From ff981f106bde4ce6a74aa4f4a572c943f5a395b2 Mon Sep 17 00:00:00 2001 From: julie Date: Tue, 16 Dec 2008 17:06:58 +0000 Subject: --- SRC/stfsm.f | 905 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 905 insertions(+) create mode 100644 SRC/stfsm.f (limited to 'SRC/stfsm.f') diff --git a/SRC/stfsm.f b/SRC/stfsm.f new file mode 100644 index 00000000..3c6438e8 --- /dev/null +++ b/SRC/stfsm.f @@ -0,0 +1,905 @@ + SUBROUTINE STFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, + + B, LDB ) +* +* -- LAPACK routine (version 3.2) -- +* +* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- +* -- November 2008 -- +* +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* +* .. +* .. Scalar Arguments .. + CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO + INTEGER LDB, M, N + REAL ALPHA +* .. +* .. Array Arguments .. + REAL A( 0: * ), B( 0: LDB-1, 0: * ) +* .. +* +* Purpose +* ======= +* +* Level 3 BLAS like routine for A in RFP Format. +* +* STFSM 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'. +* +* A is in Rectangular Full Packed (RFP) Format. +* +* The matrix X is overwritten on B. +* +* Arguments +* ========== +* +* TRANSR - (input) CHARACTER +* = 'N': The Normal Form of RFP A is stored; +* = 'T': The Transpose Form of RFP A is stored. +* +* SIDE - (input) CHARACTER +* 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. +* +* UPLO - (input) CHARACTER +* 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. +* +* TRANS - (input) CHARACTER +* 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. +* +* DIAG - (input) CHARACTER +* 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. +* +* M - (input) INTEGER. +* On entry, M specifies the number of rows of B. M must be at +* least zero. +* Unchanged on exit. +* +* N - (input) INTEGER. +* On entry, N specifies the number of columns of B. N must be +* at least zero. +* Unchanged on exit. +* +* ALPHA - (input) REAL. +* 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 - (input) REAL 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. +* +* B - (input/ouptut) REAL 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. +* +* LDB - (input) 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. +* +* Notes +* ===== +* +* 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 first 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 +* +* Reference +* ========= +* +* ===================================================================== +* +* .. +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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 SGEMM, STRSM, XERBLA +* .. +* .. 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( 'STFSM ', -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' +* + CALL STRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA, + + A( 0 ), M, B, LDB ) + CALL SGEMM( 'N', 'N', M2, N, M1, -ONE, A( M1 ), M, + + B, LDB, ALPHA, B( M1, 0 ), LDB ) + CALL STRSM( 'L', 'U', 'T', DIAG, M2, N, ONE, + + A( M ), M, B( M1, 0 ), LDB ) +* + ELSE +* +* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and +* TRANS = 'T' +* + CALL STRSM( 'L', 'U', 'N', DIAG, M2, N, ALPHA, + + A( M ), M, B( M1, 0 ), LDB ) + CALL SGEMM( 'T', 'N', M1, N, M2, -ONE, A( M1 ), M, + + B( M1, 0 ), LDB, ALPHA, B, LDB ) + CALL STRSM( 'L', 'L', 'T', DIAG, M1, N, ONE, + + A( 0 ), M, B, LDB ) +* + 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 STRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA, + + A( M2 ), M, B, LDB ) + CALL SGEMM( 'T', 'N', M2, N, M1, -ONE, A( 0 ), M, + + B, LDB, ALPHA, B( M1, 0 ), LDB ) + CALL STRSM( '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 STRSM( 'L', 'U', 'N', DIAG, M2, N, ALPHA, + + A( M1 ), M, B( M1, 0 ), LDB ) + CALL SGEMM( 'N', 'N', M1, N, M2, -ONE, A( 0 ), M, + + B( M1, 0 ), LDB, ALPHA, B, LDB ) + CALL STRSM( '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' +* + CALL STRSM( 'L', 'U', 'T', DIAG, M1, N, ALPHA, + + A( 0 ), M1, B, LDB ) + CALL SGEMM( 'T', 'N', M2, N, M1, -ONE, A( M1*M1 ), + + M1, B, LDB, ALPHA, B( M1, 0 ), LDB ) + CALL STRSM( 'L', 'L', 'N', DIAG, M2, N, ONE, + + A( 1 ), M1, B( M1, 0 ), LDB ) +* + ELSE +* +* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'L', and +* TRANS = 'T' +* + CALL STRSM( 'L', 'L', 'T', DIAG, M2, N, ALPHA, + + A( 1 ), M1, B( M1, 0 ), LDB ) + CALL SGEMM( 'N', 'N', M1, N, M2, -ONE, A( M1*M1 ), + + M1, B( M1, 0 ), LDB, ALPHA, B, LDB ) + CALL STRSM( 'L', 'U', 'N', DIAG, M1, N, ONE, + + A( 0 ), M1, B, LDB ) +* + 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 STRSM( 'L', 'U', 'T', DIAG, M1, N, ALPHA, + + A( M2*M2 ), M2, B, LDB ) + CALL SGEMM( 'N', 'N', M2, N, M1, -ONE, A( 0 ), M2, + + B, LDB, ALPHA, B( M1, 0 ), LDB ) + CALL STRSM( '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 STRSM( 'L', 'L', 'T', DIAG, M2, N, ALPHA, + + A( M1*M2 ), M2, B( M1, 0 ), LDB ) + CALL SGEMM( 'T', 'N', M1, N, M2, -ONE, A( 0 ), M2, + + B( M1, 0 ), LDB, ALPHA, B, LDB ) + CALL STRSM( '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 STRSM( 'L', 'L', 'N', DIAG, K, N, ALPHA, + + A( 1 ), M+1, B, LDB ) + CALL SGEMM( 'N', 'N', K, N, K, -ONE, A( K+1 ), + + M+1, B, LDB, ALPHA, B( K, 0 ), LDB ) + CALL STRSM( '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 STRSM( 'L', 'U', 'N', DIAG, K, N, ALPHA, + + A( 0 ), M+1, B( K, 0 ), LDB ) + CALL SGEMM( 'T', 'N', K, N, K, -ONE, A( K+1 ), + + M+1, B( K, 0 ), LDB, ALPHA, B, LDB ) + CALL STRSM( '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 STRSM( 'L', 'L', 'N', DIAG, K, N, ALPHA, + + A( K+1 ), M+1, B, LDB ) + CALL SGEMM( 'T', 'N', K, N, K, -ONE, A( 0 ), M+1, + + B, LDB, ALPHA, B( K, 0 ), LDB ) + CALL STRSM( '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 STRSM( 'L', 'U', 'N', DIAG, K, N, ALPHA, + + A( K ), M+1, B( K, 0 ), LDB ) + CALL SGEMM( 'N', 'N', K, N, K, -ONE, A( 0 ), M+1, + + B( K, 0 ), LDB, ALPHA, B, LDB ) + CALL STRSM( '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 STRSM( 'L', 'U', 'T', DIAG, K, N, ALPHA, + + A( K ), K, B, LDB ) + CALL SGEMM( 'T', 'N', K, N, K, -ONE, + + A( K*( K+1 ) ), K, B, LDB, ALPHA, + + B( K, 0 ), LDB ) + CALL STRSM( '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 STRSM( 'L', 'L', 'T', DIAG, K, N, ALPHA, + + A( 0 ), K, B( K, 0 ), LDB ) + CALL SGEMM( 'N', 'N', K, N, K, -ONE, + + A( K*( K+1 ) ), K, B( K, 0 ), LDB, + + ALPHA, B, LDB ) + CALL STRSM( '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 STRSM( 'L', 'U', 'T', DIAG, K, N, ALPHA, + + A( K*( K+1 ) ), K, B, LDB ) + CALL SGEMM( 'N', 'N', K, N, K, -ONE, A( 0 ), K, B, + + LDB, ALPHA, B( K, 0 ), LDB ) + CALL STRSM( '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 STRSM( 'L', 'L', 'T', DIAG, K, N, ALPHA, + + A( K*K ), K, B( K, 0 ), LDB ) + CALL SGEMM( 'T', 'N', K, N, K, -ONE, A( 0 ), K, + + B( K, 0 ), LDB, ALPHA, B, LDB ) + CALL STRSM( '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 STRSM( 'R', 'U', 'T', DIAG, M, N2, ALPHA, + + A( N ), N, B( 0, N1 ), LDB ) + CALL SGEMM( 'N', 