the initial residual vector, possibly from
+                        
+                        a previous run.
+                        
+                    </para>
+                    
+                    <para>On OUTPUT: RESID contains the final residual vector.</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>NCV</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT)</para>
+                    
+                    <para>
+                        
+                        Number of columns of the matrix V (less than or equal to N).
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        This will indicate how many Lanczos vectors are generated at
+                        
+                        each iteration. After the startup phase in which NEV Lanczos vectors
+                        
+                        are generated, the algorithm generates NCV - NEV Lanczos vectors at
+                        
+                        each subsequent update iteration. Most of the cost in generating
+                        
+                        each Lanczos vector is in the matrix-vector product OP * x. (See
+                        
+                        remark 4 below).
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>V</term>
+                
+                <listitem>
+                    
+                    <para>N by NCV array. (OUTPUT) </para>
+                    
+                    <para>The NCV columns of V contain the Lanczos basis vectors.</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>IPARAM</term>
+                
+                <listitem>
+                    
+                    <para>array of length 11. (INPUT/OUTPUT)</para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(1) = ISHIFT: method for selecting the implicit
+                                
+                                shifts. The shifts selected at each iteration are used to
+                                
+                                restart the Arnoldi iteration in an implicit fashion.
+                                
+                            </para>
+                            
+                            <itemizedlist>
+                                
+                                <listitem>
+                                    
+                                    <para>
+                                        
+                                        ISHIFT = 0: the shifts are provided by the user via
+                                        
+                                        reverse communication. The NCV eigenvalues of the current
+                                        
+                                        tridiagonal matrix T are returned in the part of WORKL array
+                                        
+                                        corresponding to RITZ. See remark 6 below.
+                                        
+                                    </para>
+                                    
+                                </listitem>
+                                
+                                <listitem>
+                                    
+                                    <para>
+                                        
+                                        ISHIFT = 1: exact shifts with respect to the reduced
+                                        
+                                        tridiagonal matrix T. This is equivalent to restarting the
+                                        
+                                        iteration with a starting vector that is a linear
+                                        
+                                        combination of Ritz vectors associated with the "wanted"
+                                        
+                                        Ritz values.
+                                        
+                                    </para>
+                                    
+                                </listitem>
+                                
+                            </itemizedlist>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(2) = LEVEC. No longer referenced. See remark 2
+                                
+                                below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>IPARAM(3) = MXITER </para>
+                            
+                            <para>
+                                
+                                On INPUT: maximum number of Arnoldi update iterations
+                                
+                                allowed.
+                                
+                            </para>
+                            
+                            <para>
+                                
+                                On OUTPUT: actual number of Arnoldi update iterations
+                                
+                                taken.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(4) = NB: blocksize to be used in the recurrence.
+                                
+                                The code currently works only for NB = 1.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(5) = NCONV: number of "converged" Ritz values. This
+                                
+                                represents the number of Ritz values that satisfy the
+                                
+                                convergence criterion.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(6) = IUPD No longer referenced. Implicit restarting
+                                
+                                is ALWAYS used.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(7) = MODE On INPUT determines what type of
+                                
+                                eigenproblem is being solved. Must be 1,2,3,4,5; See under
+                                
+                                Description of dsaupd for the five modes available.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPARAM(8) = NP When ido = 3 and the user provides shifts
+                                
+                                through reverse communication (IPARAM(1)=0), dsaupd returns NP,
+                                
+                                the number of shifts the user is to provide. 0 &lt; NP &lt;=
+                                
+                                NCV-NEV. See Remark 6 below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>IPARAM(9) = NUMOP, </para>
+                            
+                            <para>IPARAM(10) = NUMOPB, </para>
+                            
+                            <para>
+                                
+                                IPARAM(11) = NUMREO, OUTPUT: NUMOP = total number of OP*x
+                                
+                                operations, NUMOPB = total number of B*x operations if BMAT='G',
+                                
+                                NUMREO = total number of steps of re-orthogonalization.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>IPNTR</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        array of length 11. (OUTPUT)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Pointer to mark the starting locations in
+                        
+                        the WORKD and WORKL arrays for matrices/vectors used by the Lanczos
+                        
+                        iteration.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(1): pointer to the current operand vector X in
+                                
+                                WORKD.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(2): pointer to the current result vector Y in
+                                
+                                WORKD.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(3): pointer to the vector B * X in WORKD when used
+                                
+                                in the shift-and-invert mode.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(4): pointer to the next available location in WORKL
+                                
+                                that is untouched by the program.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(5): pointer to the NCV by 2 tridiagonal matrix T in
+                                
+                                WORKL.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(6): pointer to the NCV RITZ values array in
+                                
+                                WORKL.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(7): pointer to the Ritz estimates in array WORKL
+                                
+                                associated with the Ritz values located in RITZ in WORKL.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(11): pointer to the NP shifts in WORKL. See Remark 6
+                                
+                                below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                    <para>
+                        
+                        Note: IPNTR(8:10) is only referenced by dseupd . See Remark
+                        
+                        2.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(8): pointer to the NCV RITZ values of the original
