matAddCoordinate¶

Performs element-wise addition on two real matrices stored in coordinate format, \(C\leftarrow\alpha A+\beta B\).

Synopsis¶

matAddCoordinate (n, alpha, a, beta, b, nzC)

The type double function is matAddCoordinate.

Required Arguments¶

int n (Input): The order of the matrices A and B.
float alpha (Input): Scalar multiplier for A.
sparse_elem a[] (Input): Vector of length nz_a containing the location and value of each nonzero entry in the matrix A.
float beta (Input): Scalar multiplier for B.
sparse_elem b[] (Input): Vector of length nz_b containing 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 \(\alpha A+\beta B\).

Description¶

The function matAddCoordinate forms the sum \(\alpha A+\beta B\), given the scalars α and β, and the matrices A and B in coordinate format. The 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 real 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.matAddCoordinate import matAddCoordinate

a = [[0, 0, 3],
     [0, 3, -1],
     [1, 2, 5],
     [2, 0, 1],
     [3, 1, 3]]
b = [[0, 1, -2],
     [0, 3, 1],
     [1, 0, 3],
     [2, 2, 5],
     [2, 3, 1],
     [3, 0, 4],
     [3, 1, 3]]
nz_a = 5
nz_b = 7
nz_c = []
n = 4
alpha = 1.0
beta = 1.0

c = matAddCoordinate(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" % (c[i][0], c[i][1], c[i][2]))

Output¶

 row  column  value
   0     3.00
   1    -2.00
   0     3.00
   2     5.00
   0     1.00
   2     5.00
   3     1.00
   0     4.00
   1     6.00

Example 2¶

Compute \(2*A^T+2*B^T\), where

\[\begin{split}A = \begin{bmatrix} 3 & 0 & 0 & -1 \\ 0 & 0 & 5 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ \end{bmatrix} \text{ and } B = \begin{bmatrix} 0 & -2 & 0 & 1 \\ 3 & 0 & 0 & 0 \\ 0 & 0 & 5 & 1 \\ 4 & 3 & 0 & 0 \\ \end{bmatrix}\end{split}\]

from __future__ import print_function
from pyimsl.math.matAddCoordinate import matAddCoordinate

a = [[0, 0, 3],
     [0, 3, -1],
     [1, 2, 5],
     [2, 0, 1],
     [3, 1, 3]]
b = [[0, 1, -2],
     [0, 3, 1],
     [1, 0, 3],
     [2, 2, 5],
     [2, 3, 1],
     [3, 0, 4],
     [3, 1, 3]]
nz_a = 5
nz_b = 7
nz_c = []
n = 4
alpha = 2.0
beta = 2.0

c = matAddCoordinate(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" % (c[i][0], c[i][1], c[i][2]))

Output¶

 row  column  value
   0     6.00
   1     6.00
   2     2.00
   3     8.00
   0    -4.00
   3    12.00
   1    10.00
   2    10.00
   2     2.00