* `champ1()` is obsolete. Please use `champ.colored` instead.
* `setPreferencesValue` will be removed from Scilab 6.1.x. Please use `xmlSetValues` instead.
* `%sn()` is obsolete. Please use `ellipj()` instead.
+* `sysdiag()` is obsolete. Please use `blockdiag()` instead.
Removed Functions
Plant=syslin('d',Plant);
mode(-1)
end
-
+
mode(1)
//Nominal Plant
rep=x_matrix('u-weighting matrix',eye(nu,nu));
if rep==[] then return,end
Qu=evstr(rep);
- bigQ=sysdiag(Qx,Qu);
+ bigQ=blockdiag(Qx,Qu);
rep=x_matrix('x-noise covariance matrix',eye(nx,nx))
if rep==[] then return,end
Rx=evstr(rep);
rep=x_matrix('y-noise covariance matrix',eye(ny,ny))
if rep==[] then return,end
Ry=evstr(rep);
- bigR=sysdiag(Rx,Ry);
+ bigR=blockdiag(Rx,Ry);
[Plqg,r]=lqg2stan(P22,bigQ,bigR); //LQG pb as a standard problem
Klqg=lqg(Plqg,r); //LQG compensator
-
+
disp(spec(h_cl(Plqg,r,Klqg)),'closed loop eigenvalues:'); //Check internal stability
[Slqg,Rlqg,Tlqg]=sensi(P22,Klqg); //Sensitivity functions
disp(clean(ss2tf(Slqg)),'Sensitivity function');
disp(clean(ss2tf(Tlqg)),'Complementary sensitivity function');
-
+
mode(-1);
messagebox('Closed-loop response',"modal");
Klqg=lqg(Plqg,r); //Controller
spec(h_cl(Plqg,r,Klqg)) //Check internal stability
[Slqg,Rlqg,Tlqg]=sensi(P22,Klqg); //Sensitivity functions
- frq=logspace(-3,3); //10^-3 to 10^3
+ frq=logspace(-3,3); //10^-3 to 10^3
y=svplot(Slqg); //Computes singular values;
clf();
scf(100001);
w1=1/(s+1);
w2=100;
[Ptmp,r]=augment(P22,'SR'); //"S/KS" problem
- Pinf=sysdiag(w1,w2,1)*Ptmp; //Weighting functions
+ Pinf=blockdiag(w1,w2,1)*Ptmp; //Weighting functions
[Kinf,ro]=h_inf(Pinf,r,0,0.1,50);
[Sinf,Rinf,Tinf]=sensi(P22,Kinf); //Sensitivity functions
y=svplot(Sinf); //Computes singular values;
clf();t=0:0.01:30;u=sin(t);
plot2d([t',t'],[u',(flts(u,dscr(Tlqg,0.1))')])
-
+
endfunction
-
+
demo_lqg2();
-clear demo_lqg2
\ No newline at end of file
+clear demo_lqg2
\ No newline at end of file
xx=[xmin,xmin,x([1 2 2 7 4 6 3 4 5 6 3 3 5 5]);xmax,xmax,x([3,2,7,7,5,8,3,4,5,6,4,4,6,6])];
yy=[ymin,ymax,y([3,1,1,1,3,3,2,2,2,2,2,4,2,4]);ymin,ymax,y([3,3,1,3,3,3,4,4,4,4,2,4,2,4])];
-
+
scf(100001);clf();show_window();
plot2d(xx,yy,ones(1,16),'022');
xstring(28,30,'K');xstring(56,30,'Plant');xstring(12,28.80,'-');
if rep==[] then return;end
W1=evstr(rep(1));W2=evstr(rep(2));W3=evstr(rep(3));
default=rep;
- Pms=sysdiag(W1,W2,W3,eye(P22))*Pms;
+ Pms=blockdiag(W1,W2,W3,eye(P22))*Pms;
gms=['gamma min= ';'gamma max= ';'# iterations'];
vals=['0.01';'1000';'50'];
reps=x_mdialog('Set interval for gamma and #iterations',gms,vals);
fcts=['S function';'R (=K*S) function';'T function'];
www=x_mdialog('Select sensitivity function',fcts,['Yes';'No';'Yes']);
if www==[] then return,end
-
+
ww1=part(www(1),1)=='Y';
if ww1 then
scf(100002);clf();show_window();
<para>
Note that weighting functions can be introduced by left-multiplying
<literal>P</literal> by a diagonal system of appropriate dimension, e.g.,
- <literal> P = sysdiag(W1,W2,W3,eye(G))*P</literal>.
+ <literal> P = blockdiag(W1,W2,W3,eye(G))*P</literal>.
</para>
<para>
Sensitivity functions can be calculated by <literal>lft</literal>. One has:
//Same operation by LFT:
ss2tf(lft([zeros(2,2),eye(2,2);eye(2,2),-S2],S1))
//Other approach: with constant feedback
-BigS=sysdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
+BigS=blockdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
Bigclosed=BigS/.F;
W1=Bigclosed(1:2,1:2); //W1=W (in state-space).
ss2tf(W1)
<link linkend="lft">lft</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
<member>
<link linkend="augment">augment</link>
<link linkend="feedback">feedback</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
</simplelist>
</refsection>
Ko=lqe(Pd,Q_ww,R_vv); //observer gain
//----syntax [K,X]=lqe(P21)---
-bigR =sysdiag(Q_ww, R_vv);
+bigR =blockdiag(Q_ww, R_vv);
[W,Wt]=fullrf(bigR);
Bw=W(1:size(Pd.B,1),:);
Dw=W(($+1-size(Pd.C,1)):$,:);
Ko=lqe(Pd,Q_ww,R_vv); //observer gain
//----syntax [K,X]=lqe(P21)---
-bigR =sysdiag(Q_ww, R_vv);
+bigR =blockdiag(Q_ww, R_vv);
[W,Wt]=fullrf(bigR);
Bw=W(1:size(Pd.B,1),:);
Dw=W(($+1-size(Pd.C,1)):$,:);
Q_e=1; //additive input noise variance
R_vv=0.0001*eye(2,2); //measurement noise variance
Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
- Qwv=sysdiag(Q_ww,R_vv);
+ Qwv=blockdiag(Q_ww,R_vv);
//The compensator weights
Q_xx=diag([0.1 0 5 0]); //Weights on states
R_uu = 0.3; //Weight on input
- Qxu=sysdiag(Q_xx,R_uu);
+ Qxu=blockdiag(Q_xx,R_uu);
//----syntax [K,X]=lqg(P,Qxu,Qwv)---
J=lqg(Pd,Qxu,Qwv);
Q_e=1; //additive input noise variance
R_vv=0.0001*eye(2,2); //measurement noise variance
Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
- Qwv=sysdiag(Q_ww,R_vv);
+ Qwv=blockdiag(Q_ww,R_vv);
//The compensator weights
Q_xx=diag([0.1 0 5 0]); //Weights on states
R_uu = 0.3; //Weight on input
- Qxu=sysdiag(Q_xx,R_uu);
+ Qxu=blockdiag(Q_xx,R_uu);
//----syntax [K,X]=lqg(P,Qxu,Qwv)---
J=lqg(Pd,Qxu,Qwv);
Q_e=1; //additive input noise variance
R_vv=0.0001; //measurement noise variance
Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
- Qwv=sysdiag(Q_ww,R_vv);
+ Qwv=blockdiag(Q_ww,R_vv);
//The compensator weights
Q_xx=diag([0.1 0 1 0]); //Weights on states
R_uu = 0.1; //Weight on input
- Qxu=sysdiag(Q_xx,R_uu);
+ Qxu=blockdiag(Q_xx,R_uu);
//Control of the second mass position (y2)
Qi=50;
Q_e=1; //additive input noise variance
R_vv=0.0001; //measurement noise variance
Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
- Qwv=sysdiag(Q_ww,R_vv);
+ Qwv=blockdiag(Q_ww,R_vv);
//The compensator weights
Q_xx=diag([0.1 0 1 0]); //Weights on states
R_uu = 0.1; //Weight on input
- Qxu=sysdiag(Q_xx,R_uu);
+ Qxu=blockdiag(Q_xx,R_uu);
//Control of the second mass position (y2)
Qi=50;
//LQI compensator
wy=100;
- Q= wy*sysdiag(G.C'*G.C,1);
+ Q= wy*blockdiag(G.C'*G.C,1);
R=1/wy;
Kc=lqi(G,Q,R);
//full controller
following property:
</para>
<programlisting role=""><![CDATA[
-Sl1 = left*sysdiag(sys,eye(p,p))*right
+Sl1 = left*blockdiag(sys,eye(p,p))*right
]]></programlisting>
</listitem>
<listitem>
<literal>left</literal> have the following property:
</para>
<programlisting role=""><![CDATA[
- Sl1 = left*sysdiag(sys*right,eye(p,p)))
+ Sl1 = left*blockdiag(sys*right,eye(p,p)))
]]></programlisting>
</listitem>
</itemizedlist>
G=rand(n,p);
[sys1,right,left]=ss2ss(sys,rand(n,n),F1,G,2);
-// Sl1 equiv left*sysdiag(sys*right,eye(p,p)))
+// Sl1 equiv left*blockdiag(sys*right,eye(p,p)))
-res=clean(ss2tf(sys1) - ss2tf(left*sysdiag(sys*right,eye(p,p))))
+res=clean(ss2tf(sys1) - ss2tf(left*blockdiag(sys*right,eye(p,p))))
// output injection then feedback (m+p,n)
F2=rand(p,n); F=[F1;F2];
[sys2,right,left]=ss2ss(sys,rand(n,n),F,G,1);
-// Sl1 equiv left*sysdiag(sys,eye(p,p))*right
+// Sl1 equiv left*blockdiag(sys,eye(p,p))*right
-res=clean(ss2tf(sys2)-ss2tf(left*sysdiag(sys,eye(p,p))*right))
+res=clean(ss2tf(sys2)-ss2tf(left*blockdiag(sys,eye(p,p))*right))
// when F2= 0; sys1 and sys2 are the same
F2=0*rand(p,n);F=[F1;F2];
* along with this program.