+                                
+                                system.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(9): pointer to the NCV corresponding error
+                                
+                                bounds.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(10): pointer to the NCV by NCV matrix of
+                                
+                                eigenvectors of the tridiagonal matrix T. Only referenced by
+                                
+                                dseupd if RVEC = 1. See Remarks
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>WORKD</term>
+                
+                <listitem>
+                    
+                    <para>work array of length 3 * N. (REVERSE COMMUNICATION) </para>
+                    
+                    <para>
+                        
+                        Distributed array to be used in the basic Arnoldi iteration
+                        
+                        for reverse communication. The user should not use WORKD as
+                        
+                        temporary workspace during the iteration. Upon termination
+                        
+                        WORKD(1:N) contains B*RESID(1:N). If the Ritz vectors are desired
+                        
+                        subroutine dseupd uses this output. See Data Distribution Note
+                        
+                        below.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>WORKL</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        work array of length at least NCV ** 2 + 8 * NCV.
+                        
+                        (OUTPUT/WORKSPACE)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Private (replicated) array on each PE or array allocated on
+                        
+                        the front end. See Data Distribution Note below. add here the
+                        
+                        parameter description.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>INFO</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT/OUTPUT)</para>
+                    
+                    <para>
+                        
+                        If INFO = 0, a randomly initial residual vector is used, else
+                        
+                        RESID contains the initial residual vector, possibly from a previous
+                        
+                        run.
+                        
+                    </para>
+                    
+                    <para>Error flag on output.</para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>0: Normal exit.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                1: Maximum number of iterations taken. All possible
+                                
+                                eigenvalues of OP has been found. IPARAM(5) returns the number
+                                
+                                of wanted converged Ritz values.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                2: No longer an informational error. Deprecated starting
+                                
+                                with release 2 of ARPACK.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                3: No shifts could be applied during a cycle of the
+                                
+                                Implicitly restarted Arnoldi iteration. One possibility is to
+                                
+                                increase the size of NCV relative to NEV. See remark 4
+                                
+                                below.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-1: N must be positive.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-2: NEV must be positive.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -3: NCV must be greater than NEV and less than or equal to
+                                
+                                N.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -4: The maximum number of Arnoldi update iterations
+                                
+                                allowed must be greater than zero.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or
+                                
+                                'BE'.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-6: BMAT must be one of 'I' or 'G'.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -7: Length of private work array WORKL is not
+                                
+                                sufficient.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -8: Error return from trid. eigenvalue calculation;
+                                
+                                Informatinal error from LAPACK routine dsteqr.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-9: Starting vector is zero.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-10: IPARAM(7) must be 1, 2, 3, 4, 5.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-11: IPARAM(7) = 1 and BMAT = 'G' are incompatable.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-12: IPARAM(1) must be equal to 0 or 1.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-13: NEV and WHICH = 'BE' are incompatable.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -9999: Could not build an Arnoldi factorization. IPARAM(5)
+                                
+                                returns the size of the current Arnoldi factorization. The user
+                                
+                                is advised to check that enough workspace and array storage has
+                                
+                                been allocated.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+        </variablelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Description</title>
+        
+        <para>
+            
+            Reverse communication interface for the Implicitly Restarted Arnoldi
+            
+            Iteration. For symmetric problems this reduces to a variant of the Lanczos
+            
+            method. This method has been designed to compute approximations to a few
+            
+            eigenpairs of a linear operator OP that is real and symmetric with respect
+            
+            to a real positive semi-definite symmetric matrix B, i.e.<literal>
+                
+                B * OP =
+                
+                (OP`) * B
+                
+            </literal>
+            
+            .
+            
+        </para>
+        
+        <para>
+            
+            Another way to express this condition is <literal>
+                
+                &lt; x,OPy &gt; =
+                
+                &lt; OPx,y &gt; where &lt;z,w &gt; = z`Bw
+                
+            </literal>
+            
+            .
+            
+        </para>
+        
+        <para>
+            
+            In the standard eigenproblem B is the identity matrix. ( A` denotes
+            
+            transpose of A)
+            
+        </para>
+        
+        <para>
+            
+            The computed approximate eigenvalues are called Ritz values and the
+            
+            corresponding approximate eigenvectors are called Ritz vectors.
+            
+        </para>
+        
+        <para>
+            
+            dsaupd is usually called iteratively to solve one of the following
+            
+            problems:
+            
+        </para>
+        
+        <itemizedlist>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 1: A * x = lambda * x, A symmetric ===&gt; OP = A and B =
+                    
+                    I.
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 2: A * x = lambda * M * x, A symmetric, M symmetric positive
+                    
+                    definite ===&gt; OP = inv[M] * A and B = M. ===&gt; (If M can be
+                    
+                    factored see remark 3 below)
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 3: K * x = lambda * M * x, K symmetric, M symmetric positive
+                    
+                    semi-definite ===&gt; OP = (inv[K - sigma * M]) * M and B = M. ===&gt;
+                    
+                    Shift-and-Invert mode
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 4: K * x = lambda * KG * x, K symmetric positive semi-definite,
+                    
+                    KG symmetric indefinite ===&gt; OP = (inv[K - sigma * KG]) * K and B = K.
+                    
+                    ===&gt; Buckling mode
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    Mode 5: A * x = lambda * M * x, A symmetric, M symmetric positive
+                    
+                    semi-definite ===&gt; OP = inv[A - sigma * M] * [A + sigma * M] and B = M.
+                    
+                    ===&gt; Cayley transformed mode
+                    
+                </para>
+                
+            </listitem>
+            
+        </itemizedlist>
+        
+        <para>
+            
+            NOTE: The action of w &lt;- inv[A - sigma * M] * v or w &lt;- inv[M] * v
+            
+            should be accomplished either by a direct method using a sparse matrix
