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|
*> \brief \b ZTRMM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* .. Scalar Arguments ..
* COMPLEX*16 ALPHA
* INTEGER LDA,LDB,M,N
* CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
* COMPLEX*16 A(LDA,*),B(LDB,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTRMM 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**T or op( A ) = A**H.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is 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 ).
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANSA
*> \verbatim
*> TRANSA is 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**T.
*>
*> TRANSA = 'C' or 'c' op( A ) = A**H.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of B. M must be at
*> least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of B. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is COMPLEX*16
*> On entry, ALPHA specifies the scalar alpha. When alpha is
*> zero then A is not referenced and B need not be set before
*> entry.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is (input/output) COMPLEX*16 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16_blas_level3
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* -- Reference BLAS level3 routine (version 3.7.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
COMPLEX*16 ALPHA
INTEGER LDA,LDB,M,N
CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
COMPLEX*16 A(LDA,*),B(LDB,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG,MAX
* ..
* .. Local Scalars ..
COMPLEX*16 TEMP
INTEGER I,INFO,J,K,NROWA
LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
* ..
* .. Parameters ..
COMPLEX*16 ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
COMPLEX*16 ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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('ZTRMM ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (M.EQ.0 .OR. 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**T*B or B := alpha*A**H*B.
*
IF (UPPER) THEN
DO 120 J = 1,N
DO 110 I = M,1,-1
TEMP = B(I,J)
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*A(I,I)
DO 90 K = 1,I - 1
TEMP = TEMP + A(K,I)*B(K,J)
90 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(A(I,I))
DO 100 K = 1,I - 1
TEMP = TEMP + DCONJG(A(K,I))*B(K,J)
100 CONTINUE
END IF
B(I,J) = ALPHA*TEMP
110 CONTINUE
120 CONTINUE
ELSE
DO 160 J = 1,N
DO 150 I = 1,M
TEMP = B(I,J)
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*A(I,I)
DO 130 K = I + 1,M
TEMP = TEMP + A(K,I)*B(K,J)
130 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(A(I,I))
DO 140 K = I + 1,M
TEMP = TEMP + DCONJG(A(K,I))*B(K,J)
140 CONTINUE
END IF
B(I,J) = ALPHA*TEMP
150 CONTINUE
160 CONTINUE
END IF
END IF
ELSE
IF (LSAME(TRANSA,'N')) THEN
*
* Form B := alpha*B*A.
*
IF (UPPER) THEN
DO 200 J = N,1,-1
TEMP = ALPHA
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 170 I = 1,M
B(I,J) = TEMP*B(I,J)
170 CONTINUE
DO 190 K = 1,J - 1
IF (A(K,J).NE.ZERO) THEN
TEMP = ALPHA*A(K,J)
DO 180 I = 1,M
B(I,J) = B(I,J) + TEMP*B(I,K)
180 CONTINUE
END IF
190 CONTINUE
200 CONTINUE
ELSE
DO 240 J = 1,N
TEMP = ALPHA
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 210 I = 1,M
B(I,J) = TEMP*B(I,J)
210 CONTINUE
DO 230 K = J + 1,N
IF (A(K,J).NE.ZERO) THEN
TEMP = ALPHA*A(K,J)
DO 220 I = 1,M
B(I,J) = B(I,J) + TEMP*B(I,K)
220 CONTINUE
END IF
230 CONTINUE
240 CONTINUE
END IF
ELSE
*
* Form B := alpha*B*A**T or B := alpha*B*A**H.
*
IF (UPPER) THEN
DO 280 K = 1,N
DO 260 J = 1,K - 1
IF (A(J,K).NE.ZERO) THEN
IF (NOCONJ) THEN
TEMP = ALPHA*A(J,K)
ELSE
TEMP = ALPHA*DCONJG(A(J,K))
END IF
DO 250 I = 1,M
B(I,J) = B(I,J) + TEMP*B(I,K)
250 CONTINUE
END IF
260 CONTINUE
TEMP = ALPHA
IF (NOUNIT) THEN
IF (NOCONJ) THEN
TEMP = TEMP*A(K,K)
ELSE
TEMP = TEMP*DCONJG(A(K,K))
END IF
END IF
IF (TEMP.NE.ONE) THEN
DO 270 I = 1,M
B(I,K) = TEMP*B(I,K)
270 CONTINUE
END IF
280 CONTINUE
ELSE
DO 320 K = N,1,-1
DO 300 J = K + 1,N
IF (A(J,K).NE.ZERO) THEN
IF (NOCONJ) THEN
TEMP = ALPHA*A(J,K)
ELSE
TEMP = ALPHA*DCONJG(A(J,K))
END IF
DO 290 I = 1,M
B(I,J) = B(I,J) + TEMP*B(I,K)
290 CONTINUE
END IF
300 CONTINUE
TEMP = ALPHA
IF (NOUNIT) THEN
IF (NOCONJ) THEN
TEMP = TEMP*A(K,K)
ELSE
TEMP = TEMP*DCONJG(A(K,K))
END IF
END IF
IF (TEMP.NE.ONE) THEN
DO 310 I = 1,M
B(I,K) = TEMP*B(I,K)
310 CONTINUE
END IF
320 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of ZTRMM .
*
END
|