*
-->
-<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="sysdiag" xml:lang="en">
+<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="sysdiag" xml:lang="en">
<refnamediv>
<refname>sysdiag</refname>
- <refpurpose>Create a block diagonal matrix from provided inputs or block diagonal system connection</refpurpose>
+ <refpurpose>
+ Creates a block diagonal matrix from provided inputs. Block diagonal system connection.
+ <emphasis role="bold">(obsolete)</emphasis>
+ </refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Syntax</title>
- <synopsis>r=sysdiag(a1,a2,...,an)</synopsis>
+ <synopsis>r = sysdiag(a1,a2,...,an)</synopsis>
</refsynopsisdiv>
<refsection>
- <title>Description</title>
- <para>Returns the block-diagonal system made with subsystems put in the
- main diagonal
- </para>
+ <title>Arguments</title>
<variablelist>
<varlistentry>
<term>ai</term>
<listitem>
- <para>subsystems (i.e. gains, or linear systems in state-space or
- transfer form)
+ <para>
+ subsystems (i.e. gains, or linear systems in state-space or transfer form).
+ </para>
+ <para>
+ constant, boolean, polynomial or rational matrices of any size.
</para>
- <para>constant, boolean, polynomial or rational matrices of any size </para>
</listitem>
</varlistentry>
<varlistentry>
<term>r</term>
<listitem>
- <para>a matrix with a1, a2, a3, ... on the diagonal </para>
+ <para>
+ a matrix with a1, a2, a3, ... on the diagonal.
+ </para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
+ <warning>
+ <literal>sysdiag()</literal> is obsolete. Please use <literal>blockdiag()</literal> instead.
+ </warning>
<para>
- Given the inputs <varname>A</varname>, <varname>B</varname> and <varname>C</varname>,
- the output will have these matrices arranged on the diagonal:
- <latex>\begin{bmatrix} A \ \ 0 \ \ 0 \\ 0 \ \ B \ \ 0 \\ 0 \ \ 0 \ \ C \end{bmatrix}</latex>.
+ Returns the block-diagonal system made with subsystems put in the main diagonal.
</para>
<para>
- <note>
- If all the input matrices are square, the output is known as a <emphasis>block diagonal matrix</emphasis>.
- </note>
+ Given the inputs <varname>A</varname>, <varname>B</varname> and <varname>C</varname>,
+ the output will have these matrices arranged on the diagonal:
+ <latex style="display" alt="[A 0 0 ; 0 B 0 ; 0 0 C]">\begin{bmatrix} A \ \ 0 \ \ 0 \\ 0 \ \ B \ \ 0 \\ 0 \ \ 0 \ \ C \end{bmatrix}</latex>.
</para>
+ <note>
+ If all the input matrices are square, the output is known as a
+ <emphasis>block diagonal matrix</emphasis>.
+ </note>
<note>Used in particular for system interconnections.</note>
<para>
- Beside this function, you can also use <code>sparse()</code> primitive to build a <emphasis>block diagonal sparse matrix</emphasis>.
- </para>
- <para>
- For boolean matrices <code>sysdiag()</code> always returns a zero one matrix in the corresponding block
- ("true" values are replaced by 1 and "false" value by 0).
- </para>
-
- <para>
- <code>sysdiag()</code> cannot be used to arrange matrices made of character strings,
- but you can overload it (see: <link linkend="overloading">overloading</link>).
+ For boolean matrices <literal>sysdiag()</literal> always returns a zero one matrix in
+ the corresponding block ("true" values are replaced by 1 and "false" value by 0).
</para>
</refsection>
<refsection>
- <title>Remark</title>
- <para>At most 17 arguments.</para>
- </refsection>
- <refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
-s=poly(0,'s')
+s = poly(0,'s')
sysdiag(rand(2,2),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])
sysdiag(tf2ss(1/s),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])
]]></programlisting>
<programlisting role="example"><![CDATA[
// a matrix of doubles:
-A=[1 0; 0 1], B=[3 4 5; 6 7 8], C=7
-D=sysdiag(A,B,C)
+A = [1 0; 0 1], B=[3 4 5; 6 7 8], C=7
+D = sysdiag(A,B,C)
//
sysdiag([%t %f; %f %t], eye(2,2), ones(3,3))
// a polynomial matrix:
-s=%s;
+s = %s;
sysdiag([s 4*s; 4 s^4], [1 s^2 s+2; 3*s 2 s^2-1])
// a rational matrix:
sysdiag([1/s 2*s/(4*s+3)], [s; 4; 1/(s^2+2*s+1)])
// a block diagonal sparse matrix:
-S=sysdiag([1 2; 3 4], [5 6; 7 8], [9 10; 11 12], [13 14; 15 16])
-S=sparse(S)
+S = sysdiag([1 2; 3 4], [5 6; 7 8], [9 10; 11 12], [13 14; 15 16])
+S = sparse(S)
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See also</title>
<simplelist type="inline">
<member>
- <link linkend="brackets">brackets</link>
- </member>
- <member>
- <link linkend="insertion">insertion</link>
- </member>
- <member>
- <link linkend="feedback">feedback</link>
- </member>
- <member>
<link linkend="diag">diag</link>
</member>
<member>
<link linkend="bdiag">bdiag</link>
</member>
<member>
- <link linkend="sparse">sparse</link>
+ <link linkend="repmat">repmat</link>
</member>
<member>
- <link linkend="repmat">repmat</link>
+ <link linkend="brackets">brackets</link>
+ </member>
+ <member>
+ <link linkend="feedback">feedback</link>
</member>
</simplelist>
</refsection>
+ <refsection role="history">
+ <title>History</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.1.0</revnumber>
+ <revdescription>
+ sysdiag() is declared obsolete.
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
</refentry>
S1=rand(2,2);S1=S1*S1';
S2=rand(2,2);S2=S2*S2';
S3=rand(2,2);S3=S3*S3';
-P=sysdiag(S1,S2,zeros(4,4));
-Q=sysdiag(S1,zeros(2,2),S3,zeros(2,2));
+P=blockdiag(S1,S2,zeros(4,4));
+Q=blockdiag(S1,zeros(2,2),S3,zeros(2,2));
X=rand(8,8);
P=X*P*X';Q=inv(X)'*Q*inv(X);
[T,siz]=equil1(P,Q);
</para>
<para>
重み関数は,
- <literal> P = sysdiag(W1,W2,W3,eye(G))*P</literal>のように
+ <literal> P = blockdiag(W1,W2,W3,eye(G))*P</literal>のように
<literal>P</literal>に適当な次元の対角システムを
左から乗じることにより得られます.
