floraachy
/
OpenBLAS
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
OpenBLAS/lapack-netlib/SRC/dtfsm.f

1007 lines
34 KiB
Fortran
Raw Blame History

*> \brief \b DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DTFSM + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtfsm.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtfsm.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtfsm.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
* B, LDB )
*
* .. Scalar Arguments ..
* CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO
* INTEGER LDB, M, N
* DOUBLE PRECISION ALPHA
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( 0: * ), B( 0: LDB-1, 0: * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Level 3 BLAS like routine for A in RFP Format.
*>
*> DTFSM solves the matrix equation
*>
*> 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.
*>
*> A is in Rectangular Full Packed (RFP) Format.
*>
*> The matrix X is overwritten on B.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> TRANSR is CHARACTER*1
*> = 'N': The Normal Form of RFP A is stored;
*> = 'T': The Transpose Form of RFP A is stored.
*> \endverbatim
*>
*> \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.
*>
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> On entry, UPLO specifies whether the RFP matrix A came from
*> an upper or lower triangular matrix as follows:
*> UPLO = 'U' or 'u' RFP A came from an upper triangular matrix
*> UPLO = 'L' or 'l' RFP A came from a lower triangular matrix
*>
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> On entry, TRANS specifies the form of op( A ) to be used
*> in the matrix multiplication as follows:
*>
*> TRANS = 'N' or 'n' op( A ) = A.
*>
*> TRANS = 'T' or 't' op( A ) = A'.
*>
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> On entry, DIAG specifies whether or not RFP 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.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of B. M must be at
*> least zero.
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of B. N must be
*> at least zero.
*> Unchanged on exit.
*> \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.
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (NT)
*> NT = N*(N+1)/2. On entry, the matrix A in RFP Format.
*> RFP Format is described by TRANSR, UPLO and N as follows:
*> If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
*> K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
*> TRANSR = 'T' then RFP is the transpose of RFP A as
*> defined when TRANSR = 'N'. The contents of RFP A are defined
*> by UPLO as follows: If UPLO = 'U' the RFP A contains the NT
*> elements of upper packed A either in normal or
*> transpose Format. If UPLO = 'L' the RFP A contains
*> the NT elements of lower packed A either in normal or
*> transpose Format. The LDA of RFP A is (N+1)/2 when
*> TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is
*> even and is N when is odd.
*> See the Note below for more details. Unchanged on exit.
*> \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 ).
*> Unchanged on exit.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> even. We give an example where N = 6.
*>
*> AP is Upper AP is Lower
*>
*> 00 01 02 03 04 05 00
*> 11 12 13 14 15 10 11
*> 22 23 24 25 20 21 22
*> 33 34 35 30 31 32 33
*> 44 45 40 41 42 43 44
*> 55 50 51 52 53 54 55
*>
*>
*> Let TRANSR = 'N'. RFP holds AP as follows:
*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
*> the transpose of the first three columns of AP upper.
*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
*> the transpose of the last three columns of AP lower.
*> This covers the case N even and TRANSR = 'N'.
*>
*> RFP A RFP A
*>
*> 03 04 05 33 43 53
*> 13 14 15 00 44 54
*> 23 24 25 10 11 55
*> 33 34 35 20 21 22
*> 00 44 45 30 31 32
*> 01 11 55 40 41 42
*> 02 12 22 50 51 52
*>
*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
*> transpose of RFP A above. One therefore gets:
*>
*>
*> RFP A RFP A
*>
*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
*>
*>
*> We then consider Rectangular Full Packed (RFP) Format when N is
*> odd. We give an example where N = 5.
*>
*> AP is Upper AP is Lower
*>
*> 00 01 02 03 04 00
*> 11 12 13 14 10 11
*> 22 23 24 20 21 22
*> 33 34 30 31 32 33
*> 44 40 41 42 43 44
*>
*>
*> Let TRANSR = 'N'. RFP holds AP as follows:
*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
*> the transpose of the first two columns of AP upper.
*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
*> the transpose of the last two columns of AP lower.
*> This covers the case N odd and TRANSR = 'N'.
