SUBROUTINE DTRMM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, &
B, LDB )
! .. Scalar Arguments ..
CHARACTER*1 SIDE, UPLO, TRANSA, DIAG
INTEGER M, N, LDA, LDB
DOUBLE PRECISION ALPHA
! .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * )
! ..
!
! Purpose
! =======
!
! DTRMM performs one of the matrix-matrix operations
!
! B := alpha*op( A )*B, or B := alpha*B*op( A ),
!
! where alpha is a scalar, B is an m by n matrix, 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'.
!
! Parameters
! ==========
!
! SIDE - CHARACTER*1.
! On entry, SIDE specifies whether op( A ) multiplies B from
! the left or right as follows:
!
! SIDE = 'L' or 'l' B := alpha*op( A )*B.
!
! SIDE = 'R' or 'r' B := alpha*B*op( A ).
!
! 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 ) = 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 - DOUBLE PRECISION.
! 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
! Before entry, the leading m by n part of the array B must
! contain the matrix B, and on exit is overwritten by the
! transformed matrix.
!
! 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 MAX
! .. Local Scalars ..
LOGICAL LSIDE, NOUNIT, UPPER
INTEGER I, INFO, J, K, NROWA
DOUBLE PRECISION TEMP
! .. Parameters ..
DOUBLE PRECISION ONE , ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! ..
! .. Executable Statements ..
!
! Test the input parameters.
!
LSIDE = LSAME( SIDE , 'L' )
IF( LSIDE )THEN
NROWA = M
ELSE
NROWA = N
END IF
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( 'DTRMM ', 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*A*B.
!
IF( UPPER )THEN
DO 50, J = 1, N
DO 40, K = 1, M
IF( B( K, J ).NE.ZERO )THEN
TEMP = ALPHA*B( K, J )
DO 30, I = 1, K - 1
B( I, J ) = B( I, J ) + TEMP*A( I, K )
30 CONTINUE
IF( NOUNIT ) &
TEMP = TEMP*A( K, K )
B( K, J ) = TEMP
END IF
40 CONTINUE
50 CONTINUE
ELSE
DO 80, J = 1, N
DO 70 K = M, 1, -1
IF( B( K, J ).NE.ZERO )THEN
TEMP = ALPHA*B( K, J )
B( K, J ) = TEMP
IF( NOUNIT ) &
B( K, J ) = B( K, J )*A( K, K )
DO 60, I = K + 1, M
B( I, J ) = B( I, J ) + TEMP*A( I, K )
60 CONTINUE
END IF
70 CONTINUE
80 CONTINUE
END IF
ELSE
!
! Form B := alpha*A'*B.
!
IF( UPPER )THEN
DO 110, J = 1, N
DO 100, I = M, 1, -1
TEMP = B( I, J )
IF( NOUNIT ) &
TEMP = TEMP*A( I, I )
DO 90, K = 1, I - 1
TEMP = TEMP + A( K, I )*B( K, J )
90 CONTINUE
B( I, J ) = ALPHA*TEMP
100 CONTINUE
110 CONTINUE
ELSE
DO 140, J = 1, N
DO 130, I = 1, M
TEMP = B( I, J )
IF( NOUNIT ) &
TEMP = TEMP*A( I, I )
DO 120, K = I + 1, M
TEMP = TEMP + A( K, I )*B( K, J )
120 CONTINUE
B( I, J ) = ALPHA*TEMP
130 CONTINUE
140 CONTINUE
END IF
END IF
ELSE
IF( LSAME( TRANSA, 'N' ) )THEN
!
! Form B := alpha*B*A.
!
IF( UPPER )THEN
DO 180, J = N, 1, -1
TEMP = ALPHA
IF( NOUNIT ) &
TEMP = TEMP*A( J, J )
DO 150, I = 1, M
B( I, J ) = TEMP*B( I, J )
150 CONTINUE
DO 170, K = 1, J - 1
IF( A( K, J ).NE.ZERO )THEN
TEMP = ALPHA*A( K, J )
DO 160, I = 1, M
B( I, J ) = B( I, J ) + TEMP*B( I, K )
160 CONTINUE
END IF
170 CONTINUE
180 CONTINUE
ELSE
DO 220, J = 1, N
TEMP = ALPHA
IF( NOUNIT ) &
TEMP = TEMP*A( J, J )
DO 190, I = 1, M
B( I, J ) = TEMP*B( I, J )
190 CONTINUE
DO 210, K = J + 1, N
IF( A( K, J ).NE.ZERO )THEN
TEMP = ALPHA*A( K, J )
DO 200, I = 1, M
B( I, J ) = B( I, J ) + TEMP*B( I, K )
200 CONTINUE
END IF
210 CONTINUE
220 CONTINUE
END IF
ELSE
!
! Form B := alpha*B*A'.
!
IF( UPPER )THEN
DO 260, K = 1, N
DO 240, J = 1, K - 1
IF( A( J, K ).NE.ZERO )THEN
TEMP = ALPHA*A( J, K )
DO 230, I = 1, M
B( I, J ) = B( I, J ) + TEMP*B( I, K )
230 CONTINUE
END IF
240 CONTINUE
TEMP = ALPHA
IF( NOUNIT ) &
TEMP = TEMP*A( K, K )
IF( TEMP.NE.ONE )THEN
DO 250, I = 1, M
B( I, K ) = TEMP*B( I, K )
250 CONTINUE
END IF
260 CONTINUE
ELSE
DO 300, K = N, 1, -1
DO 280, J = K + 1, N
IF( A( J, K ).NE.ZERO )THEN
TEMP = ALPHA*A( J, K )
DO 270, I = 1, M
B( I, J ) = B( I, J ) + TEMP*B( I, K )
270 CONTINUE
END IF
280 CONTINUE
TEMP = ALPHA
IF( NOUNIT ) &
TEMP = TEMP*A( K, K )
IF( TEMP.NE.ONE )THEN
DO 290, I = 1, M
B( I, K ) = TEMP*B( I, K )
290 CONTINUE
END IF
300 CONTINUE
END IF
END IF
END IF
!
RETURN
!
! End of DTRMM .
!
END SUBROUTINE DTRMM