Equations of levin, lattn and lattp in Latex format 37/10937/2
Charlotte HECQUET [Thu, 21 Mar 2013 17:13:09 +0000 (18:13 +0100)]
Change-Id: I1e979d779b9e8e8e43a6ee3642baf0600c010b67

15 files changed:
scilab/modules/helptools/etc/images_md5.txt
scilab/modules/helptools/images/_LaTeX_lattn.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lattn.xml_2.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lattp.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_levin.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_levin.xml_2.png [new file with mode: 0644]
scilab/modules/helptools/images/_MathML_lattn.xml_1.png [deleted file]
scilab/modules/helptools/images/_MathML_lattn.xml_2.png [deleted file]
scilab/modules/helptools/images/_MathML_lattp.xml_1.png [deleted file]
scilab/modules/helptools/images/_MathML_levin.xml_1.png [deleted file]
scilab/modules/helptools/images/_MathML_levin.xml_2.png [deleted file]
scilab/modules/signal_processing/help/en_US/filters/levin.xml
scilab/modules/signal_processing/help/en_US/identification/lattn.xml
scilab/modules/signal_processing/help/en_US/identification/lattp.xml
scilab/modules/signal_processing/help/ja_JP/filters/levin.xml

index 9858fdd..34427b3 100644 (file)
@@ -392,7 +392,12 @@ _LaTeX_karmarkar.xml_3.png=36126a3292c13a18842b1e8f99e18b31
 _LaTeX_karmarkar.xml_4.png=2379757f440c07ab9aeffe1b508f75b6
 _LaTeX_karmarkar.xml_5.png=a35a1551eae946884ef2780daf3217c9
 _LaTeX_karmarkar.xml_6.png=d7299efdc04def35c6a385007dd15a94
+_LaTeX_lattn.xml_1.png=7ba64bdfad2c53fb336f12443f4926c6
+_LaTeX_lattn.xml_2.png=9b7ed107c9acb432bc04c8505b9d96ce
+_LaTeX_lattp.xml_1.png=7ba64bdfad2c53fb336f12443f4926c6
 _LaTeX_leastsq.xml_1.png=3d52f8613fe5a2330979b844cd60da0b
+_LaTeX_levin.xml_1.png=7ba64bdfad2c53fb336f12443f4926c6
+_LaTeX_levin.xml_2.png=f524fdf11d769933d7138962185e2606
 _LaTeX_logspace.xml_1.png=d67b97a2acf408e18565a63291c46b5a
 _LaTeX_logspace.xml_2.png=f3494bb39bebc09734755a69db8646d9
 _LaTeX_logspace.xml_3.png=d67b97a2acf408e18565a63291c46b5a
diff --git a/scilab/modules/helptools/images/_LaTeX_lattn.xml_1.png b/scilab/modules/helptools/images/_LaTeX_lattn.xml_1.png
new file mode 100644 (file)
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diff --git a/scilab/modules/helptools/images/_LaTeX_lattn.xml_2.png b/scilab/modules/helptools/images/_LaTeX_lattn.xml_2.png
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index 0000000..7866376
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diff --git a/scilab/modules/helptools/images/_LaTeX_lattp.xml_1.png b/scilab/modules/helptools/images/_LaTeX_lattp.xml_1.png
new file mode 100644 (file)
index 0000000..fbe4b67
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_lattp.xml_1.png differ
diff --git a/scilab/modules/helptools/images/_LaTeX_levin.xml_1.png b/scilab/modules/helptools/images/_LaTeX_levin.xml_1.png
new file mode 100644 (file)
index 0000000..fbe4b67
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diff --git a/scilab/modules/helptools/images/_LaTeX_levin.xml_2.png b/scilab/modules/helptools/images/_LaTeX_levin.xml_2.png
new file mode 100644 (file)
index 0000000..d2355dc
Binary files /dev/null and b/scilab/modules/helptools/images/_LaTeX_levin.xml_2.png differ
diff --git a/scilab/modules/helptools/images/_MathML_lattn.xml_1.png b/scilab/modules/helptools/images/_MathML_lattn.xml_1.png
deleted file mode 100644 (file)
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diff --git a/scilab/modules/helptools/images/_MathML_lattn.xml_2.png b/scilab/modules/helptools/images/_MathML_lattn.xml_2.png
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diff --git a/scilab/modules/helptools/images/_MathML_lattp.xml_1.png b/scilab/modules/helptools/images/_MathML_lattp.xml_1.png
deleted file mode 100644 (file)
index 2a6426b..0000000
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diff --git a/scilab/modules/helptools/images/_MathML_levin.xml_1.png b/scilab/modules/helptools/images/_MathML_levin.xml_1.png
deleted file mode 100644 (file)
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diff --git a/scilab/modules/helptools/images/_MathML_levin.xml_2.png b/scilab/modules/helptools/images/_MathML_levin.xml_2.png
deleted file mode 100644 (file)
index 7db6f8d..0000000
Binary files a/scilab/modules/helptools/images/_MathML_levin.xml_2.png and /dev/null differ
index 9c7b35f..c1758b7 100644 (file)
                         way :
                     </para>
                     <para>
-                        <inlinemediaobject>
-                            <imageobject>
-                                <imagedata>
-                                    <mml:math>
-                                        <mml:semantics>
-                                            <mml:mfenced mml:close="" mml:open="">
-                                                <mml:mtable>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>0</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>2</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mi mml:fontstyle="italic">nlags</mml:mi>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                </mml:mtable>
-                                            </mml:mfenced>
-                                            <mml:annotation mml:encoding="StarMath 5.0"> left ( matrix{R_0 ## R_1 ##
-                                                R_{2} ## dotsvert ## R_{nlags} } right )