*>
*> RFP A RFP A
*>
*> 02 03 04 00 33 43
*> 12 13 14 10 11 44
*> 22 23 24 20 21 22
*> 00 33 34 30 31 32
*> 01 11 44 40 41 42
*>
*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
*> transpose of RFP A above. One therefore gets:
*>
*> RFP A RFP A
*>
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
*> \endverbatim
*
* =====================================================================
SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
$ B, LDB )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO
INTEGER LDB, M, N
DOUBLE PRECISION ALPHA
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( 0: * ), B( 0: LDB-1, 0: * )
* ..
*
* =====================================================================
*
* ..
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LOWER, LSIDE, MISODD, NISODD, NORMALTRANSR,
$ NOTRANS
INTEGER M1, M2, N1, N2, K, INFO, I, J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, DGEMM, DTRSM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MOD
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NORMALTRANSR = LSAME( TRANSR, 'N' )
LSIDE = LSAME( SIDE, 'L' )
LOWER = LSAME( UPLO, 'L' )
NOTRANS = LSAME( TRANS, 'N' )
IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSIDE .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -2
ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
INFO = -3
ELSE IF( .NOT.NOTRANS .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
INFO = -4
ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
$ THEN
INFO = -5
ELSE IF( M.LT.0 ) THEN
INFO = -6
ELSE IF( N.LT.0 ) THEN
INFO = -7
ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
INFO = -11
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DTFSM ', -INFO )
RETURN
END IF
*
* Quick return when ( (N.EQ.0).OR.(M.EQ.0) )
*
IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
$ RETURN
*
* Quick return when ALPHA.EQ.(0D+0)
*
IF( ALPHA.EQ.ZERO ) THEN
DO 20 J = 0, N - 1
DO 10 I = 0, M - 1
B( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
RETURN
END IF
*
IF( LSIDE ) THEN
*
* SIDE = 'L'
*
* A is M-by-M.
* If M is odd, set NISODD = .TRUE., and M1 and M2.
* If M is even, NISODD = .FALSE., and M.
*
IF( MOD( M, 2 ).EQ.0 ) THEN
MISODD = .FALSE.
K = M / 2
ELSE
MISODD = .TRUE.
IF( LOWER ) THEN
M2 = M / 2
M1 = M - M2
ELSE
M1 = M / 2
M2 = M - M1
END IF
END IF
*
*
IF( MISODD ) THEN
*
* SIDE = 'L' and N is odd
*
IF( NORMALTRANSR ) THEN
*
* SIDE = 'L', N is odd, and TRANSR = 'N'
*
IF( LOWER ) THEN
*
* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'L'
*
IF( NOTRANS ) THEN
*
* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and
* TRANS = 'N'
*
IF( M.EQ.1 ) THEN
CALL DTRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA,
$ A, M, B, LDB )
ELSE
CALL DTRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA,
$ A( 0 ), M, B, LDB )
CALL DGEMM( 'N', 'N', M2, N, M1, -ONE, A( M1 ),
$ M, B, LDB, ALPHA, B( M1, 0 ), LDB )
CALL DTRSM( 'L', 'U', 'T', DIAG, M2, N, ONE,
$ A( M ), M, B( M1, 0 ), LDB )
END IF
*
ELSE
*
* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and
