{S,D,C,Z}TRSM ( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
side character*1 On entry, specifies whether (op)A is on the left side or the right side of X in the system of equations: If side = 'L' or 'l', the system is (op)A X = alpha * B. If side = 'R' or 'r', the system is X (op)A = alpha * B. On exit, side is unchanged. uplo character*1 On entry, specifies whether the matrix A is an upper- or lower-triangular matrix: If uplo = 'U' or 'u', the matrix A is an upper- triangular matrix. If uplo = 'L' or 'l', the matrix A is a lower- triangular matrix. On exit, uplo is unchanged. transa character*1 On entry, specifies the form of (op)A used in the system of equations: If transa = 'N' or 'n', (op)A = A. If transa = 'T' or 't', (op)A = transp(A). If transa = 'C' or 'c', (op)A = conjug_transp(A). On exit, transa is unchanged. diag character*1 On entry, specifies whether the matrix A is unit- triangular: If diag = 'U' or 'u', A is a unit-triangular matrix. If diag = 'N' or 'n', A is not a unit-triangular matrix. On exit, diag is unchanged. m integer*4 On entry, the number of rows m of the matrix B; m >= 0 On exit, m is unchanged. n integer*4 On entry, the number of columns n of the matrix B; n >= 0 On exit, n is unchanged. alpha real*4 | real*8 | complex*8 | complex*16 On entry, specifies the scalar alpha. On exit, alpha is unchanged. a real*4 | real*8 | complex*8 | complex*16 On entry, a two-dimensional array A with dimensions lda by k. If the multiplication is on the left side, k >= m and the leading m by m part of the array contains the matrix A. If the multiplication is on the right side, k >= n and the leading n by n part of the array A must contain the matrix A. In either case, when the leading part of the array is specified as the upper part, the upper triangular part of array A contains the upper-triangular part of the matrix A, and the lower-triangular part of matrix A is not referenced. When the lower part is specified, the lower triangular part of the array A contains the lower triangular part of the matrix A, and the upper- triangular part of A is not referenced. If matrix A is unit-triangular, its diagonal elements are assumed to be unity and are not referenced. On exit, a is unchanged. lda integer*4 On entry, the first dimension of A. When multiplication is on the left, lda >= MAX(1,m). When multiplication is on the right, lda >= MAX(1,n). On exit, lda is unchanged. b real*4 | real*8 | complex*8 | complex*16 On entry, a two-dimensional array B of dimensions ldb by at least n. The leading m by n part of the array B must contain the right-hand-side matrix B. On exit, b is overwritten by the m by n solution matrix X. ldb integer*4 On entry, the first dimension of B; ldb >= MAX(1,m) On exit, ldb is unchanged.
The _TRSM routines solve a triangular system of equations where the coefficient matrix A is a triangular matrix: (op)AX = alpha * B X(op)A = alpha * B (op)A = A, transp(A), or conjug_transp(A) , alpha is a scalar, X and B are m by n matrices, and A is a unit or non-unit, upper- or lower- triangular matrix.
REAL*8 A(100,40), B(40,20), alpha M = 16 N = 18 LDA = 100 LDB = 40 alpha = 2.0D0 CALL DTRSM ('L','U','N','U',M,N,alpha,A,LDA,B,LDB) This FORTRAN code solves the system AX=alpha * B where A is an upper- triangular real matrix with a unit diagonal. X and B are 16 by 18 matrices. The leading 16 by 16 upper-triangular part of the array A must contain the upper-triangular matrix A. The leading 16 by 18 part of the array B must contain the matrix B. The lower-triangular part of A and the diagonal are not referenced. The leading 16 by 18 part of B is overwritten by the solution matrix X.