-                                            </mml:annotation>
-                                        </mml:semantics>
-                                    </mml:math>
-                                </imagedata>
-                            </imageobject>
-                        </inlinemediaobject>
+                        <latex>
+                            \begin{eqnarray}
+                            \begin{pmatrix}
+                            R_0\\R_1\\R_2\\ \vdots \\R_{nlags}
+                            \end{pmatrix}
+                            \end{eqnarray}
+                        </latex>
                     </para>
                 </listitem>
             </varlistentry>
             (normal equations)
         </para>
         <para>
-            <inlinemediaobject>
-                <imageobject>
-                    <imagedata>
-                        <mml:math>
-                            <mml:semantics>
-                                <mml:mrow>
-                                    <mml:mrow>
-                                        <mml:mfenced mml:close="" mml:open="">
-                                            <mml:mtable>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:mi>I</mml:mi>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mrow>
-                                                            <mml:mo mml:stretchy="false">−</mml:mo>
-                                                            <mml:msub>
-                                                                <mml:mi>A</mml:mi>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mrow>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mrow>
-                                                            <mml:mo mml:stretchy="false">−</mml:mo>
-                                                            <mml:msub>
-                                                                <mml:mi>A</mml:mi>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:msub>
-                                                        </mml:mrow>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                            </mml:mtable>
-                                        </mml:mfenced>
-                                        <mml:mo mml:stretchy="false">∗</mml:mo>
-                                        <mml:mfenced mml:close="" mml:open="">
-                                            <mml:mtable>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>1</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>2</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mi>n</mml:mi>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>0</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>1</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>n</mml:mi>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>0</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>n</mml:mi>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>2</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mn>2</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mn>3</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>1</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mn>1</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mn>2</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>0</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                            </mml:mtable>
-                                        </mml:mfenced>
-                                    </mml:mrow>
-                                    <mml:mo mml:stretchy="false">=</mml:mo>
-                                    <mml:mn>0</mml:mn>
-                                </mml:mrow>
-                                <mml:annotation mml:encoding="StarMath 5.0">left ( matrix{I # -A_1
-                                    # dotsaxis #-A_n} right )* left ( matrix{R_1 # R_2 # dotsaxis #R_n
-                                    ## R_0 # R_1 # dotsaxis #R_{n-1}## R_{-1} # R_0 # dotsaxis
-                                    #R_{n-2}## dotsvert # dotsvert# dotsaxis # dotsvert## R_{2-n} #
-                                    R_{3-n} # dotsaxis #R_{1}## R_{1-n} # R_{2-n} # dotsaxis #R_{0}
-                                    }right ) = 0
-                                </mml:annotation>
-                            </mml:semantics>
-                        </mml:math>
-                    </imagedata>
-                </imageobject>
-            </inlinemediaobject>
+           <latex>
+                \begin{eqnarray}
+                \begin{pmatrix}
+                I&amp;-A_1&amp;\cdots&amp;-A_n
+                \end{pmatrix}
+                \ast
+                \begin{pmatrix}
+                R_1&amp;R_2&amp;\cdots&amp;R_n \\
+                R_0&amp;R_1&amp;\cdots&amp;R_{n-1} \\
+                R_{-1}&amp;R_0&amp;\cdots&amp;R_{n-2} \\
+                \vdots&amp;\vdots&amp;\cdots&amp;\vdots \\
+                R_{2-n}&amp;R_{3-n}&amp;\cdots&amp;R_1 \\
+                R_{1-n}&amp;R_{2-n}&amp;\cdots&amp;R_0
+                \end{pmatrix}
+                = 0
+                \end{eqnarray}
+            </latex>
         </para>
         <para>
             where {<literal>Rk;k=1:nlag</literal>} is the sequence of
index 8be09d0..f4148da 100644 (file)