* TRANS = 'T'
*
IF( M.EQ.1 ) THEN
CALL DTRSM( 'L', 'L', 'T', DIAG, M1, N, ALPHA,
$ A( 0 ), M, B, LDB )
ELSE
CALL DTRSM( 'L', 'U', 'N', DIAG, M2, N, ALPHA,
$ A( M ), M, B( M1, 0 ), LDB )
CALL DGEMM( 'T', 'N', M1, N, M2, -ONE, A( M1 ),
$ M, B( M1, 0 ), LDB, ALPHA, B, LDB )
CALL DTRSM( 'L', 'L', 'T', DIAG, M1, N, ONE,
$ A( 0 ), M, B, LDB )
END IF
*
END IF
*
ELSE
*
* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'U'
*
IF( .NOT.NOTRANS ) THEN
*
* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and
* TRANS = 'N'
*
CALL DTRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA,
$ A( M2 ), M, B, LDB )
CALL DGEMM( 'T', 'N', M2, N, M1, -ONE, A( 0 ), M,
$ B, LDB, ALPHA, B( M1, 0 ), LDB )
CALL DTRSM( 'L', 'U', 'T', DIAG, M2, N, ONE,
$ A( M1 ), M, B( M1, 0 ), LDB )
*
ELSE
*
* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and
* TRANS = 'T'
*
CALL DTRSM( 'L', 'U', 'N', DIAG, M2, N, ALPHA,
$ A( M1 ), M, B( M1, 0 ), LDB )
CALL DGEMM( 'N', 'N', M1, N, M2, -ONE, A( 0 ), M,
$ B( M1, 0 ), LDB, ALPHA, B, LDB )
CALL DTRSM( 'L', 'L', 'T', DIAG, M1, N, ONE,
$ A( M2 ), M, B, LDB )
*
END IF
*
END IF
*
ELSE
*
* SIDE = 'L', N is odd, and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* SIDE ='L', N is odd, TRANSR = 'T', and UPLO = 'L'
*
IF( NOTRANS ) THEN
*
* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'L', and
* TRANS = 'N'
*
IF( M.EQ.1 ) THEN
CALL DTRSM( 'L', 'U', 'T', DIAG, M1, N, ALPHA,
$ A( 0 ), M1, B, LDB )
ELSE
CALL DTRSM( 'L', 'U', 'T', DIAG, M1, N, ALPHA,
$ A( 0 ), M1, B, LDB )
CALL DGEMM( 'T', 'N', M2, N, M1, -ONE,
$ A( M1*M1 ), M1, B, LDB, ALPHA,
$ B( M1, 0 ), LDB )
CALL DTRSM( 'L', 'L', 'N', DIAG, M2, N, ONE,
$ A( 1 ), M1, B( M1, 0 ), LDB )
END IF
*
ELSE
*
* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'L', and
* TRANS = 'T'
*
IF( M.EQ.1 ) THEN
CALL DTRSM( 'L', 'U', 'N', DIAG, M1, N, ALPHA,
$ A( 0 ), M1, B, LDB )
ELSE
CALL DTRSM( 'L', 'L', 'T', DIAG, M2, N, ALPHA,
$ A( 1 ), M1, B( M1, 0 ), LDB )
CALL DGEMM( 'N', 'N', M1, N, M2, -ONE,
$ A( M1*M1 ), M1, B( M1, 0 ), LDB,
$ ALPHA, B, LDB )
CALL DTRSM( 'L', 'U', 'N', DIAG, M1, N, ONE,
$ A( 0 ), M1, B, LDB )
END IF
*
END IF
*
ELSE
*
* SIDE ='L', N is odd, TRANSR = 'T', and UPLO = 'U'
*
IF( .NOT.NOTRANS ) THEN
*
* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'U', and
* TRANS = 'N'
*
CALL DTRSM( 'L', 'U', 'T', DIAG, M1, N, ALPHA,
$ A( M2*M2 ), M2, B, LDB )
CALL DGEMM( 'N', 'N', M2, N, M1, -ONE, A( 0 ), M2,
$ B, LDB, ALPHA, B( M1, 0 ), LDB )
CALL DTRSM( 'L', 'L', 'N', DIAG, M2, N, ONE,
$ A( M1*M2 ), M2, B( M1, 0 ), LDB )
*
ELSE
*
* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'U', and
* TRANS = 'T'
*
CALL DTRSM( 'L', 'L', 'T', DIAG, M2, N, ALPHA,
$ A( M1*M2 ), M2, B( M1, 0 ), LDB )
CALL DGEMM( 'T', 'N', M1, N, M2, -ONE, A( 0 ), M2,
$ B( M1, 0 ), LDB, ALPHA, B, LDB )
CALL DTRSM( 'L', 'U', 'N', DIAG, M1, N, ONE,
$ A( M2*M2 ), M2, B, LDB )
*
END IF
*
END IF
*
END IF
*
ELSE
*
* SIDE = 'L' and N is even
*
IF( NORMALTRANSR ) THEN
*
* SIDE = 'L', N is even, and TRANSR = 'N'
*
IF( LOWER ) THEN
*
* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'L'
