Difference between revisions of "ApCoCoA-1:Num.SimDiag"
From ApCoCoAWiki
(Added SimDiag command) |
|||
| Line 21: | Line 21: | ||
M1 := Transposed(M1); | M1 := Transposed(M1); | ||
M2 := Transposed(M2); | M2 := Transposed(M2); | ||
| − | Result := Num.SimDiag([M1],10); | + | Result := Num.SimDiag([M1,M2],10); |
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([ | ||
| + | [<quote>0.062</quote>, <quote>0.016</quote>, <quote>0.000</quote>, <quote>0.006</quote>], | ||
| + | [<quote>0.021</quote>, <quote>0.030</quote>, <quote>-0.002</quote>, <quote>-0.000</quote>], | ||
| + | [<quote>0.000</quote>, <quote>0.005</quote>, <quote>1.006</quote>, <quote>-0.035</quote>], | ||
| + | [<quote>-0.000</quote>, <quote>-0.000</quote>, <quote>-0.031</quote>, <quote>0.982</quote>] | ||
| + | ]) | ||
| + | ------------------------------- | ||
| + | Mat([ | ||
| + | [<quote>0.048</quote>, <quote>0.000</quote>, <quote>0.030</quote>, <quote>-0.005</quote>], | ||
| + | [<quote>0.000</quote>, <quote>0.991</quote>, <quote>-0.002</quote>, <quote>-0.021</quote>], | ||
| + | [<quote>0.020</quote>, <quote>0.005</quote>, <quote>0.029</quote>, <quote>-0.000</quote>], | ||
| + | [<quote>0.000</quote>, <quote>-0.030</quote>, <quote>-0.000</quote>, <quote>0.982</quote>] | ||
| + | ]) | ||
</example> | </example> | ||
</description> | </description> | ||
Revision as of 13:46, 7 October 2010
Num.SimDiag
Computes an approximate diagonalization of a set of matrices.
Syntax
Num.SimDiag(A:LSIT):[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.
@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([ [<quote>0.062</quote>, <quote>0.016</quote>, <quote>0.000</quote>, <quote>0.006</quote>], [<quote>0.021</quote>, <quote>0.030</quote>, <quote>-0.002</quote>, <quote>-0.000</quote>], [<quote>0.000</quote>, <quote>0.005</quote>, <quote>1.006</quote>, <quote>-0.035</quote>], [<quote>-0.000</quote>, <quote>-0.000</quote>, <quote>-0.031</quote>, <quote>0.982</quote>] ]) ------------------------------- Mat([ [<quote>0.048</quote>, <quote>0.000</quote>, <quote>0.030</quote>, <quote>-0.005</quote>], [<quote>0.000</quote>, <quote>0.991</quote>, <quote>-0.002</quote>, <quote>-0.021</quote>], [<quote>0.020</quote>, <quote>0.005</quote>, <quote>0.029</quote>, <quote>-0.000</quote>], [<quote>0.000</quote>, <quote>-0.030</quote>, <quote>-0.000</quote>, <quote>0.982</quote>] ])
See also