+            
+            factorization and solving <literal>
+                
+                [A - sigma * M] * w = v or M * w =
+                
+                v
+                
+            </literal>
+            
+            ,
+            
+        </para>
+        
+        <para>
+            
+            or through an iterative method for solving these systems. If an
+            
+            iterative method is used, the convergence test must be more stringent than
+            
+            the accuracy requirements for the eigenvalue approximations.
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Remarks</title>
+        
+        <para>
+            
+            1. The converged Ritz values are always returned in ascending
+            
+            algebraic order. The computed Ritz values are approximate eigenvalues of
+            
+            OP. The selection of WHICH should be made with this in mind when Mode =
+            
+            3, 4, 5. After convergence, approximate eigenvalues of the original problem
+            
+            may be obtained with the ARPACK subroutine dseupd .
+            
+        </para>
+        
+        <para>
+            
+            2. If the Ritz vectors corresponding to the converged Ritz values
+            
+            are needed, the user must call dseupd immediately following completion of
+            
+            dsaupd . This is new starting with version 2.1 of ARPACK.
+            
+        </para>
+        
+        <para>
+            
+            3. If M can be factored into a Cholesky factorization M = LL` then
+            
+            Mode = 2 should not be selected. Instead one should use Mode = 1 with OP =
+            
+            inv(L) * A * inv(L`). Appropriate triangular linear systems should be solved
+            
+            with L and L` rather than computing inverses. After convergence, an
+            
+            approximate eigenvector z of the original problem is recovered by solving
+            
+            L`z = x where x is a Ritz vector of OP.
+            
+        </para>
+        
+        <para>
+            
+            4. At present there is no a-priori analysis to guide the selection
+            
+            of NCV relative to NEV. The only formal requirement is that NCV &gt; NEV.
+            
+            However, it is recommended that NCV &gt;= 2 * NEV. If many problems of the
+            
+            same type are to be solved, one should experiment with increasing NCV
+            
+            while keeping NEV fixed for a given test problem. This will usually
+            
+            decrease the required number of OP * x operations but it also increases the
+            
+            work and storage required to maintain the orthogonal basis vectors. The
+            
+            optimal "cross-over" with respect to CPU time is problem dependent and
+            
+            must be determined empirically.
+            
+        </para>
+        
+        <para>
+            
+            5. If IPARAM(7) = 2 then in the Reverse communication interface the
+            
+            user must do the following. When IDO = 1, Y = OP * X is to be computed.
+            
+            When IPARAM(7) = 2 OP = inv(B) * A. After computing A * X the user must
+            
+            overwrite X with A * X. Y is then the solution to the linear set of
+            
+            equations B * Y = A * X.
+            
+        </para>
+        
+        <para>
+            
+            6. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the NP
+            
+            = IPARAM(8) shifts in locations: 1 WORKL(IPNTR(11)) 2 WORKL(IPNTR(11) + 1) .
+            
+            . . NP WORKL(IPNTR(11) + NP - 1). The eigenvalues of the current tridiagonal
+            
+            matrix are located in WORKL(IPNTR(6)) through WORKL(IPNTR(6) + NCV - 1). They
+            
+            are in the order defined by WHICH. The associated Ritz estimates are
+            
+            located in WORKL(IPNTR(8)), WORKL(IPNTR(8) + 1), ... ,
+            
+            WORKL(IPNTR(8) + NCV - 1).
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Example</title>
+        
+        <programlisting role="example">
+            
+            <![CDATA[
+
+// The following sets dimensions for this problem.
+
+nx    = 10;
+
+nev   = 3;
+ncv   = 6;
+bmat  = 'I';
+which = 'LM';
+
+// Local Arrays
+
+iparam  = zeros(11, 1);
+ipntr   = zeros(14, 1);
+_select = zeros(ncv, 1);
+d       = zeros(nev, 1);
+z       = zeros(nx, nev);
+resid   = zeros(nx, 1);
+v       = zeros(nx, ncv);
+workd   = zeros(3 * nx, 1);
+workl   = zeros(ncv * ncv + 8 * ncv, 1);
+
+// Build the symmetric test matrix
+
+A            = diag(10 * ones(nx,1));
+A(1:$-1,2:$) = A(1:$-1,2:$) + diag(6 * ones(nx-1,1));
+A(2:$,1:$-1) = A(2:$,1:$-1) + diag(6 * ones(nx-1,1));
+
+tol    = 0;
+ido    = 0;
+
+ishfts = 1;
+maxitr = 300;
+mode1  = 1;
+
+iparam(1) = ishfts;
+iparam(3) = maxitr;
+iparam(7) = mode1;
+
+sigma = 0; // the real part of the shift
+info_dsaupd = 0;
+
+// M A I N   L O O P (Reverse communication)
+
+while(ido <> 99)
+  // Repeatedly call the routine DSAUPD and take actions indicated by parameter IDO until
+  // either convergence is indicated or maxitr has been exceeded.
+
+  [ido, resid, v, iparam, ipntr, workd, workl, info_dsaupd] = dsaupd(ido, bmat, nx, which, nev, tol, resid, ncv, v, iparam, ipntr, workd, workl, info_dsaupd);
+
+  if(info_dsaupd < 0)
+    printf('\nError with dsaupd, info = %d\n',info_dsaupd);
+    printf('Check the documentation of dsaupd\n\n');
+  end
+
+  if(ido == -1 | ido == 1)
+    // Perform matrix vector multiplication
+    workd(ipntr(2):ipntr(2) + nx - 1) = A * workd(ipntr(1):ipntr(1) + nx - 1);
+  end
+end
+
+// Post-Process using DSEUPD.
+rvec    = 1;
+howmany = 'A';
+info_dseupd = 0;
+
+[d, z, resid, v, iparam, ipntr, workd, workl, info_dseupd] = dseupd(rvec, howmany, _select, d, z, sigma, bmat, nx, which, nev, tol, resid, ncv, v, ...
+                                                                    iparam, ipntr, workd, workl, info_dseupd);
+
+if(info_dseupd < 0)
+  printf('\nError with dseupd, info = %d\n', info_dseupd);
+  printf('Check the documentation of dseupd.\n\n');
+end
+
+
+// Done with program dssimp.
+printf('\nDSSIMP\n');
+printf('======\n');
+printf('\n');
+printf('Size of the matrix is %d\n', nx);
+printf('The number of Ritz values requested is %d\n', nev);
+printf('The number of Arnoldi vectors generated (NCV) is %d\n', ncv);
+printf('What portion of the spectrum: %s\n', which);
+printf('The number of Implicit Arnoldi update iterations taken is %d\n', iparam(3));
+printf('The number of OP*x is %d\n', iparam(9));
+printf('The convergence criterion is %d\n', tol);
+
+]]>
+            
+        </programlisting>
+        
+    </refsection>
+    
+    <refsection role="see also">
+        
+        <title>See Also</title>
+        
+        <simplelist type="inline">
+            
+            <member>
+                
+                <link linkend="dnaupd">dnaupd</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="dseupd">dseupd</link>
+                
+            </member>
+            
+        </simplelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Bibliography</title>
+        
+        <para>
+            
+            1. D.C. Sorensen, "Implicit Application of Polynomial Filters in a
+            
+            k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), pp
+            
+            357-385.
+            
+        </para>
+        
+        <para>
+            
+            2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
+            
+            Restarted Arnoldi Iteration", Rice University Technical Report TR95-13,
+            
+            Department of Computational and Applied Mathematics.
+            
+        </para>
+        
+        <para>
+            
+            3. B.N. Parlett and Y. Saad, "Complex Shift and Invert Strategies
+            
+            for Real Matrices", Linear Algebra and its Applications, vol 88/89, pp
+            
+            575-595, (1987).
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Used Functions</title>
+        
+        <para>Based on ARPACK routine dsaupd</para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>履歴</title>
+        
+        <revhistory>
+            
+            <revision>
+                
+                <revnumber>5.4.0</revnumber>
+                
+                <revremark>
+                    
+                    関数は廃止され,<link linkend="eigs">eigs</link>に代替されました.
+                    
+                </revremark>
+                
+            </revision>
+            
+        </revhistory>
+        
+    </refsection>
+    
+</refentry>
+
diff --git a/scilab/modules/arnoldi/help/ja_JP/dseupd.xml b/scilab/modules/arnoldi/help/ja_JP/dseupd.xml
new file mode 100644 (file)
index 0000000..67ab4fe
--- /dev/null
@@ -0,0 +1,836 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="dseupd" xml:lang="ja">
+    
+    <refnamediv>
+        
+        <refname>dseupd</refname>
+        
+        <refpurpose>
+            
+            暗黙のうちに再開されるArnoldi反復へのインターフェイスで,
+            