*
IF( NOTRANS ) THEN
*
* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L',
* and TRANS = 'N'
*
CALL DTRSM( 'L', 'L', 'N', DIAG, K, N, ALPHA,
$ A( 1 ), M+1, B, LDB )
CALL DGEMM( 'N', 'N', K, N, K, -ONE, A( K+1 ),
$ M+1, B, LDB, ALPHA, B( K, 0 ), LDB )
CALL DTRSM( 'L', 'U', 'T', DIAG, K, N, ONE,
$ A( 0 ), M+1, B( K, 0 ), LDB )
*
ELSE
*
* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L',
* and TRANS = 'T'
*
CALL DTRSM( 'L', 'U', 'N', DIAG, K, N, ALPHA,
$ A( 0 ), M+1, B( K, 0 ), LDB )
CALL DGEMM( 'T', 'N', K, N, K, -ONE, A( K+1 ),
$ M+1, B( K, 0 ), LDB, ALPHA, B, LDB )
CALL DTRSM( 'L', 'L', 'T', DIAG, K, N, ONE,
$ A( 1 ), M+1, B, LDB )
*
END IF
*
ELSE
*
* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'U'
*
IF( .NOT.NOTRANS ) THEN
*
* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U',
* and TRANS = 'N'
*
CALL DTRSM( 'L', 'L', 'N', DIAG, K, N, ALPHA,
$ A( K+1 ), M+1, B, LDB )
CALL DGEMM( 'T', 'N', K, N, K, -ONE, A( 0 ), M+1,
$ B, LDB, ALPHA, B( K, 0 ), LDB )
CALL DTRSM( 'L', 'U', 'T', DIAG, K, N, ONE,
$ A( K ), M+1, B( K, 0 ), LDB )
*
ELSE
*
* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U',
* and TRANS = 'T'
CALL DTRSM( 'L', 'U', 'N', DIAG, K, N, ALPHA,
$ A( K ), M+1, B( K, 0 ), LDB )
CALL DGEMM( 'N', 'N', K, N, K, -ONE, A( 0 ), M+1,
$ B( K, 0 ), LDB, ALPHA, B, LDB )
CALL DTRSM( 'L', 'L', 'T', DIAG, K, N, ONE,
$ A( K+1 ), M+1, B, LDB )
*
END IF
*
END IF
*
ELSE
*
* SIDE = 'L', N is even, and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* SIDE ='L', N is even, TRANSR = 'T', and UPLO = 'L'
*
IF( NOTRANS ) THEN
*
* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'L',
* and TRANS = 'N'
*
CALL DTRSM( 'L', 'U', 'T', DIAG, K, N, ALPHA,
$ A( K ), K, B, LDB )
CALL DGEMM( 'T', 'N', K, N, K, -ONE,
$ A( K*( K+1 ) ), K, B, LDB, ALPHA,
$ B( K, 0 ), LDB )
CALL DTRSM( 'L', 'L', 'N', DIAG, K, N, ONE,
$ A( 0 ), K, B( K, 0 ), LDB )
*
ELSE
*
* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'L',
* and TRANS = 'T'
*
CALL DTRSM( 'L', 'L', 'T', DIAG, K, N, ALPHA,
$ A( 0 ), K, B( K, 0 ), LDB )
CALL DGEMM( 'N', 'N', K, N, K, -ONE,
$ A( K*( K+1 ) ), K, B( K, 0 ), LDB,
$ ALPHA, B, LDB )
CALL DTRSM( 'L', 'U', 'N', DIAG, K, N, ONE,
$ A( K ), K, B, LDB )
*
END IF
*
ELSE
*
* SIDE ='L', N is even, TRANSR = 'T', and UPLO = 'U'
*
IF( .NOT.NOTRANS ) THEN
*
* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'U',
* and TRANS = 'N'
*
CALL DTRSM( 'L', 'U', 'T', DIAG, K, N, ALPHA,
$ A( K*( K+1 ) ), K, B, LDB )
CALL DGEMM( 'N', 'N', K, N, K, -ONE, A( 0 ), K, B,
$ LDB, ALPHA, B( K, 0 ), LDB )
CALL DTRSM( 'L', 'L', 'N', DIAG, K, N, ONE,
$ A( K*K ), K, B( K, 0 ), LDB )
*
ELSE
*
* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'U',
* and TRANS = 'T'
*
CALL DTRSM( 'L', 'L', 'T', DIAG, K, N, ALPHA,
$ A( K*K ), K, B( K, 0 ), LDB )
CALL DGEMM( 'T', 'N', K, N, K, -ONE, A( 0 ), K,
$ B( K, 0 ), LDB, ALPHA, B, LDB )
CALL DTRSM( 'L', 'U', 'N', DIAG, K, N, ONE,
$ A( K*( K+1 ) ), K, B, LDB )
*
END IF
*
END IF
*
END IF
*
END IF
*
ELSE
*
* SIDE = 'R'
*
* A is N-by-N.
