学习BLAS库 -- DTRSM
函数语法:
XTRSM(SIDE, UPLD, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
功能：
Solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A**T.
The matrix X is overwritten on B.
参数释：
SIDE
SIDE is CHARACTER*1
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
UPLO
UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
TRANSA
TRANSA is CHARACTER*1
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A**T.
TRANSA = 'C' or 'c' op( A ) = A**T.
DIAG
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
M
M is INTEGER
On entry, M specifies the number of rows of B. M must be at
least zero.
N
N is INTEGER
On entry, N specifies the number of columns of B. N must be
at least zero.
ALPHA
ALPHA is REAL
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
A
A is REAL array of DIMENSION ( LDA, k ),
where k is m when SIDE = 'L' or 'l'
and k is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
LDA
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
B
B is REAL array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
LDB
LDB is INTEGER
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
使用方法：
测试DTRSM函数
/******************************************************************************/
/*
Purpose:
TEST03 tests DTRSM.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
07 April 2014
Author:
John Burkardt
*/
void test_dtrsm()
{
double *a;
double alpha;
double *b;
char diag;
int i;
int j;
int lda;
int ldb;
int m;
int n;
char side;
char transa;
char transb;
char uplo;
char functionName[] = "DTRSM";
printf("================================================ \n");
printf("Testing BLAS library function -- %s \n", functionName);
printf("\n");
//printf ( "TEST DTRSM\n" );
printf(" DTRSM solves a linear system involving a triangular\n");
printf(" matrix A and a rectangular matrix B.\n");
printf("\n");
printf(" 1: Solve A * X = alpha * B;\n");
printf(" 2: Solve A' * X = alpha * B;\n");
printf(" 3: Solve X * A = alpha * B;\n");
printf(" 4: Solve X * A' = alpha * B;\n");
/*
Solve A * X = alpha * B.
*/
side = 'L';
uplo = 'U';
transa = 'N';
diag = 'N';
m = 4;
n = 5;
alpha = 2.0;
lda = m;
ldb = m;
a = (double *) malloc(lda * m * sizeof(double));
for (j = 0; j < m; j++)
{
for (i = 0; i <= j; i++)
{
a[i + j * lda] = (double) (i + j + 2);
//a[i+j*lda] = 0 ;
}
for (i = j + 1; i < m; i++)
{
a[i + j * lda] = 0.0;
}
//a[j+j*lda] = 1 ;
}
transb = 'N';
for ( j = 0; j < m; j++ )
{
for ( i = 0; i 运行结果:
Testing BLAS library function -- DTRSM
DTRSM solves a linear system involving a triangular
matrix A and a rectangular matrix B.
1: Solve A * X = alpha * B;
2: Solve A' * X = alpha * B;
3: Solve X * A = alpha * B;
4: Solve X * A' = alpha * B;
Test matrix
A =
Col: 0 1 2 3
Row
0: 2 3 4 5
1: 0 4 5 6
2: 0 0 6 7
3: 0 0 0 8
B:
Col: 0 1 2 3 4
Row
0: 11 12 13 14 15
1: 21 22 23 24 25
2: 31 32 33 34 35
3: 41 42 43 44 45
X = inv ( A ) * alpha * B:
Col: 0 1 2 3 4
Row
0: -7.10938 -6.92708 -6.74479 -6.5625 -6.38021
1: -2.84375 -2.77083 -2.69792 -2.625 -2.55208
2: -1.625 -1.58333 -1.54167 -1.5 -1.45833
3: 10.25 10.5 10.75 11 11.25
X = inv ( A' ) * alpha * B:
Col: 0 1 2 3 4
Row
0: 11 12 13 14 15
1: 2.25 2 1.75 1.5 1.25
2: 1.125 1 0.875 0.75 0.625
3: 0.703125 0.625 0.546875 0.46875 0.390625
Test matrix
A =
Col: 0 1 2 3 4
Row
0: 2 3 4 5 6
1: 0 4 5 6 7
2: 0 0 6 7 8
3: 0 0 0 8 9
4: 0 0 0 0 10
B =
Col: 0 1 2 3 4
Row
0: 11 12 13 14 15
1: 21 22 23 24 25
2: 31 32 33 34 35
3: 41 42 43 44 45
X = alpha * B * inv ( A ):
Col: 0 1 2 3 4
Row
0: 11 -2.25 -1.125 -0.703125 -0.492188
1: 21 -4.75 -2.375 -1.48438 -1.03906
2: 31 -7.25 -3.625 -2.26563 -1.58594
3: 41 -9.75 -4.875 -3.04688 -2.13281
X = alpha * B * inv ( A' ):
Col: 0 1 2 3 4
Row
0: 0.820313 0.328125 0.1875 0.125 3
1: 2.46094 0.984375 0.5625 0.375 5
2: 4.10156 1.64063 0.9375 0.625 7
3: 5.74219 2.29688 1.3125 0.875 9参考文献
http://people.sc.fsu.edu/~jburkardt/c_src/super_blas/super_blas.html
http://www.netlib.org/lapack/explore-html/