+            A * z = lambda * B * z の固有値を収束的近似により計算します.
+            
+            <emphasis role="bold">
+                
+                この関数は廃止されました. <link linkend="eigs">eigs</link>を使用してください
+                
+            </emphasis>
+            
+        </refpurpose>
+        
+    </refnamediv>
+    
+    <refsynopsisdiv>
+        
+        <title>Calling Sequence</title>
+        
+        <synopsis>
+            
+            [D, Z, RESID, V, IPARAM, IPNTR, WORKD, WORKL, INFO] = dseupd(RVEC, HOWMANY, SELECT, D, Z, SIGMA, BMAT, N, WHICH,
+            
+            NEV, TOL, RESID, NCV, V, IPARAM, IPNTR, WORKD, WORKL, INFO)
+            
+        </synopsis>
+        
+    </refsynopsisdiv>
+    
+    <refsection>
+        
+        <title>Arguments</title>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>RVEC</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT) </para>
+                    
+                    <para>
+                        
+                        Specifies whether Ritz vectors corresponding to the Ritz value
+                        
+                        approximations to the eigenproblem A * z = lambda * B * z are
+                        
+                        computed.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>RVEC = 0 Compute Ritz values only.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>RVEC = 1 Compute Ritz vectors.</para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>HOWMNY</term>
+                
+                <listitem>
+                    
+                    <para>Character*1. (INPUT) </para>
+                    
+                    <para>
+                        
+                        Specifies how many Ritz vectors are wanted and the form of Z
+                        
+                        the matrix of Ritz vectors. See remark 1 below.
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>'A': compute NEV Ritz vectors;</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                'S': compute some of the Ritz vectors, specified by the
+                                
+                                integer array SELECT.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>SELECT</term>
+                
+                <listitem>
+                    
+                    <para>Integer array of dimension NCV. (INPUT/WORKSPACE) </para>
+                    
+                    <para>
+                        
+                        If HOWMANY = 'S', SELECT specifies the Ritz vectors to be
+                        
+                        computed. To select the Ritz vector corresponding to a Ritz value
+                        
+                        D(j), SELECT(j) must be set to 1.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        If HOWMANY = 'A' , SELECT is used as a workspace for
+                        
+                        reordering the Ritz values.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>D</term>
+                
+                <listitem>
+                    
+                    <para>Double precision array of dimension NEV. (OUTPUT) </para>
+                    
+                    <para>
+                        
+                        On exit, D contains the Ritz value approximations to the
+                        
+                        eigenvalues of A * z = lambda * B * z. The values are returned in
+                        
+                        ascending order.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        If IPARAM(7) = 3, 4, 5 then D represents the Ritz values of OP
+                        
+                        computed by dsaupd transformed to those of the original eigensystem
+                        
+                        A * z = lambda * B * z.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        If IPARAM(7) = 1, 2 then the Ritz values of OP are the same as
+                        
+                        the those of A * z = lambda * B * z.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>Z</term>
+                
+                <listitem>
+                    
+                    <para>Double precision N by NEV array.</para>
+                    
+                    <para>
+                        
+                        If HOWMNY = 'A'. (OUTPUT) On exit, Z contains the
+                        
+                        B-orthonormal Ritz vectors of the eigensystemA * z = lambda * B * z
+                        
+                        corresponding to the Ritz value approximations.
+                        
+                    </para>
+                    
+                    <para>If RVEC = 0 then Z is not referenced. </para>
+                    
+                    <para>
+                        
+                        NOTE: The array Z may be set equal to first NEV columns of the
+                        
+                        Arnoldi/Lanczos basis array V computed by DSAUPD .
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>SIGMA</term>
+                
+                <listitem>
+                    
+                    <para>Double precision (INPUT) </para>
+                    
+                    <para>
+                        
+                        If IPARAM(7) = 3, 4, 5 represents the shift. Not referenced if
+                        
+                        IPARAM(7) = 1 or 2.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+        </variablelist>
+        
+        <para>
+            
+            NOTE: The remaining arguments BMAT, N, WHICH, NEV, TOL, RESID, NCV,
+            
+            V, IPARAM, IPNTR, WORKD, WORKL, LWORKL, INFO must be passed directly to
+            
+            DSEUPD following the last call to DSAUPD .
+            
+        </para>
+        
+        <para>
+            
+            These arguments MUST NOT BE MODIFIED between the last call to
+            
+            DSAUPD and the call to DSEUPD.
+            
+        </para>
+        
+        <para>
+            
+            Two of these parameters (WORKL, INFO) are also output
+            
+            parameters.
+            
+        </para>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>WORKL</term>
+                
+                <listitem>
+                    
+                    <para>
+                        
+                        Double precision work array of length LWORKL.
+                        
+                        (OUTPUT/WORKSPACE)
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        WORKL(1:4*ncv) contains information obtained in dsaupd. They
+                        
+                        are not changed by dseupd.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        WORKL(4*ncv+1:ncv*ncv+8*ncv) holds the untransformed Ritz
+                        
+                        values, the computed error estimates, and the associated eigenvector
+                        
+                        matrix of H.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        Note: IPNTR(8:10) contains the pointer into WORKL for
+                        
+                        addresses of the above information computed by dseupd .
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(8): pointer to the NCV RITZ values of the original
+                                
+                                system.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(9): pointer to the NCV corresponding error bounds.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IPNTR(10): pointer to the NCV by NCV matrix of
+                                
+                                eigenvectors of the tridiagonal matrix T. Only referenced by
+                                
+                                dseupd if RVEC = 1 See Remarks.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>INFO</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (OUTPUT) </para>
+                    
+                    <para>Error flag on output.</para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>0: Normal exit.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-1: N must be positive.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-2: NEV must be positive.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -3: NCV must be greater than NEV and less than or equal to
+                                
+                                N.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or
+                                
+                                'BE'.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-6: BMAT must be one of 'I' or 'G'.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -7: Length of private work WORKL array is not
+                                
+                                sufficient.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -8: Error return from trid. eigenvalue calculation;
+                                
+                                Information error from LAPACK routine dsteqr.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-9: Starting vector is zero.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-10: IPARAM(7) must be 1, 2, 3, 4, 5.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-11: IPARAM(7) = 1 and BMAT = 'G' are incompatible.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-12: NEV and WHICH = 'BE' are incompatible.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -14: DSAUPD did not find any eigenvalues to sufficient