* If N is odd, set NISODD = .TRUE., and N1 and N2.
* If N is even, NISODD = .FALSE., and K.
*
IF( MOD( N, 2 ).EQ.0 ) THEN
NISODD = .FALSE.
K = N / 2
ELSE
NISODD = .TRUE.
IF( LOWER ) THEN
N2 = N / 2
N1 = N - N2
ELSE
N1 = N / 2
N2 = N - N1
END IF
END IF
*
IF( NISODD ) THEN
*
* SIDE = 'R' and N is odd
*
IF( NORMALTRANSR ) THEN
*
* SIDE = 'R', N is odd, and TRANSR = 'N'
*
IF( LOWER ) THEN
*
* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'L'
*
IF( NOTRANS ) THEN
*
* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and
* TRANS = 'N'
*
CALL DTRSM( 'R', 'U', 'T', DIAG, M, N2, ALPHA,
$ A( N ), N, B( 0, N1 ), LDB )
CALL DGEMM( 'N', 'N', M, N1, N2, -ONE, B( 0, N1 ),
$ LDB, A( N1 ), N, ALPHA, B( 0, 0 ),
$ LDB )
CALL DTRSM( 'R', 'L', 'N', DIAG, M, N1, ONE,
$ A( 0 ), N, B( 0, 0 ), LDB )
*
ELSE
*
* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and
* TRANS = 'T'
*
CALL DTRSM( 'R', 'L', 'T', DIAG, M, N1, ALPHA,
$ A( 0 ), N, B( 0, 0 ), LDB )
CALL DGEMM( 'N', 'T', M, N2, N1, -ONE, B( 0, 0 ),
$ LDB, A( N1 ), N, ALPHA, B( 0, N1 ),
$ LDB )
CALL DTRSM( 'R', 'U', 'N', DIAG, M, N2, ONE,
$ A( N ), N, B( 0, N1 ), LDB )
*
END IF
*
ELSE
*
* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'U'
*
IF( NOTRANS ) THEN
*
* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and
* TRANS = 'N'
*
CALL DTRSM( 'R', 'L', 'T', DIAG, M, N1, ALPHA,
$ A( N2 ), N, B( 0, 0 ), LDB )
CALL DGEMM( 'N', 'N', M, N2, N1, -ONE, B( 0, 0 ),
$ LDB, A( 0 ), N, ALPHA, B( 0, N1 ),
$ LDB )
CALL DTRSM( 'R', 'U', 'N', DIAG, M, N2, ONE,
$ A( N1 ), N, B( 0, N1 ), LDB )
*
ELSE
*
* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and
* TRANS = 'T'
*
CALL DTRSM( 'R', 'U', 'T', DIAG, M, N2, ALPHA,
$ A( N1 ), N, B( 0, N1 ), LDB )
CALL DGEMM( 'N', 'T', M, N1, N2, -ONE, B( 0, N1 ),
$ LDB, A( 0 ), N, ALPHA, B( 0, 0 ), LDB )
CALL DTRSM( 'R', 'L', 'N', DIAG, M, N1, ONE,
$ A( N2 ), N, B( 0, 0 ), LDB )
*
END IF
*
END IF
*
ELSE
*
* SIDE = 'R', N is odd, and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* SIDE ='R', N is odd, TRANSR = 'T', and UPLO = 'L'
*
IF( NOTRANS ) THEN
*
* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'L', and
* TRANS = 'N'
*
CALL DTRSM( 'R', 'L', 'N', DIAG, M, N2, ALPHA,
$ A( 1 ), N1, B( 0, N1 ), LDB )
CALL DGEMM( 'N', 'T', M, N1, N2, -ONE, B( 0, N1 ),
$ LDB, A( N1*N1 ), N1, ALPHA, B( 0, 0 ),
