matMulRectComplex¶

Computes the transpose of a matrix, the conjugate-transpose of a matrix, a matrix-vector product, a matrix-matrix product, the bilinear form, or any triple product.

Synopsis¶

matMulRectComplex (string)

Required Arguments¶

char string (Input): String indicating matrix multiplication to be performed.

Return Value¶

The result of the multiplication. This is always a complex, even if the result is a single number. If no answer was computed, then None is returned.

Optional Arguments¶

aMatrix, complex a (Input): The nrowa × ncola matrix A.
bMatrix, complex b (Input): The nrowb × ncolb matrix B.
xVector, complex x (Input): The vector x of size nx.
yVector, complex y (Input): The vector y of size ny.

Description¶

This function computes a matrix-vector product, a matrix-matrix product, a bilinear form of a matrix, or a triple product according to the specification given by string. For example, if “A × x” is given, Ax is computed. In string, the matrices A and B and the vectors x and y can be used. Any of these four names can be used with trans, indicating transpose, or with ctrans, indicating conjugate (or Hermitian) transpose. The vectors x and y are treated as n × 1 matrices.

If string contains only one item, such as “x” or “trans(A)”, then a copy of the array, or its transpose, is returned. If string contains one multiplication, such as “A × x” or “B × A”, then the indicated product is returned. Some other legal values for string are “trans(y) × A”, “A × ctrans(B)”, “x × trans(y)”, or “ctrans(x) × y”.

The matrices and/or vectors referred to in string must be given as optional arguments. If string is “B × x”, then bMatrix and xVector must be given.

Example¶

Let

\[\begin{split}\begin{array}{l} A = \begin{bmatrix} 1+4i & 2+3i & 9+6i \\ 5+2i & 4-3i & 7+1 \\ \end{bmatrix} \phantom{...} B = \begin{bmatrix} 3-6i & 2+4i \\ 7+3i & 4-5i \\ 9+2i & 1+3i \\ \end{bmatrix} \\ x = \begin{bmatrix} 7+4i \\ 2+2i \\ 1-5i \\ \end{bmatrix} \phantom{...} y = \begin{bmatrix} 3+4i \\ 4+2i \\ 2-3i \\ \end{bmatrix} \end{array}\end{split}\]

The arrays \(A^H\), Ax, \(x^T A^T\), AB, \(B^H A^T\), \(x^Ty\), and \(xy^H\) are computed and printed.

from pyimsl.math.matMulRectComplex import matMulRectComplex
from pyimsl.math.writeMatrixComplex import writeMatrixComplex
from pyimsl.util.imslUtils import isLinux64
a = [[1 + 4j, 2 + 3j, 9 + 6j], [5 + 2j, 4 - 3j, 7 + 1j]]
b = [[3 - 6j, 2 + 4j], [7 + 3j, 4 - 5j], [9 + 2j, 1 + 3j]]
x = [7 + 4j, 2 + 2j, 1 - 5j]
y = [3 + 4j, 4 - 2j, 2 + 3j]

ans = matMulRectComplex("ctrans(A)", aMatrix=a)
writeMatrixComplex("ctrans(A)", ans)

ans = matMulRectComplex("A*x", aMatrix=a, xVector=x)
writeMatrixComplex("A*x", ans)

ans = matMulRectComplex("trans(x)*trans(A)", aMatrix=a, xVector=x)
writeMatrixComplex("trans(x)*trans(A)", ans)

ans = matMulRectComplex("A*B", aMatrix=a, bMatrix=b)
writeMatrixComplex("A*B", ans)

ans = matMulRectComplex("ctrans(B)*trans(A)", aMatrix=a, bMatrix=b)
writeMatrixComplex("ctrans(B)*trans(A)", ans)
if not isLinux64():
    ans = matMulRectComplex("trans(x)*y", xVector=x, yVector=y)
    writeMatrixComplex("trans(x)*y", ans)

ans = matMulRectComplex("x*ctrans(y)", xVector=x, yVector=y)
writeMatrixComplex("x*ctrans(y)", ans)

Output¶

 
                       ctrans(A)
                           1                          2
1  (          1,         -4)  (          5,         -2)
2  (          2,         -3)  (          4,          3)
3  (          9,         -6)  (          7,         -1)
 
                         A*x
                        1                          2
(         28,          3)  (         53,          2)
 
                  trans(x)*trans(A)
                        1                          2
(         28,          3)  (         53,          2)
 
                          A*B
                           1                          2
1  (        101,        105)  (          0,         47)
2  (        125,        -10)  (          7,         14)
 
                  ctrans(B)*trans(A)
                           1                          2
1  (         95,         69)  (         87,         -2)
2  (         38,          5)  (         59,        -28)
 
       trans(x)*y
(         34,         37)
 
                      x*ctrans(y)
                           1                          2
1  (         37,        -16)  (         20,         30)
2  (         14,         -2)  (          4,         12)
3  (        -17,        -19)  (         14,        -18)
 
                           3
1  (         26,        -13)
2  (         10,         -2)
3  (        -13,        -13)