+                                
+                                accuracy.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-15: HOWMNY must be one of 'A' or 'S' if RVEC = 1.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>-16: HOWMNY = 'S' not yet implemented.</para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                -17: DSEUPD got a different count of the number of
+                                
+                                converged Ritz values than DSAUPD got. This indicates the user
+                                
+                                probably made an error in passing data from DSAUPD to DSEUPD or
+                                
+                                that the data was modified before entering DSEUPD.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+        </variablelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Description</title>
+        
+        <para>
+            
+            This subroutine returns the converged approximations to eigenvalues
+            
+            of A * z = lambda * B * z and (optionally):
+            
+        </para>
+        
+        <orderedlist>
+            
+            <listitem>
+                
+                <para>the corresponding approximate eigenvectors,</para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>
+                    
+                    an orthonormal (Lanczos) basis for the associated approximate
+                    
+                    invariant subspace,
+                    
+                </para>
+                
+            </listitem>
+            
+            <listitem>
+                
+                <para>Both. </para>
+                
+            </listitem>
+            
+        </orderedlist>
+        
+        <para>
+            
+            There is negligible additional cost to obtain eigenvectors. An
+            
+            orthonormal (Lanczos) basis is always computed. There is an additional
+            
+            storage cost of n*nev if both are requested (in this case a separate array
+            
+            Z must be supplied).
+            
+        </para>
+        
+        <para>
+            
+            These quantities are obtained from the Lanczos factorization
+            
+            computed by DSAUPD for the linear operator OP prescribed by the MODE
+            
+            selection (see IPARAM(7) in DSAUPD documentation.) DSAUPD must be called
+            
+            before this routine is called.
+            
+        </para>
+        
+        <para>
+            
+            These approximate eigenvalues and vectors are commonly called Ritz
+            
+            values and Ritz vectors respectively. They are referred to as such in the
+            
+            comments that follow.
+            
+        </para>
+        
+        <para>
+            
+            The computed orthonormal basis for the invariant subspace
+            
+            corresponding to these Ritz values is referred to as a Lanczos basis.
+            
+        </para>
+        
+        <para>
+            
+            See documentation in the header of the subroutine DSAUPD for a
+            
+            definition of OP as well as other terms and the relation of computed Ritz
+            
+            values and vectors of OP with respect to the given problem A * z = lambda * B * z.
+            
+        </para>
+        
+        <para>
+            
+            The approximate eigenvalues of the original problem are returned in
+            
+            ascending algebraic order.
+            
+        </para>
+        
+        <para>
+            
+            The user may elect to call this routine once for each desired Ritz
+            
+            vector and store it peripherally if desired. There is also the option of
+            
+            computing a selected set of these vectors with a single call.
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Remarks</title>
+        
+        <para>
+            
+            1. The converged Ritz values are always returned in increasing
+            
+            (algebraic) order. c 2. Currently only HOWMNY = 'A' is implemented. It is
+            
+            included at this stage for the user who wants to incorporate it.
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Example</title>
+        
+        <programlisting role="example">
+            
+            <![CDATA[ 
+
+// The following sets dimensions for this problem.
+
+nx    = 10;
+
+nev   = 3;
+ncv   = 6;
+bmat  = 'I';
+which = 'LM';
+
+// Local Arrays
+
+iparam  = zeros(11, 1);
+ipntr   = zeros(14, 1);
+_select = zeros(ncv, 1);
+d       = zeros(nev, 1);
+z       = zeros(nx, nev);
+resid   = zeros(nx, 1); 
+v       = zeros(nx, ncv);
+workd   = zeros(3 * nx, 1); 
+workl   = zeros(ncv * ncv + 8 * ncv, 1);
+
+// Build the symmetric test matrix
+
+A            = diag(10 * ones(nx,1));
+A(1:$-1,2:$) = A(1:$-1,2:$) + diag(6 * ones(nx-1,1));
+A(2:$,1:$-1) = A(2:$,1:$-1) + diag(6 * ones(nx-1,1));
+
+tol    = 0;
+ido    = 0;
+
+ishfts = 1;
+maxitr = 300;
+mode1  = 1;
+
+iparam(1) = ishfts;
+iparam(3) = maxitr;
+iparam(7) = mode1;
+
+sigma = 0; // the real part of the shift
+info_dsaupd = 0;
+
+// M A I N   L O O P (Reverse communication)
+
+while(ido <> 99)
+  // Repeatedly call the routine DSAUPD and take actions indicated by parameter IDO until
+  // either convergence is indicated or maxitr has been exceeded.
+
+  [ido, resid, v, iparam, ipntr, workd, workl, info_dsaupd] = dsaupd(ido, bmat, nx, which, nev, tol, resid, ncv, v, iparam, ipntr, workd, workl, info_dsaupd);
+  
+  if(info_dsaupd < 0)
+    printf('\nError with dsaupd, info = %d\n',info_dsaupd);
+    printf('Check the documentation of dsaupd\n\n');
+  end
+  
+  if(ido == -1 | ido == 1)
+    // Perform matrix vector multiplication 
+    workd(ipntr(2):ipntr(2) + nx - 1) = A * workd(ipntr(1):ipntr(1) + nx - 1);
+  end
+end
+
+// Post-Process using DSEUPD.
+rvec    = 1;
+howmany = 'A';
+info_dseupd = 0;
+
+[d, z, resid, v, iparam, ipntr, workd, workl, info_dseupd] = dseupd(rvec, howmany, _select, d, z, sigma, bmat, nx, which, nev, tol, resid, ncv, v, ...
+                                                                    iparam, ipntr, workd, workl, info_dseupd);
+
+if(info_dseupd < 0)
+  printf('\nError with dseupd, info = %d\n', info_dseupd);
+  printf('Check the documentation of dseupd.\n\n');
+end
+
+
+// Done with program dssimp.
+printf('\nDSSIMP\n');
+printf('======\n');
+printf('\n');
+printf('Size of the matrix is %d\n', nx);
+printf('The number of Ritz values requested is %d\n', nev);
+printf('The number of Arnoldi vectors generated (NCV) is %d\n', ncv);
+printf('What portion of the spectrum: %s\n', which);
+printf('The number of Implicit Arnoldi update iterations taken is %d\n', iparam(3));
+printf('The number of OP*x is %d\n', iparam(9));
+printf('The convergence criterion is %d\n', tol);
+
+]]>
+            
+        </programlisting>
+        
+    </refsection>
+    
+    <refsection role="see also">
+        
+        <title>See Also</title>
+        
+        <simplelist type="inline">
+            
+            <member>
+                
+                <link linkend="dsaupd">dsaupd</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="dneupd">dneupd</link>
+                
+            </member>
+            
+        </simplelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Bibliography</title>
+        
+        <para>
+            
+            1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
+            
+            k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), pp
+            
+            357-385.
+            
+        </para>
+        
+        <para>
+            
+            2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly
+            
+            Restarted Arnoldi Iteration", Rice University Technical Report TR95-13,
+            
+            Department of Computational and Applied Mathematics.
+            
+        </para>
+        
+        <para>
+            
+            3. B.N. Parlett and Y. Saad, "Complex Shift and Invert Strategies
+            
+            for Real Matrices", Linear Algebra and its Applications, vol 88/89, pp
+            
+            575-595, (1987).
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>Used Functions</title>
+        
+        <para>Based on ARPACK routine dseupd</para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>履歴</title>
+        
+        <revhistory>
+            
+            <revision>
+                
+                <revnumber>5.4.0</revnumber>
+                
+                <revremark>
+                    
+                    関数は廃止され,<link linkend="eigs">eigs</link>に代替されました.
+                    
+                </revremark>
+                
+            </revision>
+            
+        </revhistory>
+        
+    </refsection>
+    
+</refentry>
+
index f2dbc8d..20ea084 100644 (file)
@@ -58,7 +58,7 @@
                 
