*> \brief \b CTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CTPRFB + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CTPRFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, * V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK ) * * .. Scalar Arguments .. * CHARACTER DIRECT, SIDE, STOREV, TRANS * INTEGER K, L, LDA, LDB, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. * COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), * \$ V( LDV, * ), WORK( LDWORK, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CTPRFB applies a complex "triangular-pentagonal" block reflector H or its *> conjugate transpose H**H to a complex matrix C, which is composed of two *> blocks A and B, either from the left or right. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply H or H**H from the Left *> = 'R': apply H or H**H from the Right *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply H (No transpose) *> = 'C': apply H**H (Conjugate transpose) *> \endverbatim *> *> \param[in] DIRECT *> \verbatim *> DIRECT is CHARACTER*1 *> Indicates how H is formed from a product of elementary *> reflectors *> = 'F': H = H(1) H(2) . . . H(k) (Forward) *> = 'B': H = H(k) . . . H(2) H(1) (Backward) *> \endverbatim *> *> \param[in] STOREV *> \verbatim *> STOREV is CHARACTER*1 *> Indicates how the vectors which define the elementary *> reflectors are stored: *> = 'C': Columns *> = 'R': Rows *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix B. *> M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix B. *> N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The order of the matrix T, i.e. the number of elementary *> reflectors whose product defines the block reflector. *> K >= 0. *> \endverbatim *> *> \param[in] L *> \verbatim *> L is INTEGER *> The order of the trapezoidal part of V. *> K >= L >= 0. See Further Details. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is COMPLEX array, dimension *> (LDV,K) if STOREV = 'C' *> (LDV,M) if STOREV = 'R' and SIDE = 'L' *> (LDV,N) if STOREV = 'R' and SIDE = 'R' *> The pentagonal matrix V, which contains the elementary reflectors *> H(1), H(2), ..., H(K). See Further Details. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V. *> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); *> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); *> if STOREV = 'R', LDV >= K. *> \endverbatim *> *> \param[in] T *> \verbatim *> T is COMPLEX array, dimension (LDT,K) *> The triangular K-by-K matrix T in the representation of the *> block reflector. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. *> LDT >= K. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX array, dimension *> (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' *> On entry, the K-by-N or M-by-K matrix A. *> On exit, A is overwritten by the corresponding block of *> H*C or H**H*C or C*H or C*H**H. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDC >= max(1,K); *> If SIDE = 'R', LDC >= max(1,M). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX array, dimension (LDB,N) *> On entry, the M-by-N matrix B. *> On exit, B is overwritten by the corresponding block of *> H*C or H**H*C or C*H or C*H**H. See Further Details. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. *> LDB >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension *> (LDWORK,N) if SIDE = 'L', *> (LDWORK,K) if SIDE = 'R'. *> \endverbatim *> *> \param[in] LDWORK *> \verbatim *> LDWORK is INTEGER *> The leading dimension of the array WORK. *> If SIDE = 'L', LDWORK >= K; *> if SIDE = 'R', LDWORK >= M. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complexOTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix C is a composite matrix formed from blocks A and B. *> The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K, *> and if SIDE = 'L', A is of size K-by-N. *> *> If SIDE = 'R' and DIRECT = 'F', C = [A B]. *> *> If SIDE = 'L' and DIRECT = 'F', C = [A] *> [B]. *> *> If SIDE = 'R' and DIRECT = 'B', C = [B A]. *> *> If SIDE = 'L' and DIRECT = 'B', C = [B] *> [A]. *> *> The pentagonal matrix V is composed of a rectangular block V1 and a *> trapezoidal block V2. The size of the trapezoidal block is determined by *> the parameter L, where 0<=L<=K. If L=K, the V2 block of V is triangular; *> if L=0, there is no trapezoidal block, thus V = V1 is rectangular. *> *> If DIRECT = 'F' and STOREV = 'C': V = [V1] *> [V2] *> - V2 is upper trapezoidal (first L rows of K-by-K upper triangular) *> *> If DIRECT = 'F' and STOREV = 'R': V = [V1 V2] *> *> - V2 is lower trapezoidal (first L columns of K-by-K lower triangular) *> *> If DIRECT = 'B' and STOREV = 'C': V = [V2] *> [V1] *> - V2 is lower trapezoidal (last L rows of K-by-K lower triangular) *> *> If DIRECT = 'B' and STOREV = 'R': V = [V2 V1] *> *> - V2 is upper trapezoidal (last L columns of K-by-K upper triangular) *> *> If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K. *> *> If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K. *> *> If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L. *> *> If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L. *> \endverbatim *> * ===================================================================== SUBROUTINE CTPRFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, \$ V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK ) * * -- LAPACK auxiliary 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 DIRECT, SIDE, STOREV, TRANS INTEGER K, L, LDA, LDB, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), \$ V( LDV, * ), WORK( LDWORK, * ) * .. * * ========================================================================== * * .. Parameters .. COMPLEX ONE, ZERO PARAMETER ( ONE = (1.0,0.0), ZERO = (0.0,0.0) ) * .. * .. Local Scalars .. INTEGER I, J, MP, NP, KP LOGICAL LEFT, FORWARD, COLUMN, RIGHT, BACKWARD, ROW * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CGEMM, CTRMM * .. * .. Intrinsic Functions .. INTRINSIC CONJG * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 .OR. K.LE.0 .OR. L.LT.0 ) RETURN * IF( LSAME( STOREV, 'C' ) ) THEN COLUMN = .TRUE. ROW = .FALSE. ELSE IF ( LSAME( STOREV, 'R' ) ) THEN COLUMN = .FALSE. ROW = .TRUE. ELSE COLUMN = .FALSE. ROW = .FALSE. END IF * IF( LSAME( SIDE, 