$ LDB )
CALL DTRSM( 'R', 'U', 'T', DIAG, M, N1, ONE,
$ A( 0 ), N1, B( 0, 0 ), LDB )
*
ELSE
*
* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'L', and
* TRANS = 'T'
*
CALL DTRSM( 'R', 'U', 'N', DIAG, M, N1, ALPHA,
$ A( 0 ), N1, B( 0, 0 ), LDB )
CALL DGEMM( 'N', 'N', M, N2, N1, -ONE, B( 0, 0 ),
$ LDB, A( N1*N1 ), N1, ALPHA, B( 0, N1 ),
$ LDB )
CALL DTRSM( 'R', 'L', 'T', DIAG, M, N2, ONE,
$ A( 1 ), N1, B( 0, N1 ), LDB )
*
END IF
*
ELSE
*
* SIDE ='R', N is odd, TRANSR = 'T', and UPLO = 'U'
*
IF( NOTRANS ) THEN
*
* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'U', and
* TRANS = 'N'
*
CALL DTRSM( 'R', 'U', 'N', DIAG, M, N1, ALPHA,
$ A( N2*N2 ), N2, B( 0, 0 ), LDB )
CALL DGEMM( 'N', 'T', M, N2, N1, -ONE, B( 0, 0 ),
$ LDB, A( 0 ), N2, ALPHA, B( 0, N1 ),
$ LDB )
CALL DTRSM( 'R', 'L', 'T', DIAG, M, N2, ONE,
$ A( N1*N2 ), N2, B( 0, N1 ), LDB )
*
ELSE
*
* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'U', and
* TRANS = 'T'
*
CALL DTRSM( 'R', 'L', 'N', DIAG, M, N2, ALPHA,
$ A( N1*N2 ), N2, B( 0, N1 ), LDB )
CALL DGEMM( 'N', 'N', M, N1, N2, -ONE, B( 0, N1 ),
$ LDB, A( 0 ), N2, ALPHA, B( 0, 0 ),
$ LDB )
CALL DTRSM( 'R', 'U', 'T', DIAG, M, N1, ONE,
$ A( N2*N2 ), N2, B( 0, 0 ), LDB )
*
END IF
*
END IF
*
END IF
*
ELSE
*
* SIDE = 'R' and N is even
*
IF( NORMALTRANSR ) THEN
*
* SIDE = 'R', N is even, and TRANSR = 'N'
*
IF( LOWER ) THEN
*
* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'L'
*
IF( NOTRANS ) THEN
*
* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L',
* and TRANS = 'N'
*
CALL DTRSM( 'R', 'U', 'T', DIAG, M, K, ALPHA,
$ A( 0 ), N+1, B( 0, K ), LDB )
CALL DGEMM( 'N', 'N', M, K, K, -ONE, B( 0, K ),
$ LDB, A( K+1 ), N+1, ALPHA, B( 0, 0 ),
$ LDB )
CALL DTRSM( 'R', 'L', 'N', DIAG, M, K, ONE,
$ A( 1 ), N+1, B( 0, 0 ), LDB )
*
ELSE
*
* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L',
* and TRANS = 'T'
*
CALL DTRSM( 'R', 'L', 'T', DIAG, M, K, ALPHA,
$ A( 1 ), N+1, B( 0, 0 ), LDB )
CALL DGEMM( 'N', 'T', M, K, K, -ONE, B( 0, 0 ),
$ LDB, A( K+1 ), N+1, ALPHA, B( 0, K ),
$ LDB )
CALL DTRSM( 'R', 'U', 'N', DIAG, M, K, ONE,
$ A( 0 ), N+1, B( 0, K ), LDB )
*
END IF
*
ELSE
*
* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'U'
*
IF( NOTRANS ) THEN
*
* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U',
* and TRANS = 'N'
*