                 <listitem>
                     
-                    <para>a full or sparse, real or complex, symmetric or non-symmetric square matrix</para>
+                    <para>通常または疎, 実数または複素数, 対称または非対称正方行列</para>
                     
                 </listitem>
                 
@@ -70,7 +70,7 @@
                 
                 <listitem>
                     
-                    <para>a function</para>
+                    <para>関数</para>
                     
                 </listitem>
                 
@@ -84,7 +84,7 @@
                     
                     <para>
                         
-                        a scalar, defined only if <literal>A</literal> is a function
+                        スカラー, Aが関数の場合のみ <literal>A</literal> 定義
                         
                     </para>
                     
                     
                     <para>
                         
-                        a sparse, real or complex, square matrix with same dimensions as
+                        <literal> A</literal>と同じ次元の
                         
-                        <literal> A</literal>
+                        疎, 実数または複素数, 正方行列
                         
                     </para>
                     
                 
                 <listitem>
                     
-                    <para>an integer, number of eigenvalues to be computed</para>
+                    <para>整数, 計算する固有値の数</para>
                     
                 </listitem>
                 
                 
                 <listitem>
                     
-                    <para>a real scalar or a string of length 2</para>
+                    <para>実スカラーまたは長さ2の文字列</para>
                     
                 </listitem>
                 
                 
                 <listitem>
                     
-                    <para>a structure</para>
+                    <para>構造体</para>
                     
                 </listitem>
                 
                 
                 <listitem>
                     
-                    <para>a real or complex eigenvalues vector or diagonal matrix (eigenvalues along the diagonal)</para>
+                    <para>実数または複素数の固有値ベクトルまたは対角行列 (対角項に固有値)</para>
                     
                 </listitem>
                 
                     
                     <para>
                         
-                        real or complex eigenvector matrix
+                        実数または複素数の固有ベクトル行列
                         
                     </para>
                     
         
         <para>
             
-            The purpose of the eigs function is to compute the largest eigenvalues of sparse, large matrices.
+            eigs関数の目的は,疎で大きな行列の最大固有値を計算することです.
             
         </para>
         
             
             <varlistentry>
                 
-                <term>d = eigs(A) or d = eigs(Af, n)</term>
+                <term>d = eigs(A) または d = eigs(Af, n)</term>
                 
                 <listitem>
                     
                     <para>
                         
-                        solves the eigenvalue problem <literal>A * v = lambda * v</literal>. This calling returns a vector <literal>d</literal> containing the six largest magnitude eigenvalues.
+                        は,固有値問題<literal>A * v = lambda * v</literal>を解きます. 
                         
-                        <literal>A</literal> is either a square matrix, which can be symmetric or non-symmetric, real or complex, full or sparse.
+                        このコールは,大きさが最大の6個の固有値を有する
+                        
+                        ベクトル <literal>d</literal>を返します.
+                        
+                        <literal>A</literal> は正方行列で,
+                        
+                        対称または非対称, 実数または複素数, 通常または複素数
+                        
+                        とすることができます.
                         
                     </para>
                     
                     <para>
                         
-                        <literal>A</literal> should be represented by a function <literal>Af</literal>. In this instance, a scalar <literal>n</literal> designating
+                        <literal>A</literal> は関数<literal>Af</literal>で
+                        
+                        表すことも可能です.この場合,
+                        
+                        ベクトル引数の長さを指定するスカラー<literal>n</literal>を
                         
-                        the length of the vector argument, must be defined. It must have the following header :
+                        定義する必要があります.
+                        
+                        この関数は,以下のヘッダを有する必要があります:
                         
                     </para>
                     
@@ -222,7 +236,7 @@ function y = A ( x )
                     
                     <para>
                         
-                        This function <literal>Af</literal> must return one of the four following expressions :
+                        この関数 <literal>Af</literal> は以下の4つの式の1つを返す必要があります:
                         
                         <itemizedlist>
                             
@@ -230,7 +244,7 @@ function y = A ( x )
                                 
                                 <term>A * x</term>
                                 
-                                <para> if sigma is not given or is a string other than 'SM'.</para>
+                                <para> sigmaが指定されないか文字列が'SM'以外の場合.</para>
                                 
                             </listitem>
                             
@@ -238,7 +252,7 @@ function y = A ( x )
                                 
                                 <term>A \ x</term>
                                 
-                                <para> if sigma is 0 or 'SM'.</para>
+                                <para>sigmaが0または'SM'の場合.</para>
                                 
                             </listitem>
                             
@@ -246,7 +260,7 @@ function y = A ( x )
                                 
                                 <term>(A - sigma * I) \ x</term>
                                 
-                                <para>for the standard eigenvalue problem, where I is the identity matrix.</para>
+                                <para>標準固有値問題の場合, ただし I は単位行列.</para>
                                 
                             </listitem>
                             
@@ -254,7 +268,7 @@ function y = A ( x )
                                 
                                 <term>(A - sigma * B) \ x</term>
                                 
-                                <para> for the generalized eigenvalue problem.</para>
+                                <para> 一般化固有値問題の場合.</para>
                                 
                             </listitem>
                             
@@ -274,9 +288,11 @@ function y = A ( x )
                     
                     <para>
                         
-                        returns a diagonal matrix <literal>d</literal> containing the six largest magnitude eigenvalues on the diagonal.
+                        は,6個の最大固有値を対角項に有する対角行列 <literal>d</literal> を返します.
+                        
+                        <literal>v</literal> は n行6列の行列で,
                         
-                        <literal>v</literal> is a n by six matrix whose columns are the six eigenvectors corresponding to the returned eigenvalues.
+                        その列は返された固有値に対応する6個の固有値ベクトルです.
                         
                     </para>
                     
@@ -292,7 +308,11 @@ function y = A ( x )
                     
                     <para>
                         
-                        solves the generalized eigenvalue problem <literal>A * v = lambda  * B * v </literal> with positive, definite matrix <literal>B</literal>.
+                        は,正定行列<literal>B</literal>を指定して,
+                        
+                        一般化固有値問題 <literal>A * v = lambda  * B * v </literal> 
+                        
+                        を解きます.
                         
                     </para>
                     
@@ -302,7 +322,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                if <literal>B</literal> is not specified, <literal>B = []</literal> is used.
+                                <literal>B</literal> が指定されない場合, 
+                                
+                                <literal>B = []</literal> が使用されます.
                                 
