ApCoCoA-1:Num.SimDiag: Difference between revisions
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<command> | {{Version|1}} | ||
<command> | |||
<title>Num.SimDiag</title> | <title>Num.SimDiag</title> | ||
<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>@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> | <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>B</tt>.</item> | |||
</itemize> | </itemize> | ||
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Dec(Result[2]*M1*Result[1],3); | Dec(Result[2]*M1*Result[1],3); | ||
Dec(Result[2]*M2*Result[1],3); | Dec(Result[2]*M2*Result[1],3); | ||
Mat([ | Mat([ | ||
[ | ["0.062", "0.016", "0.000", "0.006"], | ||
[ | ["0.021", "0.030", "-0.002", "-0.000"], | ||
[ | ["0.000", "0.005", "1.006", "-0.035"], | ||
[ | ["-0.000", "-0.000", "-0.031", "0.982"] | ||
]) | ]) | ||
------------------------------- | ------------------------------- | ||
Mat([ | Mat([ | ||
[ | ["0.048", "0.000", "0.030", "-0.005"], | ||
[ | ["0.000", "0.991", "-0.002", "-0.021"], | ||
[ | ["0.020", "0.005", "0.029", "-0.000"], | ||
[ | ["0.000", "-0.030", "-0.000", "0.982"] | ||
]) | ]) | ||
----------------------------- | |||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
<see>Introduction to CoCoAServer</see> | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
<see>Num.QR</see> | <see>ApCoCoA-1:Num.QR|Num.QR</see> | ||
<see>Num.SVD</see> | <see>ApCoCoA-1:Num.SVD|Num.SVD</see> | ||
<see>Num.EigenValues</see> | <see>ApCoCoA-1:Num.EigenValues|Num.EigenValues</see> | ||
<see>Num.EigenValuesAndVectors</see> | <see>ApCoCoA-1:Num.EigenValuesAndVectors|Num.EigenValuesAndVectors</see> | ||
<see>Num.EigenValuesAndAllVectors</see> | <see>ApCoCoA-1:Num.EigenValuesAndAllVectors|Num.EigenValuesAndAllVectors</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 56: | Line 60: | ||
<key>num.simdiag</key> | <key>num.simdiag</key> | ||
<key>numerical.simdiag</key> | <key>numerical.simdiag</key> | ||
<wiki-category>Package_numerical</wiki-category> | <wiki-category>ApCoCoA-1:Package_numerical</wiki-category> | ||
</command> | </command> | ||
Latest revision as of 13:48, 29 October 2020
| This article is about a function from ApCoCoA-1. |
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 B.
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([ ["0.062", "0.016", "0.000", "0.006"], ["0.021", "0.030", "-0.002", "-0.000"], ["0.000", "0.005", "1.006", "-0.035"], ["-0.000", "-0.000", "-0.031", "0.982"] ]) ------------------------------- Mat([ ["0.048", "0.000", "0.030", "-0.005"], ["0.000", "0.991", "-0.002", "-0.021"], ["0.020", "0.005", "0.029", "-0.000"], ["0.000", "-0.030", "-0.000", "0.982"] ]) -----------------------------
See also