                         matrix containing the <literal>Rk</literal>'s (<literal>d*d</literal> matrices for a d-dimensional process).It must be given the following way
                     </para>
                     <para>
-                        <inlinemediaobject>
-                            <imageobject>
-                                <imagedata>
-                                    <mml:math>
-                                        <mml:semantics>
-                                            <mml:mfenced mml:close=")" mml:open="(">
-                                                <mml:mtable>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>0</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>2</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mi mml:fontstyle="italic">nlags</mml:mi>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                </mml:mtable>
-                                            </mml:mfenced>
-                                            <mml:annotation mml:encoding="StarMath 5.0"> left ( matrix{R_0 ## R_1 
-                                            R_2 ## dotsvert ## R_nlags } right )
-                                            </mml:annotation>
-                                        </mml:semantics>
-                                    </mml:math>
-                                </imagedata>
-                            </imageobject>
-                        </inlinemediaobject>
+                        <latex>
+                            \begin{eqnarray}
+                            \begin{pmatrix}
+                            R_0\\R_1\\R_2\\ \vdots \\R_{nlags}
+                            \end{pmatrix}
+                            \end{eqnarray}
+                        </latex>
                     </para>
                 </listitem>
             </varlistentry>
             the following system (normal equations), i.e. identifies
             the AR part (poles) of a vector ARMA(n,p) process,
         </para>
-
+            <latex>
+                \begin{eqnarray}
+                \begin{pmatrix}
+                I&amp;-A_1&amp;\cdots&amp;-A_n
+                \end{pmatrix}
+                \ast
+                \begin{pmatrix}
+                R_{p+1}&amp;R_{p+2}&amp;\cdots&amp;R_{p+n} \\
+                R_p&amp;R_{p+1}&amp;\cdots&amp;R_{p+n-1} \\
+                R_{p+n-1}&amp;R_p&amp;\cdots&amp;R_{p+n-2} \\
+                \vdots&amp;\vdots&amp;\cdots&amp;\vdots \\
+                R_{p+1-n}&amp;R_{p+2-n}&amp;\cdots&amp;R_p
+                \end{pmatrix}
+                = 0
+                \end{eqnarray}
+            </latex>
         <para>
-            <inlinemediaobject>
-                <imageobject>
-                    <imagedata>
-                        <mml:math>
-                            <mml:semantics>
-                                <mml:mrow>
-                                    <mml:mrow>
-                                        <mml:mfenced mml:close="" mml:open="">
-                                            <mml:mtable>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:mi>I</mml:mi>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mrow>
-                                                            <mml:mo mml:stretchy="false">−</mml:mo>
-                                                            <mml:msub>
-                                                                <mml:mi>A</mml:mi>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mrow>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mrow>
-                                                            <mml:mo mml:stretchy="false">−</mml:mo>
-                                                            <mml:msub>
-                                                                <mml:mi>A</mml:mi>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:msub>
-                                                        </mml:mrow>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                            </mml:mtable>
-                                        </mml:mfenced>
-                                        <mml:mo mml:stretchy="false">∗</mml:mo>
-                                        <mml:mfenced mml:close="" mml:open="">
-                                            <mml:mtable>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mn>2</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>p</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>p</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>2</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mn>2</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mn>3</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>p</mml:mi>
-                                                                <mml:mo mml:stretchy="false">+</mml:mo>
-                                                                <mml:mn>2</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>p</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                            </mml:mtable>
-                                        </mml:mfenced>
-                                    </mml:mrow>
-                                    <mml:mo mml:stretchy="false">=</mml:mo>
-                                    <mml:mn>0</mml:mn>
-                                </mml:mrow>
-                                <mml:annotation mml:encoding="StarMath 5.0">left ( matrix{I # -A_1