</para>
//Same operation by LFT:
ss2tf(lft([zeros(2,2),eye(2,2);eye(2,2),-S2],S1))
//Other approach: with constant feedback
-BigS=sysdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
+BigS=blockdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
Bigclosed=BigS/.F;
W1=Bigclosed(1:2,1:2); //W1=W (in state-space).
ss2tf(W1)
<link linkend="lft">lft</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
<member>
<link linkend="augment">augment</link>
<link linkend="feedback">feedback</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
</simplelist>
</refsection>
以下の特徴を有します:
</para>
<programlisting role=""><![CDATA[
-Sl1 = left*sysdiag(sys,eye(p,p))*right
+Sl1 = left*blockdiag(sys,eye(p,p))*right
]]></programlisting>
</listitem>
<listitem>
<literal>left</literal>は以下の特徴を有します:
</para>
<programlisting role=""><![CDATA[
- Sl1 = left*sysdiag(sys*right,eye(p,p)))
+ Sl1 = left*blockdiag(sys*right,eye(p,p)))
]]></programlisting>
</listitem>
</itemizedlist>
F1=rand(m,n);
G=rand(n,p);
[sys1,right,left]=ss2ss(sys,rand(n,n),F1,G,2);
-// Sl1 equiv left*sysdiag(sys*right,eye(p,p)))
-res=clean(ss2tf(sys1) - ss2tf(left*sysdiag(sys*right,eye(p,p))))
+// Sl1 equiv left*blockdiag(sys*right,eye(p,p)))
+res=clean(ss2tf(sys1) - ss2tf(left*blockdiag(sys*right,eye(p,p))))
// output injection then feedback (m+p,n)
F2=rand(p,n); F=[F1;F2];
[sys2,right,left]=ss2ss(sys,rand(n,n),F,G,1);
-// Sl1 equiv left*sysdiag(sys,eye(p,p))*right
-res=clean(ss2tf(sys2)-ss2tf(left*sysdiag(sys,eye(p,p))*right))
+// Sl1 equiv left*blockdiag(sys,eye(p,p))*right
+res=clean(ss2tf(sys2)-ss2tf(left*blockdiag(sys,eye(p,p))*right))
// when F2= 0; sys1 and sys2 are the same
F2=0*rand(p,n);F=[F1;F2];
[sys2,right,left]=ss2ss(sys,rand(n,n),F,G,1);
<?xml version="1.0" encoding="UTF-8"?>
-
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
* along with this program.
*
-->
-
-<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="sysdiag" xml:lang="ja">
-
+<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="sysdiag" xml:lang="ja">
<refnamediv>
-
<refname>sysdiag</refname>
-
- <refpurpose>ブロック対角システム接続</refpurpose>
-
+ <refpurpose>
+ ブロック対角システム接続 <emphasis role="bold">(obsolete)</emphasis>
+ </refpurpose>
</refnamediv>
-
<refsynopsisdiv>
-
<title>呼び出し手順</title>
-
- <synopsis>r=sysdiag(a1,a2,...,an)</synopsis>
-
+ <synopsis>r = sysdiag(a1,a2,...,an)</synopsis>
</refsynopsisdiv>
-
<refsection>
-
- <title>説明</title>
-
- <para>
-
- 主対角項にサブシステムを配置したブロック対角システムを返します.
-
- </para>
-
+ <title>設定</title>
<variablelist>
-
<varlistentry>
-
<term>ai</term>
-
<listitem>
-
<para>
-
サブシステム (すなわち,ゲインまたは状態空間表現または
-
伝達関数表現の線形システム)
-
</para>
-
<para>任意の大きさの定数, 論理値, 多項式または有理数行列</para>
-
</listitem>
-
</varlistentry>
-
<varlistentry>
-
<term>r</term>
-
<listitem>
-
<para>a1, a2, a3, ... を対角項に有する行列</para>
-
</listitem>
-
</varlistentry>
-
</variablelist>
-
</refsection>
-
<refsection>
-
<title>説明</title>
-
+ <warning>
+ <literal>sysdiag()</literal> is obsolete. Please use <literal>blockdiag()</literal> instead.
+ </warning>
<para>
-
- 入力<varname>A</varname>, <varname>B</varname> および
-
- <varname>C</varname>を指定すると,
-
- 出力はこれらの行列を以下のように対角項に配置したものになります:
-
- <latex>\begin{bmatrix} A \ \ 0 \ \ 0 \\ 0 \ \ B \ \ 0 \\ 0 \ \ 0 \ \ C \end{bmatrix}</latex>.
-
+ 主対角項にサブシステムを配置したブロック対角システムを返します.
</para>
-
<para>
-
- <note>
-
- 入力行列が全て正方の場合, 出力は
-
- <emphasis>ブロック対角行列</emphasis>として
-
- 知られたものになります.
-
- </note>
-
+ 入力<varname>A</varname>, <varname>B</varname> および <varname>C</varname>を指定すると,
+ 出力はこれらの行列を以下のように対角項に配置したものになります:
+ <latex style="display">\begin{bmatrix} A \ \ 0 \ \ 0 \\ 0 \ \ B \ \ 0 \\ 0 \ \ 0 \ \ C \end{bmatrix}</latex>.
</para>
-
-
+ <note>
+ 入力行列が全て正方の場合, 出力は
+ <emphasis>ブロック対角行列</emphasis>として
+ 知られたものになります.
+ </note>
<note>特にシステムの相互接続で使用されます.</note>
-
<para>
-
- この関数以外では,
-
- <emphasis>ブロック対角疎行列</emphasis>.を
-
- 構築するために<code>sparse()</code>プリミティブも使用できます.
-
- </para>
-
- <para>
-
論理値行列の場合,<code>sysdiag()</code> は常に
-
対応するブロックに 0 または 1を要素とする行列
-
("true"値は1,"false"値は0で置換されます)を返します.
-
- </para>
-
-
-
- <para>
-
- <code>sysdiag()</code> は文字列からなる
-
- 行列を配置する際に使用できませんが,
-
- オーバーロードすることが可能です
-
- (参照: <link linkend="overloading">オーバーローディング</link>).
-
</para>
-
</refsection>
-
<refsection>
-
<title>注意</title>
-
<para>引数の数は最大17個に制限されています.</para>
-
</refsection>
-
<refsection>
-
<title>例</title>
-
<programlisting role="example"><![CDATA[
-s=poly(0,'s')
+s = poly(0,'s')
sysdiag(rand(2,2),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])
sysdiag(tf2ss(1/s),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])
]]></programlisting>
-
<programlisting role="example"><![CDATA[
// a matrix of doubles:
-A=[1 0; 0 1], B=[3 4 5; 6 7 8], C=7
-D=sysdiag(A,B,C)
+A = [1 0; 0 1], B=[3 4 5; 6 7 8], C=7
+D = sysdiag(A,B,C)
//
sysdiag([%t %f; %f %t], eye(2,2), ones(3,3))
// a polynomial matrix:
-s=%s;
+s = %s;
sysdiag([s 4*s; 4 s^4], [1 s^2 s+2; 3*s 2 s^2-1])
// a rational matrix:
sysdiag([1/s 2*s/(4*s+3)], [s; 4; 1/(s^2+2*s+1)])
// a block diagonal sparse matrix:
-S=sysdiag([1 2; 3 4], [5 6; 7 8], [9 10; 11 12], [13 14; 15 16])
-S=sparse(S)
+S = sysdiag([1 2; 3 4], [5 6; 7 8], [9 10; 11 12], [13 14; 15 16])
+S = sparse(S)
]]></programlisting>
-
</refsection>
-
<refsection role="see also">
-
<title>参照</title>
-
<simplelist type="inline">
-
- <member>
-
- <link linkend="brackets">brackets</link>
-
- </member>
-
- <member>
-
- <link linkend="insertion">insertion</link>
-
- </member>
-
<member>
-
- <link linkend="feedback">feedback</link>
-
- </member>
-
- <member>
-
<link linkend="diag">diag</link>
-
</member>
-
<member>
-
<link linkend="bdiag">bdiag</link>
-
</member>
-
<member>
-
- <link linkend="sparse">sparse</link>
-
+ <link linkend="repmat">repmat</link>
</member>
-
<member>
-
- <link linkend="repmat">repmat</link>
-
+ <link linkend="brackets">brackets</link>
+ </member>
+ <member>
+ <link linkend="feedback">feedback</link>
</member>
-
</simplelist>
-
</refsection>
-
-</refentry>
-
+ <refsection role="history">
+ <title>履歴</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.1.0</revnumber>
+ <revdescription>
+ sysdiag() is declared obsolete.
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
+</refentry>
\ No newline at end of file
S1=rand(2,2);S1=S1*S1';
S2=rand(2,2);S2=S2*S2';
S3=rand(2,2);S3=S3*S3';
-P=sysdiag(S1,S2,zeros(4,4));
-Q=sysdiag(S1,zeros(2,2),S3,zeros(2,2));
+P=blockdiag(S1,S2,zeros(4,4));
+Q=blockdiag(S1,zeros(2,2),S3,zeros(2,2));
X=rand(8,8);
P=X*P*X';Q=inv(X)'*Q*inv(X);
[T,siz]=equil1(P,Q);
* along with this program.
*
-->
-<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="sysdiag" xml:lang="pt">
+<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="sysdiag" xml:lang="pt">
<refnamediv>
<refname>sysdiag</refname>
- <refpurpose>conexão de sistemas diagonais em blocos</refpurpose>
+ <refpurpose>
+ conexão de sistemas diagonais em blocos <emphasis role="bold">(obsolete)</emphasis>
+ </refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Seqüência de Chamamento</title>
- <synopsis>r=sysdiag(a1,a2,...,an)</synopsis>
+ <synopsis>r = sysdiag(a1,a2,...,an)</synopsis>
</refsynopsisdiv>
<refsection>
- <title>Descrição</title>
- <para>Retorna um sistema diagonal em blocos feito de subsistemas postos na
- diagonal principal.
