IMSL_SP_MVMUL

The IMSL_SP_MVMUL function computes a matrix-vector product involving sparse matrix and a dense vector.

Note
This routine requires an IDL Advanced Math and Stats license. For more information, contact your ITT Visual Information Solutions sales or technical support representative.

Syntax

Matrix stored in coordinate format:

Result = IMSL_SP_MVMUL(n_rows, n_cols, a, x [, SYMMETRIC=value] )

Matrix stored in band format:

Result = IMSL_SP_MVMUL(n_rows, n_cols, nlca, nuca, a, x [, SYMMETRIC=value] )

Return Value

A one-dimensional array containing the product Ax = b.

Arguments

nrows

Number of rows in the matrix a.

ncols

Number of columns in the matrix a.

nlca

Number of lower codiagonals in a. nuca should be used if a is stored in band format.

nuca

Number of upper codiagonals in a. nlca should be used if a is stored in band format.

a

If in coordinate format, a sparse matrix stored as an array of structures. If banded, an array of size (nlca + nuca + 1) x nrows containing the nrows x ncols banded coefficient matrix in band storage mode. If banded, and the keyword SYMMETRIC is set, an array of size (nlca + 1) x nrows containing the nrows x ncols banded coefficient matrix in band symmetric storage mode A(i,j). See Band Storage Format for a description of band storage mode.

x

One-dimensional matrix containing the vector to be multiplied by a.

Keywords

SYMMETRIC

If present and nonzero, then a is stored in symmetric mode. If A is in coordinate format, then Ax + A^Tx – diag(A) is returned. If A is banded, then it must be in band symmetric storage mode. See Band Storage Format for a description of band storage modes.

Discussion

The IMSL_SP_MVMUL function computes a matrix-vector product involving a sparse matrix and a dense vector.

If A is stored in coordinate format, then the arguments nrows, ncols, a, and x should be used. If the keyword SYMMETRIC is set, then Ax + A^Tx – diag(A) is returned.

If A is a banded, then the arguments nrows, ncols, nlca, nuca, a, and x should be used. If the keyword SYMMETRIC is set, then A must be in band symmetric storage mode, and the number of codiagonals should be used for both nlca and nuca.

Examples

Example 1

This example computes Ax, where A is stored in coordinate format.

Let x^T = (1, 2, 3, 4, 5, 6)

A = replicate(imsl_f_sp_elem, 15) 
; Define the sparse matrix A using coordinate storage format. 
a(*).row = [0, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5] 
a(*).col = [0, 1, 2, 3, 2, 0, 3, 4, 0, 3, 4, 5, 0, 1, 5] 
a(*).val = [10, 10, -3, -1, 15, -2, 10, -1, -1, -5, $ 
   1, -3, -1, -2, 6] 
x = [1, 2, 3, 4, 5, 6] 
ax = IMSL_SP_MVMUL(6, 6, a, x) 
PM, ax 
    10.000000 
    7.0000000 
    45.000000 
    33.000000 
   -34.000000 
    31.000000

Example 2

This example computes Ax, where A is stored in band mode. Consider the 1000 x 1000 banded matrix below:

Let x(*) = 2.

n_rows = 1000L 
nlca = 1L 
nuca = 1L 
a = DBLARR(n_rows*(nlca+nuca+1)) 
a(1:n_rows-1) = 4 
a(n_rows:2*n_rows-1) = -1 
a(2*n_rows:*) = 4 
; Fill A with the values of the bands. 
x = DBLARR(n_rows) 
x(*) = 2 
; Fill up x. 
expected = DBLARR(n_rows) 
expected(*) = 14 
expected(0) = 6 
expected(n_rows-1) = 6 
; Define the expected result. 
ax = IMSL_SP_MVMUL(n_rows, n_rows, nlca, nuca, a, x) 
; Compute the product, then output the difference between the  
; computed result and the expected result. 
PRINT, TOTAL(ABS(ax-expected)) 
   0.0000000

Example 3

This example computes Ax, where A is stored in band symmetric mode. Let

n = 4L 
ncoda = 2L 
a = DBLARR((ncoda+1)*n) 
a(0:n-1) = [0, 0, -1, 1] 
a(n:2L*n-1) = [0, 0, 2, -1] 
a(2L*n:*) = [2, 4, 7, 3] 
; Fill up contents of A. 
x = [4, -6, 2, 9] 
ax = IMSL_SP_MVMUL(n, n, ncoda, ncoda, a, x, /Symmetric) 
; Call IMSL_SP_MVMUL with the keyword Symmetric set. 
PM, ax 
    6.0000000 
   -11.000000 
   -11.000000 
    19.000000

Version History


6.4	Introduced