Difference between revisions of "ApCoCoA-1:Num.SimDiag"
From ApCoCoAWiki
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<short_description>Computes an approximate diagonalization of a set of matrices.</short_description> | <short_description>Computes an approximate diagonalization of a set of matrices.</short_description> | ||
<syntax> | <syntax> | ||
| − | Num.SimDiag(A: | + | Num.SimDiag(A:LIST, MaxIt:INT):[B:MAT, C:MAT] |
</syntax> | </syntax> | ||
<description> | <description> | ||
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<itemize> | <itemize> | ||
<item>@param <em>A</em> A list of quadratic matrices with rational entries.</item> | <item>@param <em>A</em> A list of quadratic matrices with rational entries.</item> | ||
| + | <item>@param <em>MaxIt</em> The maximum number of iterations.</item> | ||
<item>@return The output is a list of two matrices <tt>[B:MAT, C:MAT]</tt>. The first matrix <tt>B</tt> contains the real almost eigenvectors of the matrices in <tt>A</tt>. The matrix <tt>C</tt> is the inverse of <tt>A</tt>.</item> | <item>@return The output is a list of two matrices <tt>[B:MAT, C:MAT]</tt>. The first matrix <tt>B</tt> contains the real almost eigenvectors of the matrices in <tt>A</tt>. The matrix <tt>C</tt> is the inverse of <tt>A</tt>.</item> | ||
</itemize> | </itemize> | ||
Revision as of 13:54, 7 October 2010
Num.SimDiag
Computes an approximate diagonalization of a set of matrices.
Syntax
Num.SimDiag(A:LIST, MaxIt:INT):[B:MAT, C:MAT]
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
This function returns a list of two matrices, containing the approximate (almost) eigenvectors of the matrices in A and its inverse.
@param A A list of quadratic matrices with rational entries.
@param MaxIt The maximum number of iterations.
@return The output is a list of two matrices [B:MAT, C:MAT]. The first matrix B contains the real almost eigenvectors of the matrices in A. The matrix C is the inverse of A.
Example
M1 := Mat([[0, 0, -0.079, -0.018],[0, 0, 0.032, -0.012], [1, 0, 1.056, -0.012],[0, 1, -0.060, 1.025]]); M2 := Mat([[0, -0.063, 0, -0.018],[1, 1.026, 0, -0.012], [0, 0, 0, -0.012], [0, 0, 1, 1.025]]); M1 := Transposed(M1); M2 := Transposed(M2); Result := Num.SimDiag([M1,M2],10); Dec(Result[2]*M1*Result[1],3); Dec(Result[2]*M2*Result[1],3); Mat([ [<quotes>0.062</quotes>, <quotes>0.016</quotes>, <quotes>0.000</quotes>, <quotes>0.006</quotes>], [<quotes>0.021</quotes>, <quotes>0.030</quotes>, <quotes>-0.002</quotes>, <quotes>-0.000</quotes>], [<quotes>0.000</quotes>, <quotes>0.005</quotes>, <quotes>1.006</quotes>, <quotes>-0.035</quotes>], [<quotes>-0.000</quotes>, <quotes>-0.000</quotes>, <quotes>-0.031</quotes>, <quotes>0.982</quotes>] ]) ------------------------------- Mat([ [<quotes>0.048</quotes>, <quotes>0.000</quotes>, <quotes>0.030</quotes>, <quotes>-0.005</quotes>], [<quotes>0.000</quotes>, <quotes>0.991</quotes>, <quotes>-0.002</quotes>, <quotes>-0.021</quotes>], [<quotes>0.020</quotes>, <quotes>0.005</quotes>, <quotes>0.029</quotes>, <quotes>-0.000</quotes>], [<quotes>0.000</quotes>, <quotes>-0.030</quotes>, <quotes>-0.000</quotes>, <quotes>0.982</quotes>] ]) -----------------------------
See also