- </para>
+ <title>Parâmetros</title>
<variablelist>
<varlistentry>
<term>ai</term>
<listitem>
+ <para>
+ constant, boolean, polynomial or rational matrices of any size.
+ </para>
<para>subsistemas (i.e. ganhos, ou sistema linear em forma de espaço
de estados ou de transferência)
</para>
</listitem>
</varlistentry>
+ <varlistentry>
+ <term>r</term>
+ <listitem>
+ <para>a matrix with a1, a2, a3, ... on the diagonal</para>
+ </listitem>
+ </varlistentry>
</variablelist>
- <para>Usado em particular para interconexões de sistemas.</para>
</refsection>
<refsection>
- <title>Observação</title>
- <para>No máximo 17 argumentos.</para>
+ <title>Descrição</title>
+ <warning>
+ <literal>sysdiag()</literal> is obsolete. Please use <literal>blockdiag()</literal> instead.
+ </warning>
+ <para>Retorna um sistema diagonal em blocos feito de subsistemas postos na
+ diagonal principal.
+ </para>
+ <para>
+ Given the inputs <varname>A</varname>, <varname>B</varname> and <varname>C</varname>,
+ the output will have these matrices arranged on the diagonal:
+ <latex style="display" alt="[A 0 0 ; 0 B 0 ; 0 0 C]">\begin{bmatrix} A \ \ 0 \ \ 0 \\ 0 \ \ B \ \ 0 \\ 0 \ \ 0 \ \ C \end{bmatrix}</latex>.
+ </para>
+ <note>
+ If all the input matrices are square, the output is known as a <emphasis>block diagonal matrix</emphasis>.
+ </note>
+ <note>Usado em particular para interconexões de sistemas.</note>
+ <para>
+ For boolean matrices <literal>sysdiag()</literal> always returns a zero one matrix in
+ the corresponding block ("true" values are replaced by 1 and "false" value by 0).
+ </para>
</refsection>
<refsection>
<title>Exemplos</title>
<programlisting role="example"><![CDATA[
-s=poly(0,'s')
+s = poly(0,'s')
sysdiag(rand(2,2),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])
sysdiag(tf2ss(1/s),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])
]]></programlisting>
+ <programlisting role="example"><![CDATA[
+// a matrix of doubles:
+A = [1 0; 0 1], B=[3 4 5; 6 7 8], C=7
+D = sysdiag(A,B,C)
+//
+sysdiag([%t %f; %f %t], eye(2,2), ones(3,3))
+// a polynomial matrix:
+s = %s;
+sysdiag([s 4*s; 4 s^4], [1 s^2 s+2; 3*s 2 s^2-1])
+// a rational matrix:
+sysdiag([1/s 2*s/(4*s+3)], [s; 4; 1/(s^2+2*s+1)])
+// a block diagonal sparse matrix:
+S = sysdiag([1 2; 3 4], [5 6; 7 8], [9 10; 11 12], [13 14; 15 16])
+S = sparse(S)
+ ]]></programlisting>
</refsection>
<refsection role="see also">
<title>Ver Também</title>
<simplelist type="inline">
<member>
- <link linkend="brackets">brackets</link>
+ <link linkend="diag">diag</link>
</member>
<member>
- <link linkend="insertion">insertion</link>
+ <link linkend="bdiag">bdiag</link>
+ </member>
+ <member>
+ <link linkend="repmat">repmat</link>
+ </member>
+ <member>
+ <link linkend="brackets">brackets</link>
</member>
<member>
<link linkend="feedback">feedback</link>
</member>
</simplelist>
</refsection>
+ <refsection role="history">
+ <title>Histórico</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.1.0</revnumber>
+ <revdescription>
+ sysdiag() is declared obsolete.
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
</refentry>
* along with this program.
*
-->
-<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="sysdiag" xml:lang="ru">
+<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="sysdiag" xml:lang="ru">
<refnamediv>
<refname>sysdiag</refname>
- <refpurpose>соединение блочно-диагональной системы</refpurpose>
+ <refpurpose>
+ соединение блочно-диагональной системы <emphasis role="bold">(obsolete)</emphasis>
+ </refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Синтаксис</title>
- <synopsis>r=sysdiag(a1,a2,...,an)</synopsis>
+ <synopsis>r = sysdiag(a1,a2,...,an)</synopsis>
</refsynopsisdiv>
<refsection>
- <title>Описание</title>
- <para>
- Возвращает блочно-диагональную систему, созданную из подсистем, расположенных по главной диагонали.
- </para>
+ <title>Аргументы</title>
<variablelist>
<varlistentry>
<term>ai</term>
<listitem>
<para>
- подсистемы (т. е. усилители или линейные системы в пространстве состояний или в передаточной форме)
+ constant, boolean, polynomial or rational matrices of any size.
</para>
+ <para>
+ подсистемы (т. е. усилители или линейные системы в пространстве состояний
+ или в передаточной форме)
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>r</term>
+ <listitem>
+ <para>a matrix with a1, a2, a3, ... on the diagonal.</para>
</listitem>
</varlistentry>
</variablelist>
- <para>Особенно используется в системных взаимосвязях.</para>
</refsection>
<refsection>
- <title>Примечание</title>
- <para>Не больше 17 аргументов.</para>
+ <title>Описание</title>
+ <warning>
+ <literal>sysdiag()</literal> is obsolete. Please use <literal>blockdiag()</literal> instead.
+ </warning>
+ <para>
+ Возвращает блочно-диагональную систему, созданную из подсистем, расположенных по главной диагонали.
+ </para>
+ <para>
+ Given the inputs <varname>A</varname>, <varname>B</varname> and <varname>C</varname>,
+ the output will have these matrices arranged on the diagonal:
+ <latex style="display" alt="[A 0 0 ; 0 B 0 ; 0 0 C]">\begin{bmatrix} A \ \ 0 \ \ 0 \\ 0 \ \ B \ \ 0 \\ 0 \ \ 0 \ \ C \end{bmatrix}</latex>.
+ </para>
+ <note>
+ If all the input matrices are square, the output is known as a <emphasis>block diagonal matrix</emphasis>.
+ </note>
+ <note>Особенно используется в системных взаимосвязях.</note>
+ <para>
+ For boolean matrices <literal>sysdiag()</literal> always returns a zero one matrix in
+ the corresponding block ("true" values are replaced by 1 and "false" value by 0).
+ </para>
</refsection>
<refsection>
<title>Примеры</title>
<programlisting role="example"><![CDATA[
-s=poly(0,'s')
+s = poly(0,'s')
sysdiag(rand(2,2),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])
sysdiag(tf2ss(1/s),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])
]]></programlisting>
+ <programlisting role="example"><![CDATA[
+// a matrix of doubles:
+A = [1 0; 0 1], B=[3 4 5; 6 7 8], C=7
+D = sysdiag(A,B,C)
+//
+sysdiag([%t %f; %f %t], eye(2,2), ones(3,3))
+// a polynomial matrix:
+s = %s;
+sysdiag([s 4*s; 4 s^4], [1 s^2 s+2; 3*s 2 s^2-1])
+// a rational matrix:
+sysdiag([1/s 2*s/(4*s+3)], [s; 4; 1/(s^2+2*s+1)])
+// a block diagonal sparse matrix:
+S = sysdiag([1 2; 3 4], [5 6; 7 8], [9 10; 11 12], [13 14; 15 16])
+S = sparse(S)
+ ]]></programlisting>
</refsection>
<refsection role="see also">
<title>Смотрите также</title>
<simplelist type="inline">
<member>
- <link linkend="brackets">brackets</link>
+ <link linkend="diag">diag</link>
</member>
<member>
- <link linkend="insertion">insertion</link>
+ <link linkend="bdiag">bdiag</link>
+ </member>
+ <member>
+ <link linkend="repmat">repmat</link>
+ </member>
+ <member>
+ <link linkend="brackets">brackets</link>
</member>
<member>
<link linkend="feedback">feedback</link>
</member>
</simplelist>
</refsection>
+ <refsection role="history">
+ <title>История</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.1.0</revnumber>
+ <revdescription>
+ sysdiag() is declared obsolete.
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
</refentry>
F1t=stabil(A11,B11,Alfa);
F=[U*[F1t;F1bar],F2]*X';
- X=X*sysdiag(eye(Ur),U2);
+ X=X*blockdiag(eye(Ur),U2);
select flag
case "ge"
dims=[dimR,dimVg,dimV,dimV+nc2,dimV+ns2];
if norm(Qi.'-Qi,1)>100*%eps*norm(Qi,1) then
error(msprintf(_("%s: Wrong value for input argument #%d: Must be symmetric.\n"),"lqg",4))
end
- Kc=lqi(P,sysdiag(Qxu(1:nx,1:nx),Qi),Qxu(nx+1:$,nx+1:$),...
+ Kc=lqi(P,blockdiag(Qxu(1:nx,1:nx),Qi),Qxu(nx+1:$,nx+1:$),...
