matAddCoordinateComplex¶
Performs element-wise addition on two complex matrices stored in coordinate format, \(C\leftarrow\alpha A+\beta B\).
Synopsis¶
matAddCoordinateComplex (n, alpha, a, beta, b, nzC)
Required Arguments¶
- int
n(Input) - The order of the matrices A and B.
- complex
alpha(Input) - Scalar multiplier for A.
- sparse_elem
a[](Input) - Vector of length
nz_acontaining the location and value of each nonzero entry in the matrix A. - complex
beta(Input) - Scalar multiplier for B.
- sparse_elem
b[](Input) - Vector of length
nz_bcontaining the location and value of each nonzero entry in the matrix B. - Int
nzC(Output) - The number of nonzeros in the sum \(\alpha A+\beta B\).
Return Value¶
An array of type sparse_elem containing the computed sum. In the event of
an error or if the return matrix has no nonzero elements, None is
returned.
Optional Arguments¶
aTranspose- Replace A with \(A^T\) in the expression \(\alpha A+\beta B\).
bTranspose- Replace B with \(B^T\) in the expression \(\alpha A+\beta B\).
aConjugateTranspose- Replace A with \(A^H\) in the expression \(\alpha A+\beta B\).
bConjugateTranspose- Replace B with \(B^H\) in the expression \(\alpha A+\beta B\).
Description¶
The function matAddCoordinateComplex forms the sum \(\alpha A+\beta
B\), given the scalars αand β and the matrices A and B in coordinate
format. The transpose or conjugate transpose of A and/or B may be used
during the computation if optional arguments are specified. The method starts
by storing A in a linked list data structure, and performs the multiply by
α. Next the data in matrix B is traversed and if the coordinates of a
nonzero element correspond to those of a nonzero element in A, that entry
in the linked list is updated. Otherwise, a new node in the linked list is
created. The multiply by β occurs at this time. Lastly, the linked list
representation of C is converted to coordinate representation, omitting any
elements that may have become zero through cancellation.
Examples¶
Example 1¶
Add two complex matrices of order 4 stored in coordinate format. Matrix A has five nonzero elements. Matrix B has seven nonzero elements.
from __future__ import print_function
from pyimsl.math.matAddCoordinateComplex import matAddCoordinateComplex
a = [[0, 0, (3 + 4j)],
[0, 3, (-1 + 2j)],
[1, 2, (5 + -1j)],
[2, 0, (1 + 2j)],
[3, 1, (3 + 0j)]]
b = [[0, 1, (-2 + 1j)],
[0, 3, (1 + -2j)],
[1, 0, (3 + 0j)],
[2, 2, (5 + 2j)],
[2, 3, (1 + 4j)],
[3, 0, (4 + 0j)],
[3, 1, (3 + -2j)]]
nz_a = 5
nz_b = 7
nz_c = []
n = 4
alpha = 1 + 0j
beta = 1 + 0j
c = matAddCoordinateComplex(n, alpha, a, beta, b, nzC=nz_c)
print(" row column value")
for i in range(0, nz_c[0]):
print("%3d %5d %8.2f %8.2f" %
(c[i][0], c[i][1], (c[i][2]).real, (c[i][2]).imag))
Output¶
row column value
0 0 3.00 4.00
0 1 -2.00 1.00
1 0 3.00 0.00
1 2 5.00 -1.00
2 0 1.00 2.00
2 2 5.00 2.00
2 3 1.00 4.00
3 0 4.00 0.00
3 1 6.00 -2.00
Example 2¶
Compute \(2+3i*A^T+2-i*B^T\), where
from __future__ import print_function
from pyimsl.math.matAddCoordinateComplex import matAddCoordinateComplex
a = [[0, 0, (3 + 4j)],
[0, 3, (-1 + 2j)],
[1, 2, (5 + -1j)],
[2, 0, (1 + 2j)],
[3, 1, (3 + 0j)]]
b = [[0, 1, (-2 + 1j)],
[0, 3, (1 + -2j)],
[1, 0, (3 + 0j)],
[2, 2, (5 + 2j)],
[2, 3, (1 + 4j)],
[3, 0, (4 + 0j)],
[3, 1, (3 + -2j)]]
nz_a = 5
nz_b = 7
nz_c = []
n = 4
alpha = 2 + 3j
beta = 2 - 1j
c = matAddCoordinateComplex(n, alpha, a, beta, b, nzC=nz_c,
aTranspose=True, bTranspose=True)
print(" row column value")
for i in range(0, nz_c[0]):
print("%3d %5d %8.2f %8.2f" %
(c[i][0], c[i][1], (c[i][2]).real, (c[i][2]).imag))
Output¶
row column value
0 0 -6.00 17.00
0 1 6.00 -3.00
0 2 -4.00 7.00
0 3 8.00 -4.00
1 0 -3.00 4.00
1 3 10.00 2.00
2 1 13.00 13.00
2 2 12.00 -1.00
3 0 -8.00 -4.00
3 2 6.00 7.00