*> \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 *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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 December 2016 * *> \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 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. 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