| *> \brief \b DLARFT |
| * |
| * =========== DOCUMENTATION =========== |
| * |
| * Online html documentation available at |
| * http://www.netlib.org/lapack/explore-html/ |
| * |
| *> \htmlonly |
| *> Download DLARFT + dependencies |
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| *> [TGZ]</a> |
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| *> [ZIP]</a> |
| *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarft.f"> |
| *> [TXT]</a> |
| *> \endhtmlonly |
| * |
| * Definition: |
| * =========== |
| * |
| * SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) |
| * |
| * .. Scalar Arguments .. |
| * CHARACTER DIRECT, STOREV |
| * INTEGER K, LDT, LDV, N |
| * .. |
| * .. Array Arguments .. |
| * DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) |
| * .. |
| * |
| * |
| *> \par Purpose: |
| * ============= |
| *> |
| *> \verbatim |
| *> |
| *> DLARFT forms the triangular factor T of a real block reflector H |
| *> of order n, which is defined as a product of k elementary reflectors. |
| *> |
| *> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; |
| *> |
| *> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. |
| *> |
| *> If STOREV = 'C', the vector which defines the elementary reflector |
| *> H(i) is stored in the i-th column of the array V, and |
| *> |
| *> H = I - V * T * V**T |
| *> |
| *> If STOREV = 'R', the vector which defines the elementary reflector |
| *> H(i) is stored in the i-th row of the array V, and |
| *> |
| *> H = I - V**T * T * V |
| *> \endverbatim |
| * |
| * Arguments: |
| * ========== |
| * |
| *> \param[in] DIRECT |
| *> \verbatim |
| *> DIRECT is CHARACTER*1 |
| *> Specifies the order in which the elementary reflectors are |
| *> multiplied to form the block reflector: |
| *> = '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 |
| *> Specifies how the vectors which define the elementary |
| *> reflectors are stored (see also Further Details): |
| *> = 'C': columnwise |
| *> = 'R': rowwise |
| *> \endverbatim |
| *> |
| *> \param[in] N |
| *> \verbatim |
| *> N is INTEGER |
| *> The order of the block reflector H. N >= 0. |
| *> \endverbatim |
| *> |
| *> \param[in] K |
| *> \verbatim |
| *> K is INTEGER |
| *> The order of the triangular factor T (= the number of |
| *> elementary reflectors). K >= 1. |
| *> \endverbatim |
| *> |
| *> \param[in] V |
| *> \verbatim |
| *> V is DOUBLE PRECISION array, dimension |
| *> (LDV,K) if STOREV = 'C' |
| *> (LDV,N) if STOREV = 'R' |
| *> The matrix V. See further details. |
| *> \endverbatim |
| *> |
| *> \param[in] LDV |
| *> \verbatim |
| *> LDV is INTEGER |
| *> The leading dimension of the array V. |
| *> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. |
| *> \endverbatim |
| *> |
| *> \param[in] TAU |
| *> \verbatim |
| *> TAU is DOUBLE PRECISION array, dimension (K) |
| *> TAU(i) must contain the scalar factor of the elementary |
| *> reflector H(i). |
| *> \endverbatim |
| *> |
| *> \param[out] T |
| *> \verbatim |
| *> T is DOUBLE PRECISION array, dimension (LDT,K) |
| *> The k by k triangular factor T of the block reflector. |
| *> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is |
| *> lower triangular. The rest of the array is not used. |
| *> \endverbatim |
| *> |
| *> \param[in] LDT |
| *> \verbatim |
| *> LDT is INTEGER |
| *> The leading dimension of the array T. LDT >= K. |
| *> \endverbatim |
| * |
| * Authors: |
| * ======== |
| * |
| *> \author Univ. of Tennessee |
| *> \author Univ. of California Berkeley |
| *> \author Univ. of Colorado Denver |
| *> \author NAG Ltd. |
| * |
| *> \date April 2012 |
| * |
| *> \ingroup doubleOTHERauxiliary |
| * |
| *> \par Further Details: |
| * ===================== |
| *> |
| *> \verbatim |
| *> |
| *> The shape of the matrix V and the storage of the vectors which define |
| *> the H(i) is best illustrated by the following example with n = 5 and |
| *> k = 3. The elements equal to 1 are not stored. |
| *> |
| *> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': |
| *> |
| *> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) |
| *> ( v1 1 ) ( 1 v2 v2 v2 ) |
| *> ( v1 v2 1 ) ( 1 v3 v3 ) |
| *> ( v1 v2 v3 ) |
| *> ( v1 v2 v3 ) |
| *> |
| *> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': |
| *> |
| *> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) |
| *> ( v1 v2 v3 ) ( v2 v2 v2 1 ) |
| *> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) |
| *> ( 1 v3 ) |
| *> ( 1 ) |
| *> \endverbatim |
| *> |
| * ===================================================================== |
| SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) |
| * |
| * -- LAPACK auxiliary routine (version 3.4.1) -- |
| * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| * April 2012 |
| * |
| * .. Scalar Arguments .. |
| CHARACTER DIRECT, STOREV |
| INTEGER K, LDT, LDV, N |
| * .. |
| * .. Array Arguments .. |
| DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) |
| * .. |
| * |
| * ===================================================================== |
| * |
| * .. Parameters .. |
| DOUBLE PRECISION ONE, ZERO |
| PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
| * .. |
| * .. Local Scalars .. |
| INTEGER I, J, PREVLASTV, LASTV |
| * .. |
| * .. External Subroutines .. |
| EXTERNAL DGEMV, DTRMV |
| * .. |
| * .. External Functions .. |
| LOGICAL LSAME |
| EXTERNAL LSAME |
| * .. |
| * .. Executable Statements .. |
| * |
| * Quick return if possible |
| * |
| IF( N.EQ.0 ) |
| $ RETURN |
| * |
| IF( LSAME( DIRECT, 'F' ) ) THEN |
| PREVLASTV = N |
| DO I = 1, K |
| PREVLASTV = MAX( I, PREVLASTV ) |
| IF( TAU( I ).EQ.ZERO ) THEN |
| * |
| * H(i) = I |
| * |
| DO J = 1, I |
| T( J, I ) = ZERO |
| END DO |
| ELSE |
| * |
| * general case |
| * |
| IF( LSAME( STOREV, 'C' ) ) THEN |
| * Skip any trailing zeros. |
| DO LASTV = N, I+1, -1 |
| IF( V( LASTV, I ).NE.ZERO ) EXIT |
| END DO |
| DO J = 1, I-1 |
| