nag_superlu_matrix_product (f11mkc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_superlu_matrix_product (f11mkc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_superlu_matrix_product (f11mkc) computes a matrix-matrix or transposed matrix-matrix product involving a real, square, sparse nonsymmetric matrix stored in compressed column (Harwell–Boeing) format.

2  Specification

#include <nag.h>
#include <nagf11.h>
void  nag_superlu_matrix_product (Nag_OrderType order, Nag_TransType trans, Integer n, Integer m, double alpha, const Integer icolzp[], const Integer irowix[], const double a[], const double b[], Integer pdb, double beta, double c[], Integer pdc, NagError *fail)

3  Description

nag_superlu_matrix_product (f11mkc) computes either the matrix-matrix product CαAB+βC, or the transposed matrix-matrix product CαATB + βC, according to the value of the argument trans, where A is a real n by n sparse nonsymmetric matrix, of arbitrary sparsity pattern with nnz nonzero elements, B and C are n by m real dense matrices. The matrix A is stored in compressed column (Harwell–Boeing) storage format. The array a stores all nonzero elements of A, while arrays icolzp and irowix store the compressed column indices and row indices of A respectively.

4  References

None.

5  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     transNag_TransTypeInput
On entry: specifies whether or not the matrix A is transposed.
trans=Nag_NoTrans
αAB+βC is computed.
trans=Nag_Trans
αATB+βC is computed.
Constraint: trans=Nag_NoTrans or Nag_Trans.
3:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
4:     mIntegerInput
On entry: m, the number of columns of matrices B and C.
Constraint: m0.
5:     alphadoubleInput
On entry: α, the scalar factor in the matrix multiplication.
6:     icolzp[dim]const IntegerInput
Note: the dimension, dim, of the array icolzp must be at least n+1.
On entry: icolzp[i-1] contains the index in A of the start of a new column. See Section 2.1.3 in the f11 Chapter Introduction.
7:     irowix[dim]const IntegerInput
Note: the dimension, dim, of the array irowix must be at least icolzp[n]-1, the number of nonzeros of the sparse matrix A.
On entry: the row index array of the sparse matrix A.
8:     a[dim]const doubleInput
Note: the dimension, dim, of the array a must be at least icolzp[n]-1, the number of nonzeros of the sparse matrix A.
On entry: the array of nonzero values in the sparse matrix A.
9:     b[dim]const doubleInput
Note: the dimension, dim, of the array b must be at least
  • max1,pdb×m when order=Nag_ColMajor;
  • max1,n×pdb when order=Nag_RowMajor.
The i,jth element of the matrix B is stored in
  • b[j-1×pdb+i-1] when order=Nag_ColMajor;
  • b[i-1×pdb+j-1] when order=Nag_RowMajor.
On entry: the n by m matrix B.
10:   pdbIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array b.
Constraints:
  • if order=Nag_ColMajor, pdbmax1,n;
  • if order=Nag_RowMajor, pdbmax1,m.
11:   betadoubleInput
On entry: the scalar factor β.
12:   c[dim]doubleInput/Output
Note: the dimension, dim, of the array c must be at least
  • max1,pdc×m when order=Nag_ColMajor;
  • max1,n×pdc when order=Nag_RowMajor.
The i,jth element of the matrix C is stored in
  • c[j-1×pdc+i-1] when order=Nag_ColMajor;
  • c[i-1×pdc+j-1] when order=Nag_RowMajor.
On entry: the n by m matrix C.
On exit: C is overwritten by αAB+βC or αATB +βC depending on the value of trans.
13:   pdcIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array c.
Constraints:
  • if order=Nag_ColMajor, pdcmax1,n;
  • if order=Nag_RowMajor, pdcmax1,m.
14:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument number value had an illegal value.
On entry, argument value had an illegal value.
NE_INT
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
On entry, pdb=value.
Constraint: pdb>0.
On entry, pdc=value.
Constraint: pdc>0.
NE_INT_2
On entry, pdb=value and m=value.
Constraint: pdbmax1,m.
On entry, pdb=value and n=value.
Constraint: pdbmax1,n.
On entry, pdc=value and m=value.
Constraint: pdcmax1,m.
On entry, pdc=value and n=value.
Constraint: pdcmax1,n.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

This example reads in a sparse matrix A and a dense matrix B. It then calls nag_superlu_matrix_product (f11mkc) to compute the matrix-matrix product C=AB and the transposed matrix-matrix product C=ATB, where
A= 2.00 1.00 0 0 0 0 0 1.00 -1.00 0 4.00 0 1.00 0 1.00 0 0 0 1.00 2.00 0 -2.00 0 0 3.00   and  B= 0.70 1.40 0.16 0.32 0.52 1.04 0.77 1.54 0.28 0.56 .

9.1  Program Text

Program Text (f11mkce.c)

9.2  Program Data

Program Data (f11mkce.d)

9.3  Program Results

Program Results (f11mkce.r)


nag_superlu_matrix_product (f11mkc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012