'N', M, N1, N2, -ONE, B( 0, N1 ), + + LDB, A( N1 ), N, ALPHA, B( 0, 0 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'L', 'T', DIAG, M, N1, ALPHA, + + A( 0 ), N, B( 0, 0 ), LDB ) + CALL SGEMM( 'N', 'T', M, N2, N1, -ONE, B( 0, 0 ), + + LDB, A( N1 ), N, ALPHA, B( 0, N1 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'L', 'T', DIAG, M, N1, ALPHA, + + A( N2 ), N, B( 0, 0 ), LDB ) + CALL SGEMM( 'N', 'N', M, N2, N1, -ONE, B( 0, 0 ), + + LDB, A( 0 ), N, ALPHA, B( 0, N1 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'U', 'T', DIAG, M, N2, ALPHA, + + A( N1 ), N, B( 0, N1 ), LDB ) + CALL SGEMM( 'N', 'T', M, N1, N2, -ONE, B( 0, N1 ), + + LDB, A( 0 ), N, ALPHA, B( 0, 0 ), LDB ) + CALL STRSM( '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 STRSM( 'R', 'L', 'N', DIAG, M, N2, ALPHA, + + A( 1 ), N1, B( 0, N1 ), LDB ) + CALL SGEMM( 'N', 'T', M, N1, N2, -ONE, B( 0, N1 ), + + LDB, A( N1*N1 ), N1, ALPHA, B( 0, 0 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'U', 'N', DIAG, M, N1, ALPHA, + + A( 0 ), N1, B( 0, 0 ), LDB ) + CALL SGEMM( 'N', 'N', M, N2, N1, -ONE, B( 0, 0 ), + + LDB, A( N1*N1 ), N1, ALPHA, B( 0, N1 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'U', 'N', DIAG, M, N1, ALPHA, + + A( N2*N2 ), N2, B( 0, 0 ), LDB ) + CALL SGEMM( 'N', 'T', M, N2, N1, -ONE, B( 0, 0 ), + + LDB, A( 0 ), N2, ALPHA, B( 0, N1 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'L', 'N', DIAG, M, N2, ALPHA, + + A( N1*N2 ), N2, B( 0, N1 ), LDB ) + CALL SGEMM( 'N', 'N', M, N1, N2, -ONE, B( 0, N1 ), + + LDB, A( 0 ), N2, ALPHA, B( 0, 0 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'U', 'T', DIAG, M, K, ALPHA, + + A( 0 ), N+1, B( 0, K ), LDB ) + CALL SGEMM( 'N', 'N', M, K, K, -ONE, B( 0, K ), + + LDB, A( K+1 ), N+1, ALPHA, B( 0, 0 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'L', 'T', DIAG, M, K, ALPHA, + + A( 1 ), N+1, B( 0, 0 ), LDB ) + CALL SGEMM( 'N', 'T', M, K, K, -ONE, B( 0, 0 ), + + LDB, A( K+1 ), N+1, ALPHA, B( 0, K ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'L', 'T', DIAG, M, K, ALPHA, + + A( K+1 ), N+1, B( 0, 0 ), LDB ) + CALL SGEMM( 'N', 'N', M, K, K, -ONE, B( 0, 0 ), + + LDB, A( 0 ), N+1, ALPHA, B( 0, K ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'U', 'T', DIAG, M, K, ALPHA, + + A( K ), N+1, B( 0, K ), LDB ) + CALL SGEMM( 'N', 'T', M, K, K, -ONE, B( 0, K ), + + LDB, A( 0 ), N+1, ALPHA, B( 0, 0 ), + + LDB ) + CALL STRSM( '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 STRSM( 'R', 'L', 'N', DIAG, M, K, ALPHA, + + A( 0 ), K, B( 0, K ), LDB ) + CALL SGEMM( 'N', 'T', M, K, K, -ONE, B( 0, K ), + + LDB, A( ( K+1 )*K ), K, ALPHA, + + B( 0, 0 ), LDB ) + CALL STRSM( '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 STRSM( 'R', 'U', 'N', DIAG, M, K, ALPHA, + + A( K ), K, B( 0, 0 ), LDB ) + CALL SGEMM( 'N', 'N', M, K, K, -ONE, B( 0, 0 ), + + LDB, A( ( K+1 )*K ), K, ALPHA, + + B( 0, K ), LDB ) + CALL STRSM( '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 STRSM( 'R', 'U', 'N', DIAG, M, K, ALPHA, + + A( ( K+1 )*K ), K, B( 0, 0 ), LDB ) + CALL SGEMM( 'N', 'T', M, K, K, -ONE, B( 0, 0 ), + + LDB, A( 0 ), K, ALPHA, B( 0, K ), LDB ) + CALL STRSM( '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 STRSM( 'R', 'L', 'N', DIAG, M, K, ALPHA, + + A( K*K ), K, B( 0, K ), LDB ) + CALL SGEMM( 'N', 'N', M, K, K, -ONE, B( 0, K ), + + LDB, A( 0 ), K, ALPHA, B( 0, 0 ), LDB ) + CALL STRSM( '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 STFSM +* + END -- cgit v1.2.3