genius r692 - in trunk: . help/C lib lib/linear_algebra

[jirka svn gnome org]

Author: jirka
Date: Wed Nov 19 06:29:23 2008
New Revision: 692
URL: http://svn.gnome.org/viewvc/genius?rev=692&view=rev

Log:

Wed Nov 19 00:29:04 2008  Jiri (George) Lebl <jirka 5z com>

	* lib/linear_algebra/linear_algebra.gel:  Add Eigenvectors.
	  Currently only for 2x2 matrices where computing eigenvectors is
	  relatively easy

	* help/C/gel-function-list.xml: add Eigenvectors



Modified:
   trunk/ChangeLog
   trunk/help/C/gel-function-list.xml
   trunk/help/C/genius.txt
   trunk/lib/library-strings.c
   trunk/lib/linear_algebra/linear_algebra.gel

Modified: trunk/help/C/gel-function-list.xml
==============================================================================
--- trunk/help/C/gel-function-list.xml	(original)
+++ trunk/help/C/gel-function-list.xml	Wed Nov 19 06:29:23 2008
@@ -2778,12 +2778,32 @@
 	  </para>
           <para>
 	    See
+	    <ulink url="http://en.wikipedia.org/wiki/Eigenvalue";>Wikipedia</ulink> or
 	    <ulink url="http://planetmath.org/encyclopedia/Eigenvalue.html";>Planetmath</ulink> or
 	    <ulink url="http://mathworld.wolfram.com/Eigenvalue.html";>Mathworld</ulink> for more information.
           </para>
          </listitem>
         </varlistentry>
 
+        <varlistentry id="gel-function-Eigenvectors">
+         <term>Eigenvectors</term>
+         <listitem>
+          <synopsis>Eigenvectors (M)</synopsis>
+          <synopsis>Eigenvectors (M, &amp;eigenvalues)</synopsis>
+          <synopsis>Eigenvectors (M, &amp;eigenvalues, &amp;multiplicities)</synopsis>
+	  <para>Get the eigenvectors of a square matrix.  Optionally get also
+the eigenvalues and their algebraic multiplicities.
+	    Currently only works for matrices of size up to 2 by 2.
+	  </para>
+          <para>
+	    See
+	    <ulink url="http://en.wikipedia.org/wiki/Eigenvector";>Wikipedia</ulink> or
+	    <ulink url="http://planetmath.org/encyclopedia/Eigenvector.html";>Planetmath</ulink> or
+	    <ulink url="http://mathworld.wolfram.com/Eigenvector.html";>Mathworld</ulink> for more information.
+          </para>
+         </listitem>
+        </varlistentry>
+
         <varlistentry id="gel-function-GramSchmidt">
          <term>GramSchmidt</term>
          <listitem>

Modified: trunk/help/C/genius.txt
==============================================================================
--- trunk/help/C/genius.txt	(original)
+++ trunk/help/C/genius.txt	Wed Nov 19 06:29:23 2008
@@ -1917,6 +1917,15 @@
 
 11.2. Basic
 
+   AskString
+
+ AskString (query)
+
+           Asks a question and lets the user enter a string which it then
+           returns. If the user cancels or closes the window, then null is
+           returned. The execution of the program is blocked until the user
+           responds.
+
    Compose
 
  Compose (f,g)
@@ -1937,6 +1946,12 @@
  genius> f(f(f(7)))
  = 5764801
 
+   Evaluate
+
+ Evaluate (str)
+
+           Parses and evaluates a string.
+
    GetCurrentModulo
 
  GetCurrentModulo
@@ -2021,6 +2036,13 @@
 
            Check if argument is a number.
 
+   Parse
+
+ Parse (str)
+
+           Parses but does not evaluate a string. Note that certain
+           precomputation is done during the parsing stage.
+
    SetFunctionFlags
 
  SetFunctionFlags (id,flags...)
@@ -2056,12 +2078,6 @@
 
            Display a string and an expression with a colon to separate them.
 
-   eval
-
- eval (str)
-
-           Parses and evaluates a string.
-
    error
 
  error (str)
@@ -2098,13 +2114,6 @@
            can be any expression. It is made into a string before being
            printed.
 
-   parse
-
- parse (str)
-
-           Parses but does not evaluate a string. Note that certain
-           precomputation is done during the parsing stage.
-
    printn
 
  printn (str)
@@ -3898,7 +3907,21 @@
            matrices of size up to 4 by 4, or for triangular matrices (for
            which the eigenvalues are on the diagonal).
 