                             </para>
                             
@@ -312,7 +334,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                if <literal>B</literal> is specified, <literal>B</literal> must be the same size as A.
+                                <literal>B</literal> が指定された場合, 
+                                
+                                <literal>B</literal> はAと同じ大きさとする必要があります.
                                 
                             </para>
                             
@@ -332,9 +356,11 @@ function y = A ( x )
                     
                     <para>
                         
-                        returns in vector <literal>d</literal> the <literal>k</literal> eigenvalues.
+                        は,<literal>k</literal>個の固有値をベクトル<literal>d</literal>に返します.
+                        
+                        <literal>k</literal> が指定されない場合, 
                         
-                        If <literal>k</literal> is not specified, <literal>k = min(n, 6)</literal>, where n is the row number of A.
+                        <literal>k = min(n, 6)</literal>, ただし, nはAの行数となります.
                         
                     </para>
                     
@@ -350,11 +376,15 @@ function y = A ( x )
                     
                     <para>
                         
-                        returns in vector <literal>d</literal> the <literal>k</literal> eigenvalues determined by <literal>sigma</literal>.
+                        は,<literal>sigma</literal>で定義された<literal>k</literal>個の固有値を
+                        
+                        ベクトル<literal>d</literal>に返します.
                         
-                        <literal>sigma</literal> can be either a real or complex including 0 scalar or string.
+                        <literal>sigma</literal> は,0を含む実数または複素数,または文字列
                         
-                        If sigma is a string of length 2, it takes one of the following values :
+                        とすることができます.
+                        
+                        sigma が長さ2の文字列の場合, 以下の値のどれかとします :
                         
                     </para>
                     
@@ -364,7 +394,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'LM'</literal> compute the <varname>k</varname> largest in magnitude eigenvalues (by default).
+                                <literal>'LM'</literal> は,大きさが最大の<varname>k</varname>個の
+                                
+                                固有値を計算します(デフォルト).
                                 
                             </para>
                             
@@ -374,7 +406,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'SM'</literal> compute the <varname>k</varname> smallest in magnitude eigenvalues (same as sigma = 0).
+                                <literal>'SM'</literal> は,大きさが最小の<varname>k</varname>個の
+                                
+                                固有値を計算します(sigma = 0 と同じ).
                                 
                             </para>
                             
@@ -384,7 +418,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'LA'</literal> compute the <varname>k</varname> Largest Algebraic eigenvalues, only for real symmetric problems.
+                                <literal>'LA'</literal> は,実対称問題のみに適用され,
+                                
+                                <varname>k</varname>個の代数的最大固有値を計算します.
                                 
                             </para>
                             
@@ -394,7 +430,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'SA'</literal> compute the <varname>k</varname> Smallest Algebraic eigenvalues, only for real symmetric problems.
+                                <literal>'SA'</literal> は,実対称問題のみに適用され,
+                                
+                                <varname>k</varname>個の代数的最小固有値を計算します.
                                 
                             </para>
                             
@@ -404,9 +442,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'BE'</literal> compute <varname>k</varname> eigenvalues, half from each end of the spectrum, only for real 
+                                <literal>'BE'</literal> は,実対称問題のみに適用され,
                                 
-                                symmetric problems.
+                                スペクトラムの各端から半分づつ,<varname>k</varname>個の固有値を計算します.
                                 
                             </para>
                             
@@ -416,9 +454,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'LR'</literal> compute the <varname>k</varname> eigenvalues of Largest Real part, only for real non-symmetric or 
+                                <literal>'LR'</literal> は,実非対称または複素問題のみに適用され,
                                 
-                                complex problems.
+                                <varname>k</varname>個の実部最大の固有値を計算します.
                                 
                             </para>
                             
@@ -428,9 +466,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'SR'</literal> compute the <varname>k</varname> eigenvalues of Smallest Real part, only for real non-symmetric or 
+                                <literal>'SR'</literal> は,実非対称または複素問題のみに適用され,
                                 
-                                complex problems.
+                                <varname>k</varname>個の実部最小の固有値を計算します.
                                 
                             </para>
                             
@@ -440,9 +478,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'LI'</literal> compute the <varname>k</varname> eigenvalues of Largest Imaginary part, only for real non-symmetric 
+                                <literal>'LI'</literal> は,実非対称または複素問題のみに適用され,
                                 
-                                or complex problems.
+                                <varname>k</varname>個の虚部最大の固有値を計算します.
                                 
                             </para>
                             
@@ -452,9 +490,9 @@ function y = A ( x )
                             
                             <para>
                                 
-                                <literal>'SI'</literal> compute the <varname>k</varname> eigenvalues of Smallest Imaginary part, only for real non-symmetric 
+                                <literal>'SI'</literal> は,実非対称または複素問題のみに適用され,
                                 
-                                or complex problems.
+                                <varname>k</varname>個の虚部最小の固有値を計算します.
                                 
                             </para>
                             
@@ -474,7 +512,11 @@ function y = A ( x )
                     
                     <para>
                         
-                        If the <literal> opts </literal> structure is specified, different options can be used to compute the <literal>k</literal> eigenvalues :
+                        <literal> opts </literal> 構造体が指定された場合, 
+                        
+                        <literal>k</literal> 個の固有値を計算する際に
+                        
+                        異なるオプションを使用できます:
                         
                     </para>
                     
@@ -488,7 +530,7 @@ function y = A ( x )
                                 
                                 <para>
                                     
-                                    required convergence tolerance. By default, <literal>tol = %eps</literal>.
+                                    所要の収束閾値. デフォルトで, <literal>tol = %eps</literal>.
                                     
                                 </para>
                                 
@@ -504,7 +546,7 @@ function y = A ( x )
                                 
                                 <para>
                                     
-                                    maximum number of iterations. By default, <literal>maxiter = 300</literal>.
+                                    最大反復回数. デフォルトで, <literal>maxiter = 300</literal>.
                                     
                                 </para>
                                 
@@ -520,7 +562,21 @@ function y = A ( x )
                                 
                                 <para>
                                     
-                                    number of Lanzcos basis vectors to use. For real non-symmetric problems, the <literal>ncv</literal> value must be greater or equal than <literal>2 * k + 1 </literal> and, by default, <literal>ncv = min(max(2 * k + 1, 20), nA) </literal>. For real symmetric or complex problems, <literal>ncv</literal> must be greater or equal <literal>2 * k </literal> and, by default, <literal> ncv = min(max(2 * k, 20), nA) </literal> with <literal> nA = size(A, 2) </literal>.
+                                    使用するLanzcos基底ベクトルの数.
+                                    
+                                    実非対称問題の場合, <literal>ncv</literal>の値は
+                                    
+                                    <literal>2 * k + 1 </literal>以上とする必要があり,
+                                    
+                                    デフォルトで <literal>ncv = min(max(2 * k + 1, 20), nA) </literal>です.
+                                    
+                                    実対称または複素数問題の場合,<literal>ncv</literal>は
+                                    
+                                    <literal>2 * k </literal>以上とする必要があり,
+                                    
+                                    デフォルトで<literal> ncv = min(max(2 * k, 20), nA) </literal>
+                                    
+                                    です.ただし,<literal> nA = size(A, 2) </literal>.
                                     