[Qxu(1:nx,nx+1:nx+nu);zeros(ny,nu)]);
// Form the controller
//O=observer(P,Kf)
// [Obs,U,m]=observer(Sys); Stable observer (default)
// W=U';H=W(m+1:nx,:);[A,B,C,D]=abcd(Sys); //H*U=[0,eye(no,no)];
// Sys2=ss2tf(syslin('c',A,B,H)) //Transfer u-->z
- // Idu=eye(nu,nu);ss2tf(Obs*sysdiag(Idu,Sys)*[Idu;Idu])
+ // Idu=eye(nu,nu);ss2tf(Obs*blockdiag(Idu,Sys)*[Idu;Idu])
// Transfer u-->[u;u]-->w=[u;y=Sys*u]-->Obs*w i.e. u-->output of Obs
// this transfer must equal Sys2, the u-->z transfer (H2=eye).
// [ C+D*F1 , (D , 0)]
//
// We have then the following property
- // Sl1 equiv left*sysdiag(sys,eye(p,p))*right
+ // Sl1 equiv left*blockdiag(sys,eye(p,p))*right
//
//
n=size(A,"r");p=size(C,"r");
// [ C+D*F , (D , 0)]
// this is a generalization of the case 4
// We have then the following property
- // Sl1 equiv left*sysdiag(sys*right,eye(p,p)))
+ // Sl1 equiv left*blockdiag(sys*right,eye(p,p)))
//
p = size(C,"r");
A1=A+B*F+G*C+G*D*F;
sl=ss2ss(syslin("c",a,b,c),U);
case "ncno"
cno=flag(2);ncno=flag(3);co=flag(4);nco=flag(5);
- a=sysdiag(rand(cno,cno),rand(ncno,ncno),rand(co,co),rand(nco,nco));
+ a=blockdiag(rand(cno,cno),rand(ncno,ncno),rand(co,co),rand(nco,nco));
b=[rand(cno,nin);
zeros(ncno,nin);
rand(co,nin);
sl=ss2ss(syslin("c",a,b,c),U);
case "st"
[nc,ns,ns0]=flag(2:4);nsc=ns-nc;nsc0=ns0-ns;nxs=nstate-ns;
- a=sysdiag(rand(nc,nc),imag_axis(ns-nc,ns0-ns,nstate-ns0)),
+ a=blockdiag(rand(nc,nc),imag_axis(ns-nc,ns0-ns,nstate-ns0)),
b=[rand(nc,nin);zeros(nstate-nc,nin)];
c=rand(nout,nstate);
U=rand(nstate,nstate);
case "dt"
[n1,n2,n3]=flag(2:4);
w=imag_axis(n3-n2,n2-n1,n1,"uis");
- a=sysdiag(w,rand(nstate-n3,nstate-n3));
+ a=blockdiag(w,rand(nstate-n3,nstate-n3));
c=[zeros(nout,n3),rand(nout,nstate-n3)];b=rand(nstate,nin);
U=rand(nstate,nstate);
sl=ss2ss(syslin("c",a,b,c),U);
case "on"
[nr,ng,ng0,nv,rk]=flag(2:6);
p1=1;p2=1;
- a11=sysdiag(rand(nr,nr),imag_axis(ng-nr,ng0-ng,nv-ng0));
+ a11=blockdiag(rand(nr,nr),imag_axis(ng-nr,ng0-ng,nv-ng0));
a12=rand(nv,nstate-nv);
a21=rand(nstate-nv,nv);a22=rand(nstate-nv,nstate-nv);
b11=zeros(nv,rk);b12=[rand(nr,nin-rk);zeros(nv-nr,nin-rk)];
case "ui"
[nw,nwu,nwui,nwuis,rk]=flag(2:6)
a11=rand(nw,nw);
- a22=sysdiag(imag_axis(nwu-nw,nwui-nwu,nwuis-nwui,"uis"),...
+ a22=blockdiag(imag_axis(nwu-nw,nwui-nwu,nwuis-nwui,"uis"),...
rand(nstate-nwuis,nstate-nwuis))
a12=rand(nw,nstate-nw);
b1=rand(nw,nin);
w=[];k=int(nn/2);
rand("normal");
//rand('seed',0);
- w=sysdiag(w,st_able(rand(ns,ns),margin));
+ w=blockdiag(w,st_able(rand(ns,ns),margin));
x=rand(1,k);
for u=x
- w=sysdiag(w,[u,-2*u;u,-u]);end
- if abs(2*k-nn)>1.d-5 then w=sysdiag(w,0);end
- w=sysdiag(w,-st_able(rand(nu,nu),margin));
+ w=blockdiag(w,[u,-2*u;u,-u]);end
+ if abs(2*k-nn)>1.d-5 then w=blockdiag(w,0);end
+ w=blockdiag(w,-st_able(rand(nu,nu),margin));
rand("uniform");
//rand('seed',0);
return
w=[];k=int(nn/2);
rand("normal");
//rand('seed',0);
- w=sysdiag(w,-st_able(rand(nu,nu),margin));
+ w=blockdiag(w,-st_able(rand(nu,nu),margin));
x=rand(1,k);
for u=x
- w=sysdiag(w,[u,-2*u;u,-u]);end
- if abs(2*k-nn)>1.d-5 then w=sysdiag(w,0);end
- w=sysdiag(w,st_able(rand(ns,ns),margin));
+ w=blockdiag(w,[u,-2*u;u,-u]);end
+ if abs(2*k-nn)>1.d-5 then w=blockdiag(w,0);end
+ w=blockdiag(w,st_able(rand(ns,ns),margin));
rand("uniform");
//rand('seed',0);
end
//!
+ warnobsolete("blockdiag()","6.1.x")
+
r=varargin(1);
[m1,n1]=size(r);
for k = 2:size(varargin)
+++ /dev/null
-// =============================================================================
-// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
-// Copyright (C) 2015 - Scilab Enterprises - Adeline CARNIS
-//
-// This file is distributed under the same license as the Scilab package.
-// =============================================================================
-// <-- CLI SHELL MODE -->
-// <-- Non-regression test for bug 13750 -->
-//
-// <-- Bugzilla URL -->
-// http://bugzilla.scilab.org/show_bug.cgi?id=13750
-//
-// <-- Short Description -->
-// Calling ss2ss with flag = 2 returned an error. The variable p was missing.
-// =============================================================================
-in=1;m=2;n=2;
-sys=ssrand(in,m,n);
-F1=rand(m,n);
-G=rand(n,in);
-[sys1,right,left]=ss2ss(sys,rand(n,n),F1,G,2);
-res=clean(ss2tf(sys1) - ss2tf(left*sysdiag(sys*right,eye(1,1))));
-assert_checkalmostequal(coeff(res.num), zeros(size(res,"r"), size(res, "c")), [], %eps);
// =============================================================================
// <-- CLI SHELL MODE -->
-
+// <-- NO CHECK REF -->
+//
// <-- Non-regression test for bug 13750 -->
//
// <-- Bugzilla URL -->
F1=rand(m,n);
G=rand(n,in);
[sys1,right,left]=ss2ss(sys,rand(n,n),F1,G,2);
-res=clean(ss2tf(sys1) - ss2tf(left*sysdiag(sys*right,eye(1,1))));
+res=clean(ss2tf(sys1) - ss2tf(left*blockdiag(sys*right,eye(1,1))));
assert_checkalmostequal(coeff(res.num), zeros(size(res,"r"), size(res, "c")), [], %eps);
+++ /dev/null
-//<-- CLI SHELL MODE -->
-// =============================================================================
-// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
-// Copyright (C) 2013 - Scilab Enterprises - Charlotte HECQUET
-//
-// This file is distributed under the same license as the Scilab package.
-// =============================================================================
-//
-// <-- Non-regression test for bug 4731 -->
-//
-// <-- Bugzilla URL -->
-// http://bugzilla.scilab.org/show_bug.cgi?id=4731
-//
-// <-- Short Description -->
-// lqr fails if dt argument of syslin is a number
-A=[0.5 0.3;0.3 0.9];B=[0.9; 0.3];
-Q=diag([2,5]);R=2;
-Big=sysdiag(Q,R);
-[w,wp]=fullrf(Big);C1=wp(:,1:2);D12=wp(:,3:$);
-P=syslin(1,A,B,C1,D12);
-[K,X]=lqr(P);
-S=spec(A+B*K);
-R=norm(A'*X*A-(A'*X*B)*pinv(B'*X*B+R)*(B'*X*A)+Q-X,1);
-assert_checkalmostequal(real(S),[0.24977769272823835; 0.47346570058644721]);
-assert_checkequal(imag(S),[0;0]);
-assert_checktrue(R<100*%eps);
-//<-- CLI SHELL MODE -->
// =============================================================================
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2013 - Scilab Enterprises - Charlotte HECQUET
// This file is distributed under the same license as the Scilab package.