-           See Planetmath or Mathworld for more information.
+           See Wikipedia or Planetmath or Mathworld for more information.
+
+   Eigenvectors
+
+ Eigenvectors (M)
+
+ Eigenvectors (M, &eigenvalues)
+
+ Eigenvectors (M, &eigenvalues, &multiplicities)
+
+           Get the eigenvectors of a square matrix. Optionally get also the
+           eigenvalues and their algebraic multiplicities. Currently only
+           works for matrices of size up to 2 by 2.
+
+           See Wikipedia or Planetmath or Mathworld for more information.
 
    GramSchmidt
 

Modified: trunk/lib/library-strings.c
==============================================================================
--- trunk/lib/library-strings.c	(original)
+++ trunk/lib/library-strings.c	Wed Nov 19 06:29:23 2008
@@ -109,6 +109,7 @@
 char *fake = N_("Direct sum of matrices");
 char *fake = N_("Direct sum of a vector of matrices");
 char *fake = N_("Get the eigenvalues of a matrix (Currently only for up to 4x4 or triangular matrices)");
+char *fake = N_("Get the eigenvalues and eigenvectors of a matrix (Currently only for up to 2x2 matrices)");
 char *fake = N_("Apply the Gram-Schmidt process (to the columns) with respect to inner product given by B (if not given use hermitian product)");
 char *fake = N_("Hankel matrix");
 char *fake = N_("Hilbert matrix of order n");

Modified: trunk/lib/linear_algebra/linear_algebra.gel
==============================================================================
--- trunk/lib/linear_algebra/linear_algebra.gel	(original)
+++ trunk/lib/linear_algebra/linear_algebra.gel	Wed Nov 19 06:29:23 2008
@@ -440,6 +440,69 @@
 SetHelpAlias ("Eigenvalues", "eig")
 protect ("eig")
 
+SetHelp("Eigenvectors", "linear_algebra", "Get the eigenvalues and eigenvectors of a matrix (Currently only for up to 2x2 matrices)")
+function Eigenvectors(M, evsmults...) = (
+	evs := null;
+	mults := null;
+
+	if not IsNull(evsmults) then
+		evs := evsmults@(1);
+	if elements(evsmults) > 1 then
+		mults := evsmults@(2);
+	if not IsMatrix (M) or not IsMatrixSquare (M) then
+		(error("Eigenvectors: argument not a square matrix");bailout);
+	if columns (M) == 1 then (
+		if IsFunctionRef(evs) then
+			*evs = [ev];
+		if IsFunctionRef(mults) then
+			*mults = [2];
+		`[[1]]
+	) else if columns (M) == 2 then (
+		b := - trace (M) ; c := det (M);
+		if b^2-4*c == 0 then (
+			ev := -b/2;
+			if IsFunctionRef(evs) then
+				*evs = [ev];
+			if IsFunctionRef(mults) then
+				*mults = [2];
+			if IsZero (M-ev*I(2)) then (
+				`[[1;0], [0;1]]
+			) else (
+				row := [M@(1,1)-ev, M@(1,2)];
+				if IsZero(row) then
+					row := [M@(2,1), M@(2,2)-ev];
+				if row@(2) == 0 then (
+					`[[0;1]]
+				) else (
+					`[[1;-row@(1)/row@(2)]]
+				)
+			)
+		) else (
+			k := 1;
+			levs = [ ( -b - sqrt (b^2 - 4*c) ) / 2 ; ( -b + sqrt (b^2 - 4*c) ) / 2 ];
+			if IsFunctionRef(evs) then
+				*evs = levs;
+			if IsFunctionRef(mults) then
+				*mults = [1;1];
+			out := `[0];
+			for ev in levs do (
+				row := [M@(1,1)-ev, M@(1,2)];
+				if IsZero(row) then
+					row := [M@(2,1), M@(2,2)-ev];
+				if row@(2) == 0 then (
+					out@(k) := [0;1]
+				) else (
+					out@(k) := [1;-row@(1)/row@(2)]
+				);
+				k = k+1;
+			);
+			out
+		)
+	) else
+		(error("Eigenvectors: Currently only implemented for up to 2x2");bailout)
+)
+protect ("Eigenvectors")
+
 # Written by David W. Hutchison, dahutchi indiana edu for Genius 0.7.1
 # Copyright (C) 2004 David W. Hutchison (GPL)
 # LU decomposition of a matrix, aka Crout and/or Cholesky reduction.