SUBROUTINE CTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
$ B, LDB )
* .. Scalar Arguments ..
CHARACTER*1 SIDE, UPLO, TRANSA, DIAG
INTEGER M, N, LDA, LDB
COMPLEX ALPHA
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
* Purpose
* =======
*
* CTRSM 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' or op( A ) = conjg( A' ).
*
* The matrix X is overwritten on B.
*
* Parameters
* ==========
*
* SIDE - 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.
*
* Unchanged on exit.
*
* UPLO - 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.
*
* Unchanged on exit.
*
* TRANSA - 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'.
*
* TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
*
* Unchanged on exit.
*
* DIAG - 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.
*
* Unchanged on exit.
*
* M - INTEGER.
* On entry, M specifies the number of rows of B. M must be at
* least zero.
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the number of columns of B. N must be
* at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX .
* On entry, ALPHA specifies the scalar alpha. When alpha is
* zero then A is not referenced and B need not be set before
* entry.
* Unchanged on exit.
*
* A - COMPLEX array of DIMENSION ( LDA, k ), where k is m
* when SIDE = 'L' or 'l' and 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.
* Unchanged on exit.
*
* LDA - 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 ).
* Unchanged on exit.
*
* B - COMPLEX 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 - 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 ).
* Unchanged on exit.
*
*
* Level 3 Blas routine.
*
* -- Written on 8-February-1989.
* Jack Dongarra, Argonne National Laboratory.
* Iain Duff, AERE Harwell.
* Jeremy Du Croz, Numerical Algorithms Group Ltd.
* Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX
* .. Local Scalars ..
LOGICAL LSIDE, NOCONJ, NOUNIT, UPPER
INTEGER I, INFO, J, K, NROWA
COMPLEX TEMP
* .. Parameters ..
COMPLEX ONE
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
COMPLEX ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
LSIDE = LSAME( SIDE , 'L' )
IF( LSIDE )THEN
NROWA = M
ELSE
NROWA = N
END IF
NOCONJ = LSAME( TRANSA, 'T' )
NOUNIT = LSAME( DIAG , 'N' )
UPPER = LSAME( UPLO , 'U' )
*
INFO = 0
IF( ( .NOT.LSIDE ).AND.
$ ( .NOT.LSAME( SIDE , 'R' ) ) )THEN
INFO = 1
ELSE IF( ( .NOT.UPPER ).AND.
$ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN
INFO = 2
ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND.
$ ( .NOT.LSAME( TRANSA, 'T' ) ).AND.
$ ( .NOT.LSAME( TRANSA, 'C' ) ) )THEN
INFO = 3
ELSE IF( ( .NOT.LSAME( DIAG , 'U' ) ).AND.
$ ( .NOT.LSAME( DIAG , 'N' ) ) )THEN
INFO = 4
ELSE IF( M .LT.0 )THEN
INFO = 5
ELSE IF( N .LT.0 )THEN
INFO = 6
ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
INFO = 9
ELSE IF( LDB.LT.MAX( 1, M ) )THEN
INFO = 11
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'CTRSM ', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( N.EQ.0 )
$ RETURN
*
* And when alpha.eq.zero.
*
IF( ALPHA.EQ.ZERO )THEN
DO 20, J = 1, N
DO 10, I = 1, M
B( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
RETURN
END IF
*
* Start the operations.
*
IF( LSIDE )THEN
IF( LSAME( TRANSA, 'N' ) )THEN
*
* Form B := alpha*inv( A )*B.
*
IF( UPPER )THEN
DO 60, J = 1, N
IF( ALPHA.NE.ONE )THEN
DO 30, I = 1, M
B( I, J ) = ALPHA*B( I, J )
30 CONTINUE
END IF
DO 50, K = M, 1, -1
IF( B( K, J ).NE.ZERO )THEN
IF( NOUNIT )
$ B( K, J ) = B( K, J )/A( K, K )
DO 40, I = 1, K - 1
B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
40 CONTINUE
END IF
50 CONTINUE
60 CONTINUE
ELSE
DO 100, J = 1, N
IF( ALPHA.NE.ONE )THEN
DO 70, I = 1, M
B( I, J ) = ALPHA*B( I, J )
70 CONTINUE
END IF
DO 90 K = 1, M
IF( B( K, J ).NE.ZERO )THEN
IF( NOUNIT )
$ B( K, J ) = B( K, J )/A( K, K )
DO 80, I = K + 1, M
B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
80 CONTINUE
END IF
90 CONTINUE
100 CONTINUE
END IF
ELSE
*
* Form B := alpha*inv( A' )*B
* or B := alpha*inv( conjg( A' ) )*B.