CALL DTRSM( 'R', 'L', 'T', DIAG, M, K, ALPHA,
$ A( K+1 ), N+1, B( 0, 0 ), LDB )
CALL DGEMM( 'N', 'N', M, K, K, -ONE, B( 0, 0 ),
$ LDB, A( 0 ), N+1, ALPHA, B( 0, K ),
$ LDB )
CALL DTRSM( 'R', 'U', 'N', DIAG, M, K, ONE,
$ A( K ), N+1, B( 0, K ), LDB )
*
ELSE
*
* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U',
* and TRANS = 'T'
*
CALL DTRSM( 'R', 'U', 'T', DIAG, M, K, ALPHA,
$ A( K ), N+1, B( 0, K ), LDB )
CALL DGEMM( 'N', 'T', M, K, K, -ONE, B( 0, K ),
$ LDB, A( 0 ), N+1, ALPHA, B( 0, 0 ),
$ LDB )
CALL DTRSM( 'R', 'L', 'N', DIAG, M, K, ONE,
$ A( K+1 ), N+1, B( 0, 0 ), LDB )
*
END IF
*
END IF
*
ELSE
*
* SIDE = 'R', N is even, and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* SIDE ='R', N is even, TRANSR = 'T', and UPLO = 'L'
*
IF( NOTRANS ) THEN
*
* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'L',
* and TRANS = 'N'
*
CALL DTRSM( 'R', 'L', 'N', DIAG, M, K, ALPHA,
$ A( 0 ), K, B( 0, K ), LDB )
CALL DGEMM( 'N', 'T', M, K, K, -ONE, B( 0, K ),
$ LDB, A( ( K+1 )*K ), K, ALPHA,
$ B( 0, 0 ), LDB )
CALL DTRSM( 'R', 'U', 'T', DIAG, M, K, ONE,
$ A( K ), K, B( 0, 0 ), LDB )
*
ELSE
*
* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'L',
* and TRANS = 'T'
*
CALL DTRSM( 'R', 'U', 'N', DIAG, M, K, ALPHA,
$ A( K ), K, B( 0, 0 ), LDB )
CALL DGEMM( 'N', 'N', M, K, K, -ONE, B( 0, 0 ),
$ LDB, A( ( K+1 )*K ), K, ALPHA,
$ B( 0, K ), LDB )
CALL DTRSM( 'R', 'L', 'T', DIAG, M, K, ONE,
$ A( 0 ), K, B( 0, K ), LDB )
*
END IF
*
ELSE
*
* SIDE ='R', N is even, TRANSR = 'T', and UPLO = 'U'
*
IF( NOTRANS ) THEN
*
* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'U',
* and TRANS = 'N'
*
CALL DTRSM( 'R', 'U', 'N', DIAG, M, K, ALPHA,
$ A( ( K+1 )*K ), K, B( 0, 0 ), LDB )
CALL DGEMM( 'N', 'T', M, K, K, -ONE, B( 0, 0 ),
$ LDB, A( 0 ), K, ALPHA, B( 0, K ), LDB )
CALL DTRSM( 'R', 'L', 'T', DIAG, M, K, ONE,
$ A( K*K ), K, B( 0, K ), LDB )
*
ELSE
*
* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'U',
* and TRANS = 'T'
*
CALL DTRSM( 'R', 'L', 'N', DIAG, M, K, ALPHA,
$ A( K*K ), K, B( 0, K ), LDB )
CALL DGEMM( 'N', 'N', M, K, K, -ONE, B( 0, K ),
$ LDB, A( 0 ), K, ALPHA, B( 0, 0 ), LDB )
CALL DTRSM( 'R', 'U', 'T', DIAG, M, K, ONE,
$ A( ( K+1 )*K ), K, B( 0, 0 ), LDB )
*
END IF
*
END IF
*
END IF
*
END IF
END IF
*
RETURN
*
* End of DTFSM
*
END
Reference in New Issue View Git Blame Copy Permalink