                                 </para>
                                 
@@ -536,9 +592,13 @@ function y = A ( x )
                                 
                                 <para>
                                     
-                                    starting vector whose contains the initial residual vector, possibly from a previous run. By default,
+                                    初期残差ベクトルを有する開始ベクトルで,
+                                    
+                                    前回実行時の値を使用することもできます.
                                     
-                                    <literal>resid</literal> is a random initial vector.
+                                    デフォルトで,<literal>resid</literal> はランダムな
+                                    
+                                    初期値ベクトルです.
                                     
                                 </para>
                                 
@@ -554,7 +614,13 @@ function y = A ( x )
                                 
                                 <para>
                                     
-                                    if <literal>chol(B)</literal> is passed rather than <literal>B</literal>. By default, <literal>cholB</literal> is %f.
+                                    <literal>B</literal>ではなく
+                                    
+                                    <literal>chol(B)</literal>を指定します.
+                                    
+                                    デフォルトで
+                                    
+                                    , <literal>cholB</literal> は %f です.
                                     
                                 </para>
                                 
@@ -570,9 +636,15 @@ function y = A ( x )
                                 
                                 <para>
                                     
-                                    if <literal>Af</literal> is given, <literal>isreal</literal> can be defined. By default, <literal>isreal</literal> is %t.
+                                    <literal>Af</literal> が指定された場合, 
+                                    
+                                    <literal>isreal</literal> を定義できます.
+                                    
+                                    デフォルトで, <literal>isreal</literal> は %t です.
+                                    
+                                    この引数は,<literal>A</literal>が行列の場合,
                                     
-                                    This argument should not be indicated if <literal>A</literal> is a matrix.
+                                    指定する必要がありません.
                                     
                                 </para>
                                 
@@ -588,9 +660,15 @@ function y = A ( x )
                                 
                                 <para>
                                     
-                                    if <literal>Af</literal> is given, <literal>issym</literal> can be defined. By default, <literal>issym</literal> is %f.
+                                    <literal>Af</literal> が指定された場合, 
                                     
-                                    This argument should not be indicated if <literal>A</literal> is a matrix.
+                                    <literal>issym</literal> を定義できます. 
+                                    
+                                    デフォルトで <literal>issym</literal> は %f です.
+                                    
+                                    この引数は,<literal>A</literal>が行列の場合,
+                                    
+                                    指定する必要がありません.
                                     
                                 </para>
                                 
@@ -716,6 +794,8 @@ d = eigs(fn, 10, [], k, 4, opts)
         
         <programlisting role="example">
             
+            
+            
             <![CDATA[ 
     A            = diag(10*ones(10,1));
     A(1:$-1,2:$) = A(1:$-1,2:$) + diag(6*ones(9,1));
diff --git a/scilab/modules/arnoldi/help/ja_JP/znaupd.xml b/scilab/modules/arnoldi/help/ja_JP/znaupd.xml
new file mode 100644 (file)
index 0000000..847c715
--- /dev/null
@@ -0,0 +1,1510 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="znaupd" xml:lang="ja">
+    
+    <refnamediv>
+        
+        <refname>znaupd</refname>
+        
+        <refpurpose>
+            
+            暗黙のうちに再開されるArnoldi反復へのインターフェイスで,
+            
+            エルミート準正定実行列Bにより定義される準内積に関する
+            
+            複素線形演算子 OP の小数の固有値/ベクトルの組を近似的に計算します.
+            
+            <emphasis role="bold">
+                
+                この関数は廃止されました. <link linkend="eigs">eigs</link>を使用してください
+                
+            </emphasis>
+            
+        </refpurpose>
+        
+    </refnamediv>
+    
+    <refsynopsisdiv>
+        
+        <title>Calling Sequence</title>
+        
+        <synopsis>[IDO, RESID, V, IPARAM, IPNTR, WORKD, WORKL, RWORK, INFO] = znaupd(ID0, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, IPARAM, IPNTR, WORKD, WORKL, RWORK, INFO)</synopsis>
+        
+    </refsynopsisdiv>
+    
+    <refsection>
+        
+        <title>Arguments</title>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>IDO</term>
+                
+                <listitem>
+                    
+                    <para>Integer. (INPUT/OUTPUT) </para>
+                    
+                    <para>
+                        
+                        Reverse communication flag. IDO must be zero on the first call
+                        
+                        to znaupd. IDO will be set internally to indicate the type of
+                        
+                        operation to be performed. Control is then given back to the calling
+                        
+                        routine which has the responsibility to carry out the requested
+                        
+                        operation and call znaupd with the result.
+                        
+                    </para>
+                    
+                    <para>
+                        
+                        The operand is given in WORKD(IPNTR(1)), the result must be
+                        
+                        put in WORKD(IPNTR(2)).
+                        
+                    </para>
+                    
+                    <itemizedlist>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 0: first call to the reverse communication interface
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = -1: compute Y = OP * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for Y.
+                                
+                            </para>
+                            
+                            <para>
+                                
+                                This is for the initialization phase to force the starting
+                                
+                                vector into the range of OP.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 1: compute Y = OP * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for Y.
+                                
+                            </para>
+                            
+                            <para>
+                                
+                                In mode 3, the vector B * X is already available in
+                                
+                                WORKD(ipntr(3)). It does not need to be recomputed in forming OP
+                                
+                                * X.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 2: compute Y = M * X where IPNTR(1) is the pointer
+                                
+                                into WORKD for X, IPNTR(2) is the pointer into WORKD for
+                                
+                                Y.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>
+                                
+                                IDO = 3: compute and return the shifts in the first NP
+                                
+                                locations of WORKL.
+                                
+                            </para>
+                            
+                        </listitem>
+                        
+                        <listitem>
+                            
+                            <para>IDO = 99: done </para>
+                            
+                        </listitem>
+                        
+                    </itemizedlist>
+                    
+                    <para>
+                        
+                        After the initialization phase, when the routine is used in
+                        
+                        the "shift-and-invert" mode, the vector M * X is already available
+                        
+                        and does not need to be recomputed in forming OP*X.
+                        
+                    </para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>BMAT</term>
+                
+                <listitem>
+                    
+                    <para>Character. (INPUT) </para>
+                    
+                    <para>
+                        
+                        specifies the type of the matrix B that defines the
+                     &