'L' ) ) THEN LEFT = .TRUE. RIGHT = .FALSE. ELSE IF( LSAME( SIDE, 'R' ) ) THEN LEFT = .FALSE. RIGHT = .TRUE. ELSE LEFT = .FALSE. RIGHT = .FALSE. END IF * IF( LSAME( DIRECT, 'F' ) ) THEN FORWARD = .TRUE. BACKWARD = .FALSE. ELSE IF( LSAME( DIRECT, 'B' ) ) THEN FORWARD = .FALSE. BACKWARD = .TRUE. ELSE FORWARD = .FALSE. BACKWARD = .FALSE. END IF * * --------------------------------------------------------------------------- * IF( COLUMN .AND. FORWARD .AND. LEFT ) THEN * * --------------------------------------------------------------------------- * * Let W = [ I ] (K-by-K) * [ V ] (M-by-K) * * Form H C or H**H C where C = [ A ] (K-by-N) * [ B ] (M-by-N) * * H = I - W T W**H or H**H = I - W T**H W**H * * A = A - T (A + V**H B) or A = A - T**H (A + V**H B) * B = B - V T (A + V**H B) or B = B - V T**H (A + V**H B) * * --------------------------------------------------------------------------- * MP = MIN( M-L+1, M ) KP = MIN( L+1, K ) * DO J = 1, N DO I = 1, L WORK( I, J ) = B( M-L+I, J ) END DO END DO CALL CTRMM( 'L', 'U', 'C', 'N', L, N, ONE, V( MP, 1 ), LDV, \$ WORK, LDWORK ) CALL CGEMM( 'C', 'N', L, N, M-L, ONE, V, LDV, B, LDB, \$ ONE, WORK, LDWORK ) CALL CGEMM( 'C', 'N', K-L, N, M, ONE, V( 1, KP ), LDV, \$ B, LDB, ZERO, WORK( KP, 1 ), LDWORK ) * DO J = 1, N DO I = 1, K WORK( I, J ) = WORK( I, J ) + A( I, J ) END DO END DO * CALL CTRMM( 'L', 'U', TRANS, 'N', K, N, ONE, T, LDT, \$ WORK, LDWORK ) * DO J = 1, N DO I = 1, K A( I, J ) = A( I, J ) - WORK( I, J ) END DO END DO * CALL CGEMM( 'N', 'N', M-L, N, K, -ONE, V, LDV, WORK, LDWORK, \$ ONE, B, LDB ) CALL CGEMM( 'N', 'N', L, N, K-L, -ONE, V( MP, KP ), LDV, \$ WORK( KP, 1 ), LDWORK, ONE, B( MP, 1 ), LDB ) CALL CTRMM( 'L', 'U', 'N', 'N', L, N, ONE, V( MP, 1 ), LDV, \$ WORK, LDWORK ) DO J = 1, N DO I = 1, L B( M-L+I, J ) = B( M-L+I, J ) - WORK( I, J ) END DO END DO * * --------------------------------------------------------------------------- * ELSE IF( COLUMN .AND. FORWARD .AND. RIGHT ) THEN * * --------------------------------------------------------------------------- * * Let W = [ I ] (K-by-K) * [ V ] (N-by-K) * * Form C H or C H**H where C = [ A B ] (A is M-by-K, B is M-by-N) * * H = I - W T W**H or H**H = I - W T**H W**H * * A = A - (A + B V) T or A = A - (A + B V) T**H * B = B - (A + B V) T V**H or B = B - (A + B V) T**H V**H * * --------------------------------------------------------------------------- * NP = MIN( N-L+1, N ) KP = MIN( L+1, K ) * DO J = 1, L DO I = 1, M WORK( I, J ) = B( I, N-L+J ) END DO END DO CALL CTRMM( 'R', 'U', 'N', 'N', M, L, ONE, V( NP, 1 ), LDV, \$ WORK, LDWORK ) CALL CGEMM( 'N', 'N', M, L, N-L, ONE, B, LDB, \$ V, LDV, ONE, WORK, LDWORK ) CALL CGEMM( 'N', 'N', M, K-L, N, ONE, B, LDB, \$ V( 1, KP ), LDV, ZERO, WORK( 1, KP ), LDWORK ) * DO J = 1, K DO I = 1, M WORK( I, J ) = WORK( I, J ) + A( I, J ) END DO END DO * CALL CTRMM( 'R', 'U', TRANS, 'N', M, K, ONE, T, LDT, \$ WORK, LDWORK ) * DO J = 1, K DO I = 1, M A( I, J ) = A( I, J ) - WORK( I, J ) END DO END DO * CALL CGEMM( 'N', 'C', M, N-L, K, -ONE, WORK, LDWORK, \$ V, LDV, ONE, B, LDB ) CALL CGEMM( 'N', 'C', M, L, K-L, -ONE, WORK( 