CXML
strsm, dtrsm, ctrsm, ztrsm
Solve a triangular system of equations with a
triangular coefficient matrix
FORMAT
{S,D,C,Z}TRSM
( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
Arguments
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.
Description
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.
Example
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.
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