-                                    # dotsaxis #-A_n} right )* left ( matrix{R_{p+1} # R_{p+2} # dotsaxis #R_{p+n}
-                                    ## R_p # R_{p+1} # dotsaxis #R_{p+n-1}## R_{-1} # R_p # dotsaxis
-                                    #R_{p+n-2}## dotsvert # dotsvert# dotsaxis # dotsvert## R_{p+2-n} #
-                                    R_{p+3-n} # dotsaxis #R_{p+1}## R_{p+1-n} # R_{p+2-n} # dotsaxis #R_{p}
-                                    }right ) = 0
-                                </mml:annotation>
-                            </mml:semantics>
-                        </mml:math>
-                    </imagedata>
-                </imageobject>
-            </inlinemediaobject>
+
         </para>
 
         <para>
index d2bc876..541f67e 100644 (file)
                         matrix containing the <literal>Rk</literal>'s (<literal>d*d</literal> matrices for a d-dimensional process).It must be given the following way
                     </para>
                     <para>
-                        <inlinemediaobject>
-                            <imageobject>
-                                <imagedata>
-                                    <mml:math>
-                                        <mml:semantics>
-                                            <mml:mfenced mml:close=")" mml:open="(">
-                                                <mml:mtable>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>0</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>2</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mi mml:fontstyle="italic">nlags</mml:mi>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                </mml:mtable>
-                                            </mml:mfenced>
-                                            <mml:annotation mml:encoding="StarMath 5.0"> left ( matrix{R_0 ## R_1 
-                                            R_2 ## dotsvert ## R_nlags } right )
-                                            </mml:annotation>
-                                        </mml:semantics>
-                                    </mml:math>
-                                </imagedata>
-                            </imageobject>
-                        </inlinemediaobject>
+                        <latex>
+                            \begin{eqnarray}
+                            \begin{pmatrix}
+                            R_0\\R_1\\R_2\\ \vdots \\R_{nlags}
+                            \end{pmatrix}
+                            \end{eqnarray}
+                        </latex>
                     </para>
                 </listitem>
             </varlistentry>
index a39e5c7..4995dc5 100644 (file)
                         (<literal>d</literal>次の過程の場合は<literal>d x d</literal>行列)を有します:
                     </para>
                     <para>
-                        <inlinemediaobject>
-                            <imageobject>
-                                <imagedata>
-                                    <mml:math>
-                                        <mml:semantics>
-                                            <mml:mfenced mml:close="" mml:open="">
-                                                <mml:mtable>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>0</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mn>2</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                    <mml:mtr>
-                                                        <mml:mtd>
-                                                            <mml:msub>
-                                                                <mml:mi>R</mml:mi>
-                                                                <mml:mi mml:fontstyle="italic">nlags</mml:mi>
-                                                            </mml:msub>
-                                                        </mml:mtd>
-                                                    </mml:mtr>
-                                                </mml:mtable>
-                                            </mml:mfenced>
-                                            <mml:annotation mml:encoding="StarMath 5.0"> left ( matrix{R_0 ## R_1 ##
-                                                R_{2} ## dotsvert ## R_{nlags} } right )
-                                            </mml:annotation>
-                                        </mml:semantics>
-                                    </mml:math>
-                                </imagedata>
-                            </imageobject>
-                        </inlinemediaobject>
+                        <latex>
+                            \begin{eqnarray}
+                            \begin{pmatrix}
+                            R_0\\R_1\\R_2\\ \vdots \\R_{nlags}
+                            \end{pmatrix}
+                            \end{eqnarray}
+                        </latex>
                     </para>
                 </listitem>
             </varlistentry>
             解く関数
         </para>
         <para>
-            <inlinemediaobject>
-                <imageobject>
-                    <imagedata>
-                        <mml:math>
-                            <mml:semantics>
-                                <mml:mrow>
-                                    <mml:mrow>