// =============================================================================
//
+// <-- CLI SHELL MODE -->
+// <-- NO CHECK REF -->
+//
// <-- Non-regression test for bug 4731 -->
//
// <-- Bugzilla URL -->
A=[0.5 0.3;0.3 0.9];B=[0.9; 0.3];
Q=diag([2,5]);R=2;
-Big=sysdiag(Q,R);
+Big=blockdiag(Q,R);
[w,wp]=fullrf(Big);C1=wp(:,1:2);D12=wp(:,3:$);
P=syslin(1,A,B,C1,D12);
[K,X]=lqr(P);
+++ /dev/null
-//<-- CLI SHELL MODE -->
-// =============================================================================
-// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
-// Copyright (C) 2016 - INRIA - Serge Steer
-//
-// This file is distributed under the same license as the Scilab package.
-// =============================================================================
-A=[0 1 0;0 0 1;1 0 0];
-B=[0.3 1;0 1;-0.3 0.9];
-C=[1.9 1.3 1];
-D=[0.53 -0.61];
-Q_ww=[4 2 0;2 1 0;0 0 1];
-R_vv=0.7;
-Q_wv=sysdiag(Q_ww,R_vv);
-Q_xu=sysdiag(0.1*eye(3,3),[1 0;0 2]);
-Qi=1;
-// continuous time----------------------------------------
-sys=syslin("c",A,B,C,D);
-KLQG = lqg(sys,Q_xu,Q_wv);
-H=sys/.(-KLQG);
-assert_checktrue(and(real(spec(H.A))<0));
-[aug,r]=lqg2stan(sys,Q_xu,Q_wv);
-KLQG_a = lqg(aug,r);
-assert_checktrue(norm(KLQG.A-KLQG_a.A,1)<1e10&norm(KLQG.B-KLQG_a.B,1)<1e10&norm(KLQG.C-KLQG_a.C,1)<1e10);
-KLQG1 = lqg(sys,Q_xu,Q_wv,Qi,1);
-H1=sys/.(KLQG1);
-assert_checktrue(and(real(spec(H1.A))<0));
-KLQG2 = lqg(sys,Q_xu,Q_wv,Qi,2);
-H2=lft([1;1]*sys*KLQG2,1);
-assert_checktrue(and(real(spec(H2.A))<0));
-// dicrete time----------------------------------------
-sysd=dscr(sys,0.01);
-KLQG = lqg(sysd,Q_xu,Q_wv);
-H=sys/.(-KLQG);
-assert_checktrue(and(abs(spec(H.A))<1));
-[aug,r]=lqg2stan(sysd,Q_xu,Q_wv);
-KLQG_a = lqg(aug,r);
-assert_checktrue(norm(KLQG.A-KLQG_a.A,1)<1e10&norm(KLQG.B-KLQG_a.B,1)<1e10&norm(KLQG.C-KLQG_a.C,1)<1e10);
-KLQG1 = lqg(sysd,Q_xu,Q_wv,Qi,1);
-H1=sysd/.(KLQG1);
-assert_checktrue(and(abs(spec(H1.A))<1));
-KLQG2 = lqg(sysd,Q_xu,Q_wv,Qi,2);
-H2=lft([1;1]*sysd*KLQG2,1);
-assert_checktrue(and(abs(spec(H2.A))<1));
-//<-- CLI SHELL MODE -->
// =============================================================================
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2016 - INRIA - Serge Steer
//
// This file is distributed under the same license as the Scilab package.
// =============================================================================
+// <-- CLI SHELL MODE -->
+// <-- NO CHECK REF -->
+//
A=[0 1 0;0 0 1;1 0 0];
B=[0.3 1;0 1;-0.3 0.9];
C=[1.9 1.3 1];
D=[0.53 -0.61];
Q_ww=[4 2 0;2 1 0;0 0 1];
R_vv=0.7;
-Q_wv=sysdiag(Q_ww,R_vv);
-Q_xu=sysdiag(0.1*eye(3,3),[1 0;0 2]);
+Q_wv=blockdiag(Q_ww,R_vv);
+Q_xu=blockdiag(0.1*eye(3,3),[1 0;0 2]);
Qi=1;
// continuous time----------------------------------------
+++ /dev/null
-//<-- CLI SHELL MODE -->
-// =============================================================================
-// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
-// Copyright (C) 2016 - INRIA - Serge Steer
-//
-// This file is distributed under the same license as the Scilab package.
-// =============================================================================
-A=[0 1 0;0 0 1;1 0 0];
-B=[0.3 1;0 1;-0.3 0.9];
-C=[1.9 1.3 1;0 1 1];
-D=[0.53 -0.61;0 0];
-Q_xx=0.1*eye(3,3);
-R_uu=[1 0;0 2];
-Q_i=eye(2,2);
-Q_xu=sysdiag(0.1*eye(3,3),[1 0;0 2]);
-Q_zz=sysdiag(Q_xx,Q_i);
-// continuous time----------------------------------------
-P=syslin("c",A,B,C,D);
-[ny,nu,nx]=size(P);
-Kc=lqi(P,Q_zz,R_uu);
-//add states to the output to compute the regulated system
-Px=syslin("c",A,B,[eye(3,3);C],[zeros(3,2);D]);
-I=tf2ss(syslin("c",1/%s));
-Pa=[zeros(ny,nx) eye(ny,ny)
- eye(nx,nx) zeros(nx,ny)
- zeros(ny,nx) eye(ny,ny)]*Px*[-Kc(:,nx+1:nx+ny)*I -Kc(:,1:nx) Kc(:,nx+1:nx+ny)*I];
-H=lft(Pa,eye(5,5));
-p=spec(H.A);
-assert_checktrue(and(real(p)<10*%eps));
-assert_checktrue(size(find(abs(p)<10*%eps),"*")==2);
-//<-- CLI SHELL MODE -->
// =============================================================================
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2016 - INRIA - Serge Steer
//
// This file is distributed under the same license as the Scilab package.
// =============================================================================
+// <-- CLI SHELL MODE -->
+// <-- NO CHECK REF -->
+//
A=[0 1 0;0 0 1;1 0 0];
B=[0.3 1;0 1;-0.3 0.9];
C=[1.9 1.3 1;0 1 1];
Q_xx=0.1*eye(3,3);
R_uu=[1 0;0 2];
Q_i=eye(2,2);
-Q_xu=sysdiag(0.1*eye(3,3),[1 0;0 2]);
-Q_zz=sysdiag(Q_xx,Q_i);
+Q_xu=blockdiag(0.1*eye(3,3),[1 0;0 2]);
+Q_zz=blockdiag(Q_xx,Q_i);
// continuous time----------------------------------------
P=syslin("c",A,B,C,D);
+++ /dev/null
-//<-- CLI SHELL MODE -->
-// =============================================================================
-// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
-// Copyright (C) 2016 - INRIA - Serge Steer
-//
-// This file is distributed under the same license as the Scilab package.
