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lapack/SRC/stprfb.f
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*> \brief \b STPRFB 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 STPRFB + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stprfb.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stprfb.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stprfb.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE STPRFB( 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 ..
* REAL A( LDA, * ), B( LDB, * ), T( LDT, * ),
* $ V( LDV, * ), WORK( LDWORK, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> STPRFB applies a real "triangular-pentagonal" block reflector H or its
*> conjugate transpose H^H to a real 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 REAL 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 REAL 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 REAL 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', LDA >= max(1,K);
*> If SIDE = 'R', LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is REAL 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 REAL 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.
*
*> \ingroup realOTHERauxiliary
*
*> \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 STPRFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L,
$ V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER DIRECT, SIDE, STOREV, TRANS
INTEGER K, L, LDA, LDB, LDT, LDV, LDWORK, M, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), T( LDT, * ),
$ V( LDV, * ), WORK( LDWORK, * )
* ..
*
* ==========================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0, ZERO = 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 SGEMM, STRMM
* ..
* .. 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 STRMM( 'L', 'U', 'T', 'N', L, N, ONE, V( MP, 1 ), LDV,
$ WORK, LDWORK )
CALL SGEMM( 'T', 'N', L, N, M-L, ONE, V, LDV, B, LDB,
$ ONE, WORK, LDWORK )
CALL SGEMM( 'T', '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 STRMM( '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 SGEMM( 'N', 'N', M-L, N, K, -ONE, V, LDV, WORK, LDWORK,
$ ONE, B, LDB )
CALL SGEMM( 'N', 'N', L, N, K-L, -ONE, V( MP, KP ), LDV,
$ WORK( KP, 1 ), LDWORK, ONE, B( MP, 1 ), LDB )
CALL STRMM( '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 STRMM( 'R', 'U', 'N', 'N', M, L, ONE, V( NP, 1 ), LDV,
$ WORK, LDWORK )
CALL SGEMM( 'N', 'N', M, L, N-L, ONE, B, LDB,
$ V, LDV, ONE, WORK, LDWORK )
CALL SGEMM( '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 STRMM( '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 SGEMM( 'N', 'T', M, N-L, K, -ONE, WORK, LDWORK,
$ V, LDV, ONE, B, LDB )
CALL SGEMM( 'N', 'T', M, L, K-L, -ONE, WORK( 1, KP ), LDWORK,
$ V( NP, KP ), LDV, ONE, B( 1, NP ), LDB )
CALL STRMM( 'R', 'U', 'T', '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 STRMM( 'L', 'L', 'T', 'N', L, N, ONE, V( 1, KP ), LDV,
$ WORK( KP, 1 ), LDWORK )
CALL SGEMM( 'T', 'N', L, N, M-L, ONE, V( MP, KP ), LDV,
$ B( MP, 1 ), LDB, ONE, WORK( KP, 1 ), LDWORK )
CALL SGEMM( 'T', '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 STRMM( '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 SGEMM( 'N', 'N', M-L, N, K, -ONE, V( MP, 1 ), LDV,
$ WORK, LDWORK, ONE, B( MP, 1 ), LDB )
CALL SGEMM( 'N', 'N', L, N, K-L, -ONE, V, LDV,
$ WORK, LDWORK, ONE, B, LDB )
CALL STRMM( '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 STRMM( 'R', 'L', 'N', 'N', M, L, ONE, V( 1, KP ), LDV,
$ WORK( 1, KP ), LDWORK )
CALL SGEMM( 'N', 'N', M, L, N-L, ONE, B( 1, NP ), LDB,
$ V( NP, KP ), LDV, ONE, WORK( 1, KP ), LDWORK )
CALL SGEMM( '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 STRMM( '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 SGEMM( 'N', 'T', M, N-L, K, -ONE, WORK, LDWORK,
$ V( NP, 1 ), LDV, ONE, B( 1, NP ), LDB )
CALL SGEMM( 'N', 'T', M, L, K-L, -ONE, WORK, LDWORK,
$ V, LDV, ONE, B, LDB )
CALL STRMM( 'R', 'L', 'T', '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 STRMM( 'L', 'L', 'N', 'N', L, N, ONE, V( 1, MP ), LDV,
$ WORK, LDB )
CALL SGEMM( 'N', 'N', L, N, M-L, ONE, V, LDV,B, LDB,
$ ONE, WORK, LDWORK )
CALL SGEMM( '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 STRMM( '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 SGEMM( 'T', 'N', M-L, N, K, -ONE, V, LDV, WORK, LDWORK,
$ ONE, B, LDB )
CALL SGEMM( 'T', 'N', L, N, K-L, -ONE, V( KP, MP ), LDV,
$ WORK( KP, 1 ), LDWORK, ONE, B( MP, 1 ), LDB )
CALL STRMM( 'L', 'L', 'T', '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 STRMM( 'R', 'L', 'T', 'N', M, L, ONE, V( 1, NP ), LDV,
$ WORK, LDWORK )
CALL SGEMM( 'N', 'T', M, L, N-L, ONE, B, LDB, V, LDV,
$ ONE, WORK, LDWORK )
CALL SGEMM( 'N', 'T', 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 STRMM( '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 SGEMM( 'N', 'N', M, N-L, K, -ONE, WORK, LDWORK,
$ V, LDV, ONE, B, LDB )
CALL SGEMM( 'N', 'N', M, L, K-L, -ONE, WORK( 1, KP ), LDWORK,
$ V( KP, NP ), LDV, ONE, B( 1, NP ), LDB )
CALL STRMM( '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 STRMM( 'L', 'U', 'N', 'N', L, N, ONE, V( KP, 1 ), LDV,
$ WORK( KP, 1 ), LDWORK )
CALL SGEMM( 'N', 'N', L, N, M-L, ONE, V( KP, MP ), LDV,
$ B( MP, 1 ), LDB, ONE, WORK( KP, 1 ), LDWORK )
CALL SGEMM( '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 STRMM( '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 SGEMM( 'T', 'N', M-L, N, K, -ONE, V( 1, MP ), LDV,
$ WORK, LDWORK, ONE, B( MP, 1 ), LDB )
CALL SGEMM( 'T', 'N', L, N, K-L, -ONE, V, LDV,
$ WORK, LDWORK, ONE, B, LDB )
CALL STRMM( 'L', 'U', 'T', '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 STRMM( 'R', 'U', 'T', 'N', M, L, ONE, V( KP, 1 ), LDV,
$ WORK( 1, KP ), LDWORK )
CALL SGEMM( 'N', 'T', M, L, N-L, ONE, B( 1, NP ), LDB,
$ V( KP, NP ), LDV, ONE, WORK( 1, KP ), LDWORK )
CALL SGEMM( 'N', 'T', 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 STRMM( '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 SGEMM( 'N', 'N', M, N-L, K, -ONE, WORK, LDWORK,
$ V( 1, NP ), LDV, ONE, B( 1, NP ), LDB )
CALL SGEMM( 'N', 'N', M, L, K-L , -ONE, WORK, LDWORK,
$ V, LDV, ONE, B, LDB )
CALL STRMM( '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 STPRFB
*
END
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