-                                        <mml:mfenced mml:close="" mml:open="">
-                                            <mml:mtable>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:mi>I</mml:mi>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mrow>
-                                                            <mml:mo mml:stretchy="false">−</mml:mo>
-                                                            <mml:msub>
-                                                                <mml:mi>A</mml:mi>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:msub>
-                                                        </mml:mrow>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mrow>
-                                                            <mml:mo mml:stretchy="false">−</mml:mo>
-                                                            <mml:msub>
-                                                                <mml:mi>A</mml:mi>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:msub>
-                                                        </mml:mrow>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                            </mml:mtable>
-                                        </mml:mfenced>
-                                        <mml:mo mml:stretchy="false">∗</mml:mo>
-                                        <mml:mfenced mml:close="" mml:open="">
-                                            <mml:mtable>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>1</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>2</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mi>n</mml:mi>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>0</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>1</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>n</mml:mi>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>1</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>0</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mi>n</mml:mi>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mn>2</mml:mn>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋮</mml:mo>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mn>2</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mn>3</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>1</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                                <mml:mtr>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mn>1</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mrow>
-                                                                <mml:mn>2</mml:mn>
-                                                                <mml:mo mml:stretchy="false">−</mml:mo>
-                                                                <mml:mi>n</mml:mi>
-                                                            </mml:mrow>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:mo mml:stretchy="false">⋯</mml:mo>
-                                                    </mml:mtd>
-                                                    <mml:mtd>
-                                                        <mml:msub>
-                                                            <mml:mi>R</mml:mi>
-                                                            <mml:mn>0</mml:mn>
-                                                        </mml:msub>
-                                                    </mml:mtd>
-                                                </mml:mtr>
-                                            </mml:mtable>
-                                        </mml:mfenced>
-                                    </mml:mrow>
-                                    <mml:mo mml:stretchy="false">=</mml:mo>
-                                    <mml:mn>0</mml:mn>
-                                </mml:mrow>
-                                <mml:annotation mml:encoding="StarMath 5.0">left ( matrix{I # -A_1
-                                    # dotsaxis #-A_n} right )* left ( matrix{R_1 # R_2 # dotsaxis #R_n
-                                    ## R_0 # R_1 # dotsaxis #R_{n-1}## R_{-1} # R_0 # dotsaxis
-                                    #R_{n-2}## dotsvert # dotsvert# dotsaxis # dotsvert## R_{2-n} #
-                                    R_{3-n} # dotsaxis #R_{1}## R_{1-n} # R_{2-n} # dotsaxis #R_{0}
-                                    }right ) = 0
-                                </mml:annotation>
-                            </mml:semantics>
-                        </mml:math>
-                    </imagedata>
-                </imageobject>
-            </inlinemediaobject>
+           <latex>
+                \begin{eqnarray}
+                \begin{pmatrix}
+                I&amp;-A_1&amp;\cdots&amp;-A_n
+                \end{pmatrix}
+                \ast
+                \begin{pmatrix}
+                R_1&amp;R_2&amp;\cdots&amp;R_n \\
+                R_0&amp;R_1&amp;\cdots&amp;R_{n-1} \\
+                R_{-1}&amp;R_0&amp;\cdots&amp;R_{n-2} \\
+                \vdots&amp;\vdots&amp;\cdots&amp;\vdots \\
+                R_{2-n}&amp;R_{3-n}&amp;\cdots&amp;R_1 \\
+                R_{1-n}&amp;R_{2-n}&amp;\cdots&amp;R_0
+                \end{pmatrix}
+                = 0
+                \end{eqnarray}
+            </latex>
         </para>
         <para>
             ただし, {<literal>Rk;k=1:nlag</literal>} は