-// =============================================================================
-Q=diag([2,5]);R=2;S=[1 1];
-//full state LQ controller Continuous time plant
-//----------------------------------------------
-//S=0
-dcmotor=syslin("c",[-10,1;-0.02,-2],[0;2],[]);
-//long syntax
-[K1,X1]=lqr(dcmotor,Q,R);
-//check stability
-assert_checktrue(real(spec(dcmotor.A+dcmotor.B*K1))<0);
-//Check Riccati equation
-assert_checktrue(norm(dcmotor.A'*X1+X1*dcmotor.A-X1*(dcmotor.B/R)*dcmotor.B'*X1+Q,1)<1e-10);
-//Augmented plant syntax
-[w,wp]=fullrf(sysdiag(Q,R)); //[C1,D12]'*[C1,D12]=Big
-dcmotor.C=wp(:,1:2);
-dcmotor.D=wp(:,3:$);
-[K2,X2]=lqr(dcmotor);
-assert_checktrue(norm(X2-X1,1)<1e-12);
-assert_checktrue(norm(K2-K1,1)<1e-12);
-//Non zero S term
-dcmotor=syslin("c",[-10,1;-0.02,-2],[0;2],[]);
-//long syntax
-[K1,X1]=lqr(dcmotor,Q,R,S);
-//check stability
-assert_checktrue(real(spec(dcmotor.A+dcmotor.B*K1))<0);
-//Check Riccati equation
-Ric=(dcmotor.A-dcmotor.B/R*S)'*X1+X1*(dcmotor.A-dcmotor.B/R*S)-X1*(dcmotor.B/R)*dcmotor.B'*X1+Q-S'/R*S;
-assert_checktrue(norm(Ric,1)<1e-10);
-//Augmented plant syntax
-[w,wp]=fullrf([Q S';S R]); //[C1,D12]'*[C1,D12]=Big
-dcmotor.C=wp(:,1:2);
-dcmotor.D=wp(:,3:$);
-[K2,X2]=lqr(dcmotor);
-assert_checktrue(norm(X2-X1,1)<1e-12);
-assert_checktrue(norm(K2-K1,1)<1e-12);
-//full state LQ controller discrete time plant
-//----------------------------------------------
-dcmotor=dscr(syslin("c",[-10,1;-0.02,-2],[0;2],[]),0.01);
-//long syntax
-[K1,X1]=lqr(dcmotor,Q,R);
-//check stability
-assert_checktrue(abs(spec(dcmotor.A+dcmotor.B*K1))<1);
-//Check Riccati equation
-Ric=dcmotor.A'*X1*dcmotor.A-(dcmotor.A'*X1*dcmotor.B)*pinv(dcmotor.B'*X1*dcmotor.B+R)*(dcmotor.B'*X1*dcmotor.A)+Q-X1;
-assert_checktrue(norm(Ric,1)<1e-10);
-//Augmented plant syntax
-[w,wp]=fullrf(sysdiag(Q,R)); //[C1,D12]'*[C1,D12]=Big
-dcmotor.C=wp(:,1:2);
-dcmotor.D=wp(:,3:$);
-[K2,X2]=lqr(dcmotor);
-assert_checktrue(norm(X2-X1,1)<1e-10);
-assert_checktrue(norm(K2-K1,1)<1e-10);
-//non zero S term
-dcmotor=dscr(syslin("c",[-10,1;-0.02,-2],[0;2],[]),0.01);
-//long syntax
-[K1,X1]=lqr(dcmotor,Q,R,S);
-//check stability
-assert_checktrue(abs(spec(dcmotor.A+dcmotor.B*K1))<1);
-//Check Riccati equation
-Ric=dcmotor.A'*X1*dcmotor.A-(dcmotor.A'*X1*dcmotor.B+S')*pinv(dcmotor.B'*X1*dcmotor.B+R)*(dcmotor.B'*X1*dcmotor.A+S)+Q-X1;
-assert_checktrue(norm(Ric,1)<1e-10);
-//Augmented plant syntax
-[w,wp]=fullrf([Q S';S R]); //[C1,D12]'*[C1,D12]=Big
-dcmotor.C=wp(:,1:2);
-dcmotor.D=wp(:,3:$);
-[K2,X2]=lqr(dcmotor);
-assert_checktrue(norm(X2-X1,1)<1e-10);
-assert_checktrue(norm(K2-K1,1)<1e-10);
-//<-- CLI SHELL MODE -->
// =============================================================================
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2016 - INRIA - Serge Steer
//
// This file is distributed under the same license as the Scilab package.
// =============================================================================
+// <-- CLI SHELL MODE -->
+// <-- NO CHECK REF -->
+//
Q=diag([2,5]);R=2;S=[1 1];
//full state LQ controller Continuous time plant
//----------------------------------------------
assert_checktrue(norm(dcmotor.A'*X1+X1*dcmotor.A-X1*(dcmotor.B/R)*dcmotor.B'*X1+Q,1)<1e-10);
//Augmented plant syntax
-[w,wp]=fullrf(sysdiag(Q,R)); //[C1,D12]'*[C1,D12]=Big
+[w,wp]=fullrf(blockdiag(Q,R)); //[C1,D12]'*[C1,D12]=Big
dcmotor.C=wp(:,1:2);
dcmotor.D=wp(:,3:$);
[K2,X2]=lqr(dcmotor);
assert_checktrue(norm(Ric,1)<1e-10);
//Augmented plant syntax
-[w,wp]=fullrf(sysdiag(Q,R)); //[C1,D12]'*[C1,D12]=Big
+[w,wp]=fullrf(blockdiag(Q,R)); //[C1,D12]'*[C1,D12]=Big
dcmotor.C=wp(:,1:2);
dcmotor.D=wp(:,3:$);
[K2,X2]=lqr(dcmotor);
If <literal>vm</literal> is a sparse matrix
<literal>diag(vm,k)</literal> returns a sparse matrix.
</para>
- <para>To construct a diagonal linear system, use <literal>sysdiag</literal>.
+ <para>To construct a diagonal linear system, use <literal>blockdiag</literal>.
</para>
<para>
Note that <literal>eye(A).*A</literal> returns a diagonal matrix
<link linkend="eye">eye</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
<member>
<link linkend="spec">spec</link>
<literal>diag(vm,k)</literal> renvoie une matrice creuse.
</para>
<para>Pour construire un système linéaire diagonal, utilisez
- <literal>sysdiag</literal>.
+ <literal>blockdiag</literal>.
</para>
<para>
Notez que <literal>eye(A).*A</literal> renvoie une matrice diagonale
<link linkend="eye">eye</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
<member>
<link linkend="spec">spec</link>
<literal>diag(vm,k)</literal> は疎行列を返します.
</para>
<para>対角線形システムを構築するには,
- <literal>sysdiag</literal>を使用してください.
+ <literal>blockdiag</literal>を使用してください.
</para>
<para>
<literal>eye(A).*A</literal> は
<link linkend="eye">eye</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
<member>
<link linkend="spec">spec</link>
<literal>diag(vm,k)</literal> retorna uma matriz esparsa.
</para>
<para>Para construir um sistema linear diagonal, use
- <literal>sysdiag</literal>.
+ <literal>blockdiag</literal>.
</para>
<para>
Perceba que <literal>eye(A).*A</literal> retorna uma matriz diagonal
<link linkend="eye">eye</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
<member>
<link linkend="spec">spec</link>
Если <literal>vm</literal> является разрежённой матрицей, то <literal>diag(vm,k)</literal> возвращает разряжённую матрицу.
</para>
<para>
- Чтобы построить диагональную линейную систему, используйте <literal>sysdiag</literal>.
+ Чтобы построить диагональную линейную систему, используйте <literal>blockdiag</literal>.
</para>
<para>
Заметьте, что <literal>eye(A).*A</literal> возвращает диагональную матрицу, построенную с диагональными элементами из <literal>A</literal>. Это правильно для любой матрицы (констант, полиномиальной, рациональной, линейной системы пространств-состояний, ...).
<link linkend="eye">eye</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
<member>
<link linkend="spec">spec</link>
<link linkend="spec">spec</link>
</member>
<member>
- <link linkend="sysdiag">sysdiag</link>
+ <link linkend="blockdiag">blockdiag</link>
</member>
</simplelist>
</refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end')
-A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7);
-A=X*A*inv(X);
-[S,P,D,index]=projspec(A);
+A = blockdiag(jdrn(3),jdrn(2),rand(2,2));
+X = rand(7,7);
+A = X*A*inv(X);
+[S,P,D,index] = projspec(A);
index //size of J-block
trace(P) //sum of dimensions of J-blocks
A*S-(eye()-P)
<member>
<link linkend="spec">spec</link>
</member>
+ <member>
+ <link linkend="blockdiag">blockdiag</link>
+ </member>
</simplelist>
</refsection>
</refentry>
<?xml version="1.0" encoding="UTF-8"?>
-
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
* along with this program.
*
-->
-
<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="bdiag">
-
<refnamediv>
-
<refname>bdiag</refname>
-
<refpurpose>ブロック対角化, 一般化固有ベクトル</refpurpose>
-
</refnamediv>
-
<refsynopsisdiv>
-
<title>呼び出し手順</title>
-
<synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis>
-
</refsynopsisdiv>
-
<refsection>
-
<title>引数</title>
-
<variablelist>
-
<varlistentry>
-
<term>A</term>
-
<listitem>
-
<para>実数または複素数の正方行列</para>
-
</listitem>
-
</varlistentry>
-
<varlistentry>
-
<term>rmax</term>
-
<listitem>
-
<para>実数</para>
-
</listitem>
-
</varlistentry>
-
<varlistentry>
-
<term>Ab</term>
-
<listitem>
-
<para>実数または複素数の正方行列</para>
-
</listitem>
-
</varlistentry>
-
<varlistentry>
-
<term>X</term>
-
<listitem>
-
<para>実数または複素数の正則行列</para>
-
</listitem>
-
</varlistentry>
-
<varlistentry>
-
<term>bs</term>
-
<listitem>
-
<para>整数ベクトル</para>
-
</listitem>
-
</varlistentry>
-
</variablelist>
-
</refsection>
-
<refsection>
-
<title>説明</title>
-
<programlisting role=""><![CDATA[
[Ab [,X [,bs]]]=bdiag(A [,rmax])
]]></programlisting>
-
<para>
-
は,行列<literal>A</literal>のブロック対角化を行ないます.
-
bs はブロックの構造(個々のブロックの大きさ)を出力します.
-
<literal>X</literal> は基底変換です.
-
すなわち, <literal>Ab = inv(X)*A*X</literal> はブロック対角です.
-
</para>
-
<para>
-
<literal>rmax</literal> は<literal>X</literal>の
-
条件数を制御します;
-
デフォルト値は <literal>A</literal> の l1ノルムです.
-
</para>
-
<para>
-
(存在する場合,)対角形式を得るには<literal>rmax</literal>に
-
大きな値を指定します(例えば,<literal>rmax=1/%eps</literal>).
