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|
*> \brief \b DTRSM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA
* INTEGER LDA,LDB,M,N
* CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A(LDA,*),B(LDB,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTRSM 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**T.
*>
*> The matrix X is overwritten on B.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is 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.
*> \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**T.
*> \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 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.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension ( LDA, k ),
*> where k is m when SIDE = 'L' or 'l'
*> and k 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,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, 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.
*> \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 double_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 DTRSM(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 ..
DOUBLE PRECISION ALPHA
INTEGER LDA,LDB,M,N
CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION A(LDA,*),B(LDB,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I,INFO,J,K,NROWA
LOGICAL LSIDE,NOUNIT,UPPER
* ..
* .. Parameters ..
DOUBLE PRECISION ONE,ZERO
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
* ..
*
* 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('DTRSM ',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*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**T )*B.
*
IF (UPPER) THEN
DO 130 J = 1,N
DO 120 I = 1,M
TEMP = ALPHA*B(I,J)
DO 110 K = 1,I - 1
TEMP = TEMP - A(K,I)*B(K,J)
110 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(I,I)
B(I,J) = TEMP
120 CONTINUE
130 CONTINUE
ELSE
DO 160 J = 1,N
DO 150 I = M,1,-1
TEMP = ALPHA*B(I,J)
DO 140 K = I + 1,M
TEMP = TEMP - A(K,I)*B(K,J)
140 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(I,I)
B(I,J) = TEMP
150 CONTINUE
160 CONTINUE
END IF
END IF
ELSE
IF (LSAME(TRANSA,'N')) THEN
*
* Form B := alpha*B*inv( A ).
*
IF (UPPER) THEN
DO 210 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 170 I = 1,M
B(I,J) = ALPHA*B(I,J)
170 CONTINUE
END IF
DO 190 K = 1,J - 1
IF (A(K,J).NE.ZERO) THEN
DO 180 I = 1,M
B(I,J) = B(I,J) - A(K,J)*B(I,K)
180 CONTINUE
END IF
190 CONTINUE
IF (NOUNIT) THEN
TEMP = ONE/A(J,J)
DO 200 I = 1,M
B(I,J) = TEMP*B(I,J)
200 CONTINUE
END IF
210 CONTINUE
ELSE
DO 260 J = N,1,-1
IF (ALPHA.NE.ONE) THEN
DO 220 I = 1,M
B(I,J) = ALPHA*B(I,J)
220 CONTINUE
END IF
DO 240 K = J + 1,N
IF (A(K,J).NE.ZERO) THEN
DO 230 I = 1,M
B(I,J) = B(I,J) - A(K,J)*B(I,K)
230 CONTINUE
END IF
240 CONTINUE
IF (NOUNIT) THEN
TEMP = ONE/A(J,J)
DO 250 I = 1,M
B(I,J) = TEMP*B(I,J)
250 CONTINUE
END IF
260 CONTINUE
END IF
ELSE
*
* Form B := alpha*B*inv( A**T ).
*
IF (UPPER) THEN
DO 310 K = N,1,-1
IF (NOUNIT) THEN
TEMP = ONE/A(K,K)
DO 270 I = 1,M
B(I,K) = TEMP*B(I,K)
270 CONTINUE
END IF
DO 290 J = 1,K - 1
IF (A(J,K).NE.ZERO) THEN
TEMP = A(J,K)
DO 280 I = 1,M
B(I,J) = B(I,J) - TEMP*B(I,K)
280 CONTINUE
END IF
290 CONTINUE
IF (ALPHA.NE.ONE) THEN
DO 300 I = 1,M
B(I,K) = ALPHA*B(I,K)
300 CONTINUE
END IF
310 CONTINUE
ELSE
DO 360 K = 1,N
IF (NOUNIT) THEN
TEMP = ONE/A(K,K)
DO 320 I = 1,M
B(I,K) = TEMP*B(I,K)
320 CONTINUE
END IF
DO 340 J = K + 1,N
IF (A(J,K).NE.ZERO) THEN
TEMP = A(J,K)
DO 330 I = 1,M
B(I,J) = B(I,J) - TEMP*B(I,K)
330 CONTINUE
END IF
340 CONTINUE
IF (ALPHA.NE.ONE) THEN
DO 350 I = 1,M
B(I,K) = ALPHA*B(I,K)
350 CONTINUE
END IF
360 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of DTRSM .
*
END
|