*
IF( UPPER )THEN
DO 140, J = 1, N
DO 130, I = 1, M
TEMP = ALPHA*B( I, J )
IF( NOCONJ )THEN
DO 110, K = 1, I - 1
TEMP = TEMP - A( K, I )*B( K, J )
110 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( I, I )
ELSE
DO 120, K = 1, I - 1
TEMP = TEMP - CONJG( A( K, I ) )*B( K, J )
120 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/CONJG( A( I, I ) )
END IF
B( I, J ) = TEMP
130 CONTINUE
140 CONTINUE
ELSE
DO 180, J = 1, N
DO 170, I = M, 1, -1
TEMP = ALPHA*B( I, J )
IF( NOCONJ )THEN
DO 150, K = I + 1, M
TEMP = TEMP - A( K, I )*B( K, J )
150 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/A( I, I )
ELSE
DO 160, K = I + 1, M
TEMP = TEMP - CONJG( A( K, I ) )*B( K, J )
160 CONTINUE
IF( NOUNIT )
$ TEMP = TEMP/CONJG( A( I, I ) )
END IF
B( I, J ) = TEMP
170 CONTINUE
180 CONTINUE
END IF
END IF
ELSE
IF( LSAME( TRANSA, 'N' ) )THEN
*
* Form B := alpha*B*inv( A ).
*
IF( UPPER )THEN
DO 230, J = 1, N
IF( ALPHA.NE.ONE )THEN
DO 190, I = 1, M
B( I, J ) = ALPHA*B( I, J )
190 CONTINUE
END IF
DO 210, K = 1, J - 1
IF( A( K, J ).NE.ZERO )THEN
DO 200, I = 1, M
B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
200 CONTINUE
END IF
210 CONTINUE
IF( NOUNIT )THEN
TEMP = ONE/A( J, J )
DO 220, I = 1, M
B( I, J ) = TEMP*B( I, J )
220 CONTINUE
END IF
230 CONTINUE
ELSE
DO 280, J = N, 1, -1
IF( ALPHA.NE.ONE )THEN
DO 240, I = 1, M
B( I, J ) = ALPHA*B( I, J )
240 CONTINUE
END IF
DO 260, K = J + 1, N
IF( A( K, J ).NE.ZERO )THEN
DO 250, I = 1, M
B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
250 CONTINUE
END IF
260 CONTINUE
IF( NOUNIT )THEN
TEMP = ONE/A( J, J )
DO 270, I = 1, M
B( I, J ) = TEMP*B( I, J )
270 CONTINUE
END IF
280 CONTINUE
END IF
ELSE
*
* Form B := alpha*B*inv( A' )
* or B := alpha*B*inv( conjg( A' ) ).
*
IF( UPPER )THEN
DO 330, K = N, 1, -1
IF( NOUNIT )THEN
IF( NOCONJ )THEN
TEMP = ONE/A( K, K )
ELSE
TEMP = ONE/CONJG( A( K, K ) )
END IF
DO 290, I = 1, M
B( I, K ) = TEMP*B( I, K )
290 CONTINUE
END IF
DO 310, J = 1, K - 1
IF( A( J, K ).NE.ZERO )THEN
IF( NOCONJ )THEN
TEMP = A( J, K )
ELSE
TEMP = CONJG( A( J, K ) )
END IF
DO 300, I = 1, M
B( I, J ) = B( I, J ) - TEMP*B( I, K )
300 CONTINUE
END IF
310 CONTINUE
IF( ALPHA.NE.ONE )THEN
DO 320, I = 1, M
B( I, K ) = ALPHA*B( I, K )
320 CONTINUE
END IF
330 CONTINUE
ELSE
DO 380, K = 1, N
IF( NOUNIT )THEN
IF( NOCONJ )THEN
TEMP = ONE/A( K, K )
ELSE
TEMP = ONE/CONJG( A( K, K ) )
END IF
DO 340, I = 1, M
B( I, K ) = TEMP*B( I, K )
340 CONTINUE
END IF
DO 360, J = K + 1, N
IF( A( J, K ).NE.ZERO )THEN
IF( NOCONJ )THEN
TEMP = A( J, K )
ELSE
TEMP = CONJG( A( J, K ) )
END IF
DO 350, I = 1, M
B( I, J ) = B( I, J ) - TEMP*B( I, K )
350 CONTINUE
END IF
360 CONTINUE
IF( ALPHA.NE.ONE )THEN
DO 370, I = 1, M
B( I, K ) = ALPHA*B( I, K )
370 CONTINUE
END IF
380 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of CTRSM .
*
END