-
一般に(ランダムな実数の Aの場合) ブロックは (1x1) および (2x2) で,
-
<literal>X</literal> は固有値の行列です.
-
</para>
-
</refsection>
-
<refsection>
-
<title>例</title>
-
<programlisting role="example"><![CDATA[
//実数の場合: 1x1 および 2x2 ブロック
a=rand(5,5);[ab,x,bs]=bdiag(a);ab
+
//複素数の場合: 複素数 1x1 ブロック
[ab,x,bs]=bdiag(a+%i*0);ab
]]></programlisting>
-
</refsection>
-
<refsection role="see also">
-
<title>参照</title>
-
<simplelist type="inline">
-
<member>
-
<link linkend="schur">schur</link>
-
</member>
-
<member>
-
<link linkend="sylv">sylv</link>
-
</member>
-
<member>
-
<link linkend="spec">spec</link>
-
</member>
-
+ <member>
+ <link linkend="blockdiag">blockdiag</link>
+ </member>
</simplelist>
-
</refsection>
-
-</refentry>
-
+</refentry>
\ No newline at end of file
<?xml version="1.0" encoding="UTF-8"?>
-
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
* along with this program.
*
-->
-
<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="projspec">
-
<refnamediv>
-
<refname>projspec</refname>
-
<refpurpose>スペクトル演算子</refpurpose>
-
</refnamediv>
-
<refsynopsisdiv>
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<title>呼び出し手順</title>
-
<synopsis>[S,P,D,i]=projspec(A)</synopsis>
-
</refsynopsisdiv>
-
<refsection>
-
<title>引数</title>
-
<variablelist>
-
<varlistentry>
-
<term>A</term>
-
<listitem>
-
<para>正方行列</para>
-
</listitem>
-
</varlistentry>
-
<varlistentry>
-
<term>S, P, D</term>
-
<listitem>
-
<para>s正方行列</para>
-
</listitem>
-
</varlistentry>
-
<varlistentry>
-
<term>i</term>
-
<listitem>
-
<para>
-
整数 (<literal>A</literal>のゼロ固有値の添字).
-
</para>
-
</listitem>
-
</varlistentry>
-
</variablelist>
-
</refsection>
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<refsection>
-
<title>説明</title>
-
<para>
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<literal>A</literal>の0におけるスペクトル特性.
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</para>
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<para>
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<literal>S</literal> = 0における縮小レゾルベント
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(<literal>S</literal> = -Drazin_inverse(<literal>A</literal>)).
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</para>
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<para>
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<literal>P</literal> = 0におけるスペクトル投影.
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</para>
-
<para>
-
<literal>D</literal> = 0における冪零演算子.
-
</para>
-
<para>
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<literal>index</literal> = 0固有値の添字.
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</para>
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<para>
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特異点s=0の周りでの
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<literal>(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -...</literal>
-
が出力されます.
-
</para>
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</refsection>
-
<refsection>
-
<title>例</title>
-
<programlisting role="example"><![CDATA[
deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end')
-A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7);
-A=X*A*inv(X);
+A = blockdiag(jdrn(3),jdrn(2),rand(2,2));
+X = rand(7,7);
+A = X*A*inv(X);
[S,P,D,index]=projspec(A);
index //J-ブロックの大きさ
trace(P) //J-ブロックの次元の合計
A*S-(eye()-P)
norm(D^index,1)
]]></programlisting>
-
</refsection>
-
<refsection role="see also">
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<title>参照</title>
-
<simplelist type="inline">
-
<member>
-
<link linkend="coff">coff</link>
-
</member>
-
</simplelist>
-
</refsection>
-
-</refentry>
-
+</refentry>
\ No newline at end of file
<member>
<link linkend="spec">spec</link>
</member>
+ <member>
+ <link linkend="blockdiag">blockdiag</link>
+ </member>
</simplelist>
</refsection>
</refentry>
<title>Exemplos</title>
<programlisting role="example"><![CDATA[
deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end')
-A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7);
-A=X*A*inv(X);
-[S,P,D,index]=projspec(A);
+A = blockdiag(jdrn(3),jdrn(2),rand(2,2));
+X = rand(7,7);
+A = X*A*inv(X);
+[S,P,D,index] = projspec(A);
index //tamanho do bloco J
trace(P) //soma das dimensões dos blocos J
A*S-(eye()-P)
B=diag(ones(1,n-2),-1);
B(1,:) = -c(2:n)/c(1);
end
- A=sysdiag(A,B);
+ A=blockdiag(A,B);
end
endfunction
p=p+rec1(kk);
Mres=Mn(classe,classe);
w=kernel((Mres-eye())')';
- M=sysdiag(M,w./sum(w));
+ M=blockdiag(M,w./sum(w));
end
M=[M,zeros(size(M,1),size(P,1)-size(M,2))];
M=M(:,perminv);
for k=rec
m=rand(k,k,"u");
m=m./(sum(m,"c")*ones(1,k));
- M=sysdiag(M,m);
+ M=blockdiag(M,m);
end
if type(tr) ~= 15 then
n=r+tr;
Q=[];
for kk=1:l
nt=tr(1+2*(kk-1));
- Q=sysdiag(Q,rand(nt,nt));
+ Q=blockdiag(Q,rand(nt,nt));
end
Nt=size(Q,1);
L=[];
J=[];
for kk=infi;
- J=sysdiag(J,%jdrn(kk));
+ J=blockdiag(J,%jdrn(kk));
end
if J==[] then Infin=[],else Infin=%s*J-eye();end
if ~flageps then
for k=seps;
if k==0 then [p,q]=size(Eps); Eps=[Eps,zeros(p,1)];end
- if k<>0 then Eps=sysdiag(Eps,%epsilon(k));end
+ if k<>0 then Eps=blockdiag(Eps,%epsilon(k));end
end
end
if ~flageta then
for k=seta;
if k==0 then [p,q]=size(Eta); Eta=[Eta;zeros(1,q)];end
- if k<>0 then Eta=sysdiag(Eta,%eta(k));end
+ if k<>0 then Eta=blockdiag(Eta,%eta(k));end
end
end
- F=sysdiag(Eps,Infin,Fin,Eta);
+ F=blockdiag(Eps,Infin,Fin,Eta);
[p,q]=size(F);ncols=q;
// Which is better?
B1B2=B1B2B3(1:dima,:);[W,dimb0]=rowcomp(B1B2);W=W(dima:-1:1,:);
[n1,n2]=size(A);
- Xp=sysdiag(W,eye(n1-dima,n1-dima))*Xp;
+ Xp=blockdiag(W,eye(n1-dima,n1-dima))*Xp;
return;
end
Q=[eye(dima,dima),zeros(dima,dim-dima);
// Unpack CZ
Z=unpack(CZ,blocksizes);
w=vec2list(Z,[blocksizes;blocksizes]);
-Z=sysdiag(w(1),w(2))
+Z=blockdiag(w(1),w(2))
c'*x+trace(F0*Z)
// Check that the eigenvalues of the matrix are positive
%Z0 = %Z0 / (%Id'*%Z0(1:%ka)); // make Tr Z0 = 1
if %f then //for checking semidef
- Z=sysdiag(matrix(%Z0(1:16),4,-1),%Z0(17))
- F0=full(sysdiag(matrix(%I0v,4,-1), %M-%Id'*%I0v));
+ Z=blockdiag(matrix(%Z0(1:16),4,-1),%Z0(17))
+ F0=full(blockdiag(matrix(%I0v,4,-1), %M-%Id'*%I0v));
for i=1:10,
- Fi=full(sysdiag(matrix(%I(:,i),4,-1),-%Id'*%I(:,i)));
+ Fi=full(blockdiag(matrix(%I(:,i),4,-1),-%Id'*%I(:,i)));
mprintf("i=%d %e\n",i,abs(trace(Fi*Z)-%c(i)));
end
- F11=sysdiag(matrix(%Id,4,-1),0);
+ F11=blockdiag(matrix(%Id,4,-1),0);
mprintf("i=%d %e\n",11,abs(trace(F11*Z)-%c(11)))
end
Z=unpack(CZ,blocksizes);
w=vec2list(Z,[blocksizes;blocksizes]);
-Z=sysdiag(w(1),w(2));
+Z=blockdiag(w(1),w(2));
// Check that info states that absolute convergence occurred
assert_checkequal(info(1),2);
// Check that ul contains the expected values
return;
end
w=s1;
- for k=2:mq, w=sysdiag(w,s1);end
+ for k=2:mq, w=blockdiag(w,s1);end
s=w*M;s=Q*s;
return;
end
map.emplace(L"nanmax", L"max");
map.emplace(L"numer", L".num");
map.emplace(L"square", L"replot");
+ map.emplace(L"sysdiag", L"blockdiag");
map.emplace(L"with_tk", L"with_module('tclsci')");
map.emplace(L"xgetech", L"gca");
map.emplace(L"xinfo", L"gcf().info_message");
projects / scilab.git / commitdiff