1, KP ), LDWORK, \$ V( NP, KP ), LDV, ONE, B( 1, NP ), LDB ) CALL CTRMM( 'R', 'U', 'C', 'N', M, L, ONE, V( NP, 1 ), LDV, \$ WORK, LDWORK ) DO J = 1, L DO I = 1, M B( I, N-L+J ) = B( I, N-L+J ) - WORK( I, J ) END DO END DO * * --------------------------------------------------------------------------- * ELSE IF( COLUMN .AND. BACKWARD .AND. LEFT ) THEN * * --------------------------------------------------------------------------- * * Let W = [ V ] (M-by-K) * [ I ] (K-by-K) * * Form H C or H**H C where C = [ B ] (M-by-N) * [ A ] (K-by-N) * * H = I - W T W**H or H**H = I - W T**H W**H * * A = A - T (A + V**H B) or A = A - T**H (A + V**H B) * B = B - V T (A + V**H B) or B = B - V T**H (A + V**H B) * * --------------------------------------------------------------------------- * MP = MIN( L+1, M ) KP = MIN( K-L+1, K ) * DO J = 1, N DO I = 1, L WORK( K-L+I, J ) = B( I, J ) END DO END DO * CALL CTRMM( 'L', 'L', 'C', 'N', L, N, ONE, V( 1, KP ), LDV, \$ WORK( KP, 1 ), LDWORK ) CALL CGEMM( 'C', 'N', L, N, M-L, ONE, V( MP, KP ), LDV, \$ B( MP, 1 ), LDB, ONE, WORK( KP, 1 ), LDWORK ) CALL CGEMM( 'C', 'N', K-L, N, M, ONE, V, LDV, \$ B, LDB, ZERO, WORK, LDWORK ) * DO J = 1, N DO I = 1, K WORK( I, J ) = WORK( I, J ) + A( I, J ) END DO END DO * CALL CTRMM( 'L', 'L', TRANS, 'N', K, N, ONE, T, LDT, \$ WORK, LDWORK ) * DO J = 1, N DO I = 1, K A( I, J ) = A( I, J ) - WORK( I, J ) END DO END DO * CALL CGEMM( 'N', 'N', M-L, N, K, -ONE, V( MP, 1 ), LDV, \$ WORK, LDWORK, ONE, B( MP, 1 ), LDB ) CALL CGEMM( 'N', 'N', L, N, K-L, -ONE, V, LDV, \$ WORK, LDWORK, ONE, B, LDB ) CALL CTRMM( 'L', 'L', 'N', 'N', L, N, ONE, V( 1, KP ), LDV, \$ WORK( KP, 1 ), LDWORK ) DO J = 1, N DO I = 1, L B( I, J ) = B( I, J ) - WORK( K-L+I, J ) END DO END DO * * --------------------------------------------------------------------------- * ELSE IF( COLUMN .AND. BACKWARD .AND. RIGHT ) THEN * * --------------------------------------------------------------------------- * * Let W = [ V ] (N-by-K) * [ I ] (K-by-K) * * Form C H or C H**H where C = [ B A ] (B is M-by-N, A is M-by-K) * * H = I - W T W**H or H**H = I - W T**H W**H * * A = A - (A + B V) T or A = A - (A + B V) T**H * B = B - (A + B V) T V**H or B = B - (A + B V) T**H V**H * * --------------------------------------------------------------------------- * NP = MIN( L+1, N ) KP = MIN( K-L+1, K ) * DO J = 1, L DO I = 1, M WORK( I, K-L+J ) = B( I, J ) END DO END DO CALL CTRMM( 'R', 'L', 'N', 'N', M, L, ONE, V( 1, KP ), LDV, \$ WORK( 1, KP ), LDWORK ) CALL CGEMM( 'N', 'N', M, L, N-L, ONE, B( 1, NP ), LDB, \$ V( NP, KP ), LDV, ONE, WORK( 1, KP ), LDWORK ) CALL CGEMM( 'N', 'N', M, K-L, N, ONE, B, LDB, \$ V, LDV, ZERO, WORK, LDWORK ) * DO J = 1, K DO I = 1, M WORK( I, J ) = WORK( I, J ) + A( I, J ) END DO END DO * CALL CTRMM( 'R', 'L', TRANS, 'N', M, K, ONE, T, LDT, \$ WORK, LDWORK ) * DO J = 1, K DO I = 1, M A( I, J ) = A( I, J ) - WORK( I, J ) END DO END DO * CALL CGEMM( 'N', 'C', M, N-L, K, -ONE, WORK, LDWORK, \$ V( NP, 1 ), LDV, ONE, B( 1, NP ), LDB ) CALL CGEMM( 'N', 'C', M, L, K-L, -ONE, WORK, LDWORK, \$ V, LDV, ONE, B, LDB ) CALL CTRMM( 'R', 'L', 'C', 'N', M, L, ONE, V( 1, KP ), LDV, \$ WORK( 1, KP ), LDWORK ) DO J = 1, L DO I = 1, M B( I, J ) = B( I, J ) - WORK( I, K-L+J ) END DO END DO * * --------------------------------------------------------------------------- * ELSE IF( ROW .AND. FORWARD .AND. LEFT ) THEN * * --------------------------------------------------------------------------- * * Let W = [ I V ] ( I is K-by-K, V is K-by-M ) * * Form H C or H**H C where C = [ A ] (K-by-N) * [ B ] (M-by-N) * * H = I - W**H T W or H**H = I - W**H T**H W * * A = A - T (A + V B) or A = A - T**H (A + V B) * B = B - V**H T (A + V B) or B = B - V**H T**H (A + V B) * * --------------------------------------------------------------------------- * MP = MIN( M-L+1, M ) KP = MIN( L+1, K ) * DO J = 1, N DO I = 1, L WORK( I, J ) = B( M-L+I, J ) END DO END DO CALL CTRMM( 'L', 'L', 'N', 'N', L, N, ONE, V( 1, MP ), LDV, \$ WORK, LDB ) CALL CGEMM( 'N', 'N', L, N, M-L, ONE, V, LDV,B, LDB, \$ ONE, WORK, LDWORK ) CALL CGEMM( 'N', 'N', K-L, N, M, ONE, V( KP, 1 ), LDV, \$ B, LDB, ZERO, WORK( KP, 1 ), LDWORK ) * DO J = 1, N DO I = 1, K WORK( I, J ) = WORK( I, J ) + A( I, J ) END DO END DO * CALL CTRMM( 'L', 'U', TRANS, 'N', K, N, ONE, T, LDT, \$ WORK, LDWORK ) * DO J = 1, N DO I = 1, K A( I, J ) = A( I, J ) - WORK( I, J ) END DO END DO * CALL CGEMM( 'C', 'N', M-L, N, K, -ONE, V, LDV, WORK, LDWORK, \$ ONE, B, LDB ) CALL CGEMM( 'C', 'N', L, N, K-L, -ONE, V( KP, MP ), LDV, \$ WORK( KP, 1 ), LDWORK, ONE, B( MP, 1 ), LDB ) CALL CTRMM( 'L', 'L', 'C', 'N', L, N, ONE, V( 1, MP ), LDV, \$ WORK, LDWORK ) DO J = 1, N DO I = 1, L B( M-L+I, J ) = B( M-L+I, J ) - WORK( I, J ) END DO END DO * * --------------------------------------------------------------------------- * ELSE IF( ROW .AND. FORWARD .AND. RIGHT ) THEN * * --------------------------------------------------------------------------- * * Let W = [ I V ] ( I is K-by-K, V is K-by-N ) * * Form C H or C H**H where C = [ A B ] (A is M-by-K, B is M-by-N) * * H = I - W**H T W or H**H = I - W**H T**H W * * A = A - (A + B V**H) T or A = A - (A + B V**H) T**H * B = B - (A + B V**H) T V or B = B - (A + B V**H) T**H V * * --------------------------------------------------------------------------- * NP = MIN( N-L+1, N ) KP = MIN( L+1, K ) * DO J = 1, L DO I = 1, M WORK( I, J ) = B( I, N-L+J ) END DO END DO CALL CTRMM( 'R', 'L', 'C', 'N', M, L, ONE, V( 1, NP ), LDV, \$ WORK, LDWORK ) CALL CGEMM( 'N', 'C', M, L, N-L, ONE, B, LDB, V, LDV, \$ ONE, WORK, LDWORK ) CALL CGEMM( 'N', 'C', M, K-L, N, ONE, B, LDB, \$ V( KP, 1 ), LDV, ZERO, WORK( 1, KP ), LDWORK ) * DO J = 1, K DO I = 1, M WORK( I, J ) = WORK( I, J ) + A( I, J ) END DO END DO * CALL CTRMM( 'R', 'U', TRANS, 'N', M, K, ONE, T, LDT, \$ WORK, LDWORK ) * DO J = 1, K DO I = 1, M A( I, J ) = A( I, J ) - WORK( I, J ) END DO END DO * CALL CGEMM( 'N', 'N', M, N-L, K, -ONE, WORK, LDWORK, \$ V, LDV, ONE, B, LDB ) CALL CGEMM( 'N', 'N', M, L, K-L, -ONE, WORK( 1, KP ), LDWORK, \$ V( KP, NP ), LDV, ONE, B( 1, NP ), LDB ) CALL CTRMM( 'R', 'L', 'N', 'N', M, L, ONE, V( 1, NP ), LDV, \$ WORK, LDWORK ) DO J = 1, L DO I = 1, M B( I, N-L+J ) = B( I, N-L+J ) - WORK( I, J ) END DO END DO * * --------------------------------------------------------------------------- * ELSE IF( ROW .AND. BACKWARD .AND. LEFT ) THEN * * --------------------------------------------------------------------------- * * Let W = [ V I ] ( I is K-by-K, V is K-by-M ) * * Form H C or H**H C where C = [ B ] (M-by-N) * [ A ] (K-by-N) * * H = I - W**H T W or H**H = I - W**H T**H W * * A = A - T (A + V B) or A = A - T**H (A + V B) * B = B - V**H T (A + V B) or B = B - V**H T**H (A + V B) * * --------------------------------------------------------------------------- * MP = MIN( L+1, M ) KP = MIN( K-L+1, K ) * DO J = 1, N DO I = 1, L WORK( K-L+I, J ) = B( I, J ) END DO END DO CALL CTRMM( 'L', 'U', 'N', 'N', L, N, ONE, V( KP, 1 ), LDV, \$ WORK( KP, 1 ), LDWORK ) CALL CGEMM( 'N', 'N', L, N, M-L, ONE, V( KP, MP ), LDV, \$ B( MP, 1 ), LDB, ONE, WORK( KP, 1 ), LDWORK ) CALL CGEMM( 'N', 'N', K-L, N, M, ONE, V, LDV, B, LDB, \$ ZERO, WORK, LDWORK ) * DO J = 1, N DO I = 1, K WORK( I, J ) = WORK( I, J ) + A( I, J ) END DO END DO * CALL CTRMM( 'L', 'L ', TRANS, 'N', K, N, ONE, T, LDT, \$ WORK, LDWORK ) * DO J = 1, N DO I = 1, K A( I, J ) = A( I, J ) - WORK( I, J ) END DO END DO * CALL CGEMM( 'C', 'N', M-L, N, K, -ONE, V( 1, MP ), LDV, \$ WORK, LDWORK, ONE, B( MP, 1 ), LDB ) CALL CGEMM( 'C', 'N', L, N, K-L, -ONE, V, LDV, \$ WORK, LDWORK, ONE, B, LDB ) CALL CTRMM( 'L', 'U', 'C', 'N', L, N, ONE, V( KP, 1 ), LDV, \$ WORK( KP, 1 ), LDWORK ) DO J = 1, N DO I = 1, L B( I, J ) = B( I, J ) - WORK( K-L+I, J ) END DO END DO * * --------------------------------------------------------------------------- * ELSE IF( ROW .AND. BACKWARD .AND. RIGHT ) THEN * * --------------------------------------------------------------------------- * * Let W = [ V I ] ( I is K-by-K, V is K-by-N ) * * Form C H or C H**H where C = [ B A ] (A is M-by-K, B is M-by-N) * * H = I - W**H T W or H**H = I - W**H T**H W * * A = A - (A + B V**H) T or A = A - (A + B V**H) T**H * B = B - (A + B V**H) T V or B = B - (A + B V**H) T**H V * * --------------------------------------------------------------------------- * NP = MIN( L+1, N ) KP = MIN( K-L+1, K ) * DO J = 1, L DO I = 1, M WORK( I, K-L+J ) = B( I, J ) END DO END DO CALL CTRMM( 'R', 'U', 'C', 'N', M, L, ONE, V( KP, 1 ), LDV, \$ WORK( 1, KP ), LDWORK ) CALL CGEMM( 'N', 'C', M, L, N-L, ONE, B( 1, NP ), LDB, \$ V( KP, NP ), LDV, ONE, WORK( 1, KP ), LDWORK ) CALL CGEMM( 'N', 'C', M, K-L, N, ONE, B, LDB, V, LDV, \$ ZERO, WORK, LDWORK ) * DO J = 1, K DO I = 1, M WORK( I, J ) = WORK( I, J ) + A( I, J ) END DO END DO * CALL CTRMM( 'R', 'L', TRANS, 'N', M, K, ONE, T, LDT, \$ WORK, LDWORK ) * DO J = 1, K DO I = 1, M A( I, J ) = A( I, J ) - WORK( I, J ) END DO END DO * CALL CGEMM( 'N', 'N', M, N-L, K, -ONE, WORK, LDWORK, \$ V( 1, NP ), LDV, ONE, B( 1, NP ), LDB ) CALL CGEMM( 'N', 'N', M, L, K-L , -ONE, WORK, LDWORK, \$ V, LDV, ONE, B, LDB ) CALL CTRMM( 'R', 'U', 'N', 'N', M, L, ONE, V( KP, 1 ), LDV, \$ WORK( 1, KP ), LDWORK ) DO J = 1, L DO I = 1, M B( I, J ) = B( I, J ) - WORK( I, K-L+J ) END DO END DO * END IF * RETURN * * End of CTPRFB * END