Solution for a Triangular System of Equations

Operation	TRANSA	SIDE	Matrix A
	'N' or 'n'	'L' or 'l'	m x m
	'T' or 't'	'L' or 'l'	m x m
	'C' or 'c'	'L' or 'l'	m x m
	'N' or 'n'	'R' or 'r'	n x n
	'T' or 't'	'R' or 'r'	n x n
	'C' or 'c'	'R' or 'r'	n x n

Calling Sequence

CALL DTRSM	(SIDE, UPLO, TRANSA, DIAG, M, N, DALPHA, DA, LDA, DB, LDB)
CALL STRSM	(SIDE, UPLO, TRANSA, DIAG, M, N, SALPHA, SA, LDA, SB, LDB)
CALL ZTRSM	(SIDE, UPLO, TRANSA, DIAG, M, N, ZALPHA, ZA, LDA, ZB, LDB)
CALL CTRSM	(SIDE, UPLO, TRANSA, DIAG, M, N, CALPHA, CA, LDA, CB, LDB)
void dtrsm	(char side, char uplo, char transa, char diag, int m, int n, double dalpha, double *da, int lda, double *db, int ldb)
void strsm	(char side, char uplo, char transa, char diag, int m, int n, float salpha, float *sa, int lda, float *sb, int ldb)
void ztrsm	(char side, char uplo, char transa, char diag, int m, int n, doublecomplex *zalpha, doublecomplex *za, int lda, doublecomplex *zb, int ldb)
void ctrsm	(char side, char uplo, char transa, char diag, int m, int n, complex *calpha, complex *ca, int lda, complex *cb, int ldb)

Arguments

SIDE	Indicates how to multiply matrices:
	'L' or 'l'	Multiply general matrix by triangular matrix on the left.
	'R' or 'r'	Multiply general matrix by triangular matrix on the right.
UPLO	Indicates whether the values in a matrix reside in the upper or lower triangle of the array in which it is stored. The legal values for UPLO are listed below. Any value not listed below is illegal.
	'L' or 'l'	Only lower triangle of array will be referenced.
	'U' or 'u'	Only upper triangle of array will be referenced.
TRANSA	Indicates how to use the matrix stored in A. The legal values for TRANSA are listed below. Any value not listed below is illegal.
	'N' or 'n'	Use the matrix as it is stored in A.
	'T' or 't'	Use the transpose of the matrix stored in A.
	'C' or 'c'	Use the conjugate transpose of the matrix stored in A.
DIAG	Indicates whether the matrix is unit triangular:
	'U' or 'u'	Unit triangular
	'N' or 'n'	Not unit triangular
M, N	Indicate the size of matrix A as shown in the table above.
xALPHA	Scalar that scales the input value of the matrix stored in A.
xA	Two-dimensional array in which one of the input matrices is stored.
LDA	Leading dimension of the array A as specified in the dimension or type statement. LDA max(1,N).
	If SIDE = 'L' or 'l', LDA max(1,M).
xB	Two-dimensional array.
	On entry, one of the input matrices.
	On exit, the result matrix.
LDB	Leading dimension of the array B as specified in the dimension or type statement. LDB max(1,M).

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, LDB, M, N

PARAMETER (M = 3)

PARAMETER (LDA = M)

PARAMETER (LDB = M)

PARAMETER (N = 2)

C

DOUBLE PRECISION A(LDA,M), ALPHA, B(LDB,N)

INTEGER I, J

C

EXTERNAL DTRSM

INTRINSIC DBLE

C

C Initialize the array A to store in triangular form the

C matrix A shown below. Initialize the array B to store

C the matrix B shown below.

C

C 1 2 4 1 2

C A = 3 5 B = 1 4

C 6 1 6

C

DATA A / 1.0D0, 8D8, 8D8, 2.0D0, 3.0D0, 8D8, 4.0D0, 5.0D0,

$ 6.0D0 /

DATA B / 7.0D0, 8.0D0, 6.0D0, 3.4D1, 4.2D1, 3.6D1 /

C

PRINT 1000

PRINT 1010, A(1,1), A(1,2), A(1,3)

PRINT 1020, A(2,2), A(2,3)

PRINT 1030, A(3,3)

PRINT 1040

PRINT 1050, ((B(I,J), J = 1, N), I = 1, M)

ALPHA = 1.0D0

CALL DTRSM ('LEFT SIDE A', 'UPPER TRIANGULAR A',

$ 'NOT TRANSPOSED A', 'NOT UNIT DIAGONAL A', M, N,

$ ALPHA, A, LDA, B, LDB)

PRINT 1060

PRINT 1050, ((B(I,J), J = 1, N), I = 1, M)

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (1X, 3(2X, F5.1))

1020 FORMAT (1X, 7X, 2(2X, F5.1))

1030 FORMAT (1X, 14X, 2X, F5.1)

1040 FORMAT (/1X, 'B:')

1050 FORMAT (2(2X, F5.1))

1060 FORMAT (/1X, 'A**(-1) * B:')

C

END

Sample Output

A:
1.0 2.0 4.0
3.0 5.0
6.0
B:
7.0 34.0
8.0 42.0
6.0 36.0
A**(-1) * B:
1.0 2.0
1.0 4.0
1.0 6.0