SUBROUTINE CTFSM( 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 COMPLEX ALPHA * .. * .. Array Arguments .. COMPLEX A( 0: * ), B( 0: LDB-1, 0: * ) * .. * * Purpose * ======= * * Level 3 BLAS like routine for A in RFP Format. * * CTFSM 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 ) = conjg( 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; * = 'C': The Conjugate-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 = 'C' or 'c' op( A ) = conjg( 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) COMPLEX. * 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) COMPLEX array, dimension ( N*(N+1)/2 ); * 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 = 'C' then RFP is the Conjugate-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 * conjugate-transpose Format. If UPLO = 'L' the RFP A contains * the NT elements of lower packed A either in normal or * conjugate-transpose Format. The LDA of RFP A is (N+1)/2 when * TRANSR = 'C'. 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) COMPLEX 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 Standard Packed 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 * conjugate-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 * conjugate-transpose of the last three columns of AP lower. * To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- * 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 next consider Standard Packed 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 * conjugate-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 * conjugate-transpose of the last two columns of AP lower. * To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- * 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 * * .. * .. Parameters .. COMPLEX CONE, CZERO PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ), + CZERO = ( 0.0E+0, 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 XERBLA, CGEMM, CTRSM * .. * .. 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, 'C' ) ) 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, 'C' ) ) 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( 'CTFSM ', -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.(0E+0,0E+0) * IF( ALPHA.EQ.CZERO ) THEN DO 20 J = 0, N - 1 DO 10 I = 0, M - 1 B( I, J ) = CZERO 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 CTRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA, + A( 0 ), M, B, LDB ) CALL CGEMM( 'N', 'N', M2, N, M1, -CONE, A( M1 ), M, + B, LDB, ALPHA, B( M1, 0 ), LDB ) CALL CTRSM( 'L', 'U', 'C', DIAG, M2, N, CONE, + A( M ), M, B( M1, 0 ), LDB ) * ELSE * * SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and * TRANS = 'C' * CALL CTRSM( 'L', 'U', 'N', DIAG, M2, N, ALPHA, + A( M ), M, B( M1, 0 ), LDB ) CALL CGEMM( 'C', 'N', M1, N, M2, -CONE, A( M1 ), M, + B( M1, 0 ), LDB, ALPHA, B, LDB ) CALL CTRSM( 'L', 'L', 'C', DIAG, M1, N, CONE, + 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 CTRSM( 'L', 'L', 'N', DIAG, M1, N, ALPHA, + A( M2 ), M, B, LDB ) CALL CGEMM( 'C', 'N', M2, N, M1, -CONE, A( 0 ), M, + B, LDB, ALPHA, B( M1, 0 ), LDB ) CALL CTRSM( 'L', 'U', 'C', DIAG, M2, N, CONE, + A( M1 ), M, B( M1, 0 ), LDB ) * ELSE * * SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and * TRANS = 'C' * CALL CTRSM( 'L', 'U', 'N', DIAG, M2, N, ALPHA, + A( M1 ), M, B( M1, 0 ), LDB ) CALL CGEMM( 'N', 'N', M1, N, M2, -CONE, A( 0 ), M, + B( M1, 0 ), LDB, ALPHA, B, LDB ) CALL CTRSM( 'L', 'L', 'C', DIAG, M1, N, CONE, + A( M2 ), M, B, LDB ) * END IF * END IF * ELSE * * SIDE = 'L', N is odd, and TRANSR = 'C' * IF( LOWER ) THEN * * SIDE ='L', N is odd, TRANSR = 'C', and UPLO = 'L' * IF( NOTRANS ) THEN * * SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'L', and * TRANS = 'N' * CALL CTRSM( 'L', 'U', 'C', DIAG, M1, N, ALPHA, + A( 0 ), M1, B, LDB ) CALL CGEMM( 'C', 'N', M2, N, M1, -CONE, A( M1*M1 ), + M1, B, LDB, ALPHA, B( M1, 0 ), LDB ) CALL CTRSM( 'L', 'L', 'N', DIAG, M2, N, CONE, + A( 1 ), M1, B( M1, 0 ), LDB ) * ELSE * * SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'L', and * TRANS = 'C' * CALL CTRSM( 'L', 'L', 'C', DIAG, M2, N, ALPHA, + A( 1 ), M1, B( M1, 0 ), LDB ) CALL CGEMM( 'N', 'N', M1, N, M2, -CONE, A( M1*M1 ), + M1, B( M1, 0 ), LDB, ALPHA, B, LDB ) CALL CTRSM( 'L', 'U', 'N', DIAG, M1, N, CONE, + A( 0 ), M1, B, LDB ) * END IF * ELSE * * SIDE ='L', N is odd, TRANSR = 'C', and UPLO = 'U' * IF( .NOT.NOTRANS ) THEN * * SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'U', and * TRANS = 'N' * CALL CTRSM( 'L', 'U', 'C', DIAG, M1, N, ALPHA, + A( M2*M2 ), M2, B, LDB ) CALL CGEMM( 'N', 'N', M2, N, M1, -CONE, A( 0 ), M2, + B, LDB, ALPHA, B( M1, 0 ), LDB ) CALL CTRSM( 'L', 'L', 'N', DIAG, M2, N, CONE, + A( M1*M2 ), M2, B( M1, 0 ), LDB ) * ELSE * * SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'U', and * TRANS = 'C' * CALL CTRSM( 'L', 'L', 'C', DIAG, M2, N, ALPHA, + A( M1*M2 ), M2, B( M1, 0 ), LDB ) CALL CGEMM( 'C', 'N', M1, N, M2, -CONE, A( 0 ), M2, + B( M1, 0 ), LDB, ALPHA, B, LDB ) CALL CTRSM( 'L', 'U', 'N', DIAG, M1, N, CONE, + 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 CTRSM( 'L', 'L', 'N', DIAG, K, N, ALPHA, + A( 1 ), M+1, B, LDB ) CALL CGEMM( 'N', 'N', K, N, K, -CONE, A( K+1 ), + M+1, B, LDB, ALPHA, B( K, 0 ), LDB ) CALL CTRSM( 'L', 'U', 'C', DIAG, K, N, CONE, + A( 0 ), M+1, B( K, 0 ), LDB ) * ELSE * * SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L', * and TRANS = 'C' * CALL CTRSM( 'L', 'U', 'N', DIAG, K, N, ALPHA, + A( 0 ), M+1, B( K, 0 ), LDB ) CALL CGEMM( 'C', 'N', K, N, K, -CONE, A( K+1 ), + M+1, B( K, 0 ), LDB, ALPHA, B, LDB ) CALL CTRSM( 'L', 'L', 'C', DIAG, K, N, CONE, + 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 CTRSM( 'L', 'L', 'N', DIAG, K, N, ALPHA, + A( K+1 ), M+1, B, LDB ) CALL CGEMM( 'C', 'N', K, N, K, -CONE, A( 0 ), M+1, + B, LDB, ALPHA, B( K, 0 ), LDB ) CALL CTRSM( 'L', 'U', 'C', DIAG, K, N, CONE, + A( K ), M+1, B( K, 0 ), LDB ) * ELSE * * SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U', * and TRANS = 'C' CALL CTRSM( 'L', 'U', 'N', DIAG, K, N, ALPHA, + A( K ), M+1, B( K, 0 ), LDB ) CALL CGEMM( 'N', 'N', K, N, K, -CONE, A( 0 ), M+1, + B( K, 0 ), LDB, ALPHA, B, LDB ) CALL CTRSM( 'L', 'L', 'C', DIAG, K, N, CONE, + A( K+1 ), M+1, B, LDB ) * END IF * END IF * ELSE * * SIDE = 'L', N is even, and TRANSR = 'C' * IF( LOWER ) THEN * * SIDE ='L', N is even, TRANSR = 'C', and UPLO = 'L' * IF( NOTRANS ) THEN * * SIDE ='L', N is even, TRANSR = 'C', UPLO = 'L', * and TRANS = 'N' * CALL CTRSM( 'L', 'U', 'C', DIAG, K, N, ALPHA, + A( K ), K, B, LDB ) CALL CGEMM( 'C', 'N', K, N, K, -CONE, + A( K*( K+1 ) ), K, B, LDB, ALPHA, + B( K, 0 ), LDB ) CALL CTRSM( 'L', 'L', 'N', DIAG, K, N, CONE, + A( 0 ), K, B( K, 0 ), LDB ) * ELSE * * SIDE ='L', N is even, TRANSR = 'C', UPLO = 'L', * and TRANS = 'C' * CALL CTRSM( 'L', 'L', 'C', DIAG, K, N, ALPHA, + A( 0 ), K, B( K, 0 ), LDB ) CALL CGEMM( 'N', 'N', K, N, K, -CONE, + A( K*( K+1 ) ), K, B( K, 0 ), LDB, + ALPHA, B, LDB ) CALL CTRSM( 'L', 'U', 'N', DIAG, K, N, CONE, + A( K ), K, B, LDB ) * END IF * ELSE * * SIDE ='L', N is even, TRANSR = 'C', and UPLO = 'U' * IF( .NOT.NOTRANS ) THEN * * SIDE ='L', N is even, TRANSR = 'C', UPLO = 'U', * and TRANS = 'N' * CALL CTRSM( 'L', 'U', 'C', DIAG, K, N, ALPHA, + A( K*( K+1 ) ), K, B, LDB ) CALL CGEMM( 'N', 'N', K, N, K, -CONE, A( 0 ), K, B, + LDB, ALPHA, B( K, 0 ), LDB ) CALL CTRSM( 'L', 'L', 'N', DIAG, K, N, CONE, + A( K*K ), K, B( K, 0 ), LDB ) * ELSE * * SIDE ='L', N is even, TRANSR = 'C', UPLO = 'U', * and TRANS = 'C' * CALL CTRSM( 'L', 'L', 'C', DIAG, K, N, ALPHA, + A( K*K ), K, B( K, 0 ), LDB ) CALL CGEMM( 'C', 'N', K, N, K, -CONE, A( 0 ), K, + B( K, 0 ), LDB, ALPHA, B, LDB ) CALL CTRSM( 'L', 'U', 'N', DIAG, K, N, CONE, + 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 CTRSM( 'R', 'U', 'C', DIAG, M, N2, ALPHA, + A( N ), N, B( 0, N1 ), LDB ) CALL CGEMM( 'N', 'N', M, N1, N2, -CONE, B( 0, N1 ), + LDB, A( N1 ), N, ALPHA, B( 0, 0 ), + LDB ) CALL CTRSM( 'R', 'L', 'N', DIAG, M, N1, CONE, + A( 0 ), N, B( 0, 0 ), LDB ) * ELSE * * SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and * TRANS = 'C' * CALL CTRSM( 'R', 'L', 'C', DIAG, M, N1, ALPHA, + A( 0 ), N, B( 0, 0 ), LDB ) CALL CGEMM( 'N', 'C', M, N2, N1, -CONE, B( 0, 0 ), + LDB, A( N1 ), N, ALPHA, B( 0, N1 ), + LDB ) CALL CTRSM( 'R', 'U', 'N', DIAG, M, N2, CONE, + 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 CTRSM( 'R', 'L', 'C', DIAG, M, N1, ALPHA, + A( N2 ), N, B( 0, 0 ), LDB ) CALL CGEMM( 'N', 'N', M, N2, N1, -CONE, B( 0, 0 ), + LDB, A( 0 ), N, ALPHA, B( 0, N1 ), + LDB ) CALL CTRSM( 'R', 'U', 'N', DIAG, M, N2, CONE, + A( N1 ), N, B( 0, N1 ), LDB ) * ELSE * * SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and * TRANS = 'C' * CALL CTRSM( 'R', 'U', 'C', DIAG, M, N2, ALPHA, + A( N1 ), N, B( 0, N1 ), LDB ) CALL CGEMM( 'N', 'C', M, N1, N2, -CONE, B( 0, N1 ), + LDB, A( 0 ), N, ALPHA, B( 0, 0 ), LDB ) CALL CTRSM( 'R', 'L', 'N', DIAG, M, N1, CONE, + A( N2 ), N, B( 0, 0 ), LDB ) * END IF * END IF * ELSE * * SIDE = 'R', N is odd, and TRANSR = 'C' * IF( LOWER ) THEN * * SIDE ='R', N is odd, TRANSR = 'C', and UPLO = 'L' * IF( NOTRANS ) THEN * * SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'L', and * TRANS = 'N' * CALL CTRSM( 'R', 'L', 'N', DIAG, M, N2, ALPHA, + A( 1 ), N1, B( 0, N1 ), LDB ) CALL CGEMM( 'N', 'C', M, N1, N2, -CONE, B( 0, N1 ), + LDB, A( N1*N1 ), N1, ALPHA, B( 0, 0 ), + LDB ) CALL CTRSM( 'R', 'U', 'C', DIAG, M, N1, CONE, + A( 0 ), N1, B( 0, 0 ), LDB ) * ELSE * * SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'L', and * TRANS = 'C' * CALL CTRSM( 'R', 'U', 'N', DIAG, M, N1, ALPHA, + A( 0 ), N1, B( 0, 0 ), LDB ) CALL CGEMM( 'N', 'N', M, N2, N1, -CONE, B( 0, 0 ), + LDB, A( N1*N1 ), N1, ALPHA, B( 0, N1 ), + LDB ) CALL CTRSM( 'R', 'L', 'C', DIAG, M, N2, CONE, + A( 1 ), N1, B( 0, N1 ), LDB ) * END IF * ELSE * * SIDE ='R', N is odd, TRANSR = 'C', and UPLO = 'U' * IF( NOTRANS ) THEN * * SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'U', and * TRANS = 'N' * CALL CTRSM( 'R', 'U', 'N', DIAG, M, N1, ALPHA, + A( N2*N2 ), N2, B( 0, 0 ), LDB ) CALL CGEMM( 'N', 'C', M, N2, N1, -CONE, B( 0, 0 ), + LDB, A( 0 ), N2, ALPHA, B( 0, N1 ), + LDB ) CALL CTRSM( 'R', 'L', 'C', DIAG, M, N2, CONE, + A( N1*N2 ), N2, B( 0, N1 ), LDB ) * ELSE * * SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'U', and * TRANS = 'C' * CALL CTRSM( 'R', 'L', 'N', DIAG, M, N2, ALPHA, + A( N1*N2 ), N2, B( 0, N1 ), LDB ) CALL CGEMM( 'N', 'N', M, N1, N2, -CONE, B( 0, N1 ), + LDB, A( 0 ), N2, ALPHA, B( 0, 0 ), + LDB ) CALL CTRSM( 'R', 'U', 'C', DIAG, M, N1, CONE, + 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 CTRSM( 'R', 'U', 'C', DIAG, M, K, ALPHA, + A( 0 ), N+1, B( 0, K ), LDB ) CALL CGEMM( 'N', 'N', M, K, K, -CONE, B( 0, K ), + LDB, A( K+1 ), N+1, ALPHA, B( 0, 0 ), + LDB ) CALL CTRSM( 'R', 'L', 'N', DIAG, M, K, CONE, + A( 1 ), N+1, B( 0, 0 ), LDB ) * ELSE * * SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L', * and TRANS = 'C' * CALL CTRSM( 'R', 'L', 'C', DIAG, M, K, ALPHA, + A( 1 ), N+1, B( 0, 0 ), LDB ) CALL CGEMM( 'N', 'C', M, K, K, -CONE, B( 0, 0 ), + LDB, A( K+1 ), N+1, ALPHA, B( 0, K ), + LDB ) CALL CTRSM( 'R', 'U', 'N', DIAG, M, K, CONE, + 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 CTRSM( 'R', 'L', 'C', DIAG, M, K, ALPHA, + A( K+1 ), N+1, B( 0, 0 ), LDB ) CALL CGEMM( 'N', 'N', M, K, K, -CONE, B( 0, 0 ), + LDB, A( 0 ), N+1, ALPHA, B( 0, K ), + LDB ) CALL CTRSM( 'R', 'U', 'N', DIAG, M, K, CONE, + A( K ), N+1, B( 0, K ), LDB ) * ELSE * * SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U', * and TRANS = 'C' * CALL CTRSM( 'R', 'U', 'C', DIAG, M, K, ALPHA, + A( K ), N+1, B( 0, K ), LDB ) CALL CGEMM( 'N', 'C', M, K, K, -CONE, B( 0, K ), + LDB, A( 0 ), N+1, ALPHA, B( 0, 0 ), + LDB ) CALL CTRSM( 'R', 'L', 'N', DIAG, M, K, CONE, + A( K+1 ), N+1, B( 0, 0 ), LDB ) * END IF * END IF * ELSE * * SIDE = 'R', N is even, and TRANSR = 'C' * IF( LOWER ) THEN * * SIDE ='R', N is even, TRANSR = 'C', and UPLO = 'L' * IF( NOTRANS ) THEN * * SIDE ='R', N is even, TRANSR = 'C', UPLO = 'L', * and TRANS = 'N' * CALL CTRSM( 'R', 'L', 'N', DIAG, M, K, ALPHA, + A( 0 ), K, B( 0, K ), LDB ) CALL CGEMM( 'N', 'C', M, K, K, -CONE, B( 0, K ), + LDB, A( ( K+1 )*K ), K, ALPHA, + B( 0, 0 ), LDB ) CALL CTRSM( 'R', 'U', 'C', DIAG, M, K, CONE, + A( K ), K, B( 0, 0 ), LDB ) * ELSE * * SIDE ='R', N is even, TRANSR = 'C', UPLO = 'L', * and TRANS = 'C' * CALL CTRSM( 'R', 'U', 'N', DIAG, M, K, ALPHA, + A( K ), K, B( 0, 0 ), LDB ) CALL CGEMM( 'N', 'N', M, K, K, -CONE, B( 0, 0 ), + LDB, A( ( K+1 )*K ), K, ALPHA, + B( 0, K ), LDB ) CALL CTRSM( 'R', 'L', 'C', DIAG, M, K, CONE, + A( 0 ), K, B( 0, K ), LDB ) * END IF * ELSE * * SIDE ='R', N is even, TRANSR = 'C', and UPLO = 'U' * IF( NOTRANS ) THEN * * SIDE ='R', N is even, TRANSR = 'C', UPLO = 'U', * and TRANS = 'N' * CALL CTRSM( 'R', 'U', 'N', DIAG, M, K, ALPHA, + A( ( K+1 )*K ), K, B( 0, 0 ), LDB ) CALL CGEMM( 'N', 'C', M, K, K, -CONE, B( 0, 0 ), + LDB, A( 0 ), K, ALPHA, B( 0, K ), LDB ) CALL CTRSM( 'R', 'L', 'C', DIAG, M, K, CONE, + A( K*K ), K, B( 0, K ), LDB ) * ELSE * * SIDE ='R', N is even, TRANSR = 'C', UPLO = 'U', * and TRANS = 'C' * CALL CTRSM( 'R', 'L', 'N', DIAG, M, K, ALPHA, + A( K*K ), K, B( 0, K ), LDB ) CALL CGEMM( 'N', 'N', M, K, K, -CONE, B( 0, K ), + LDB, A( 0 ), K, ALPHA, B( 0, 0 ), LDB ) CALL CTRSM( 'R', 'U', 'C', DIAG, M, K, CONE, + A( ( K+1 )*K ), K, B( 0, 0 ), LDB ) * END IF * END IF * END IF * END IF END IF * RETURN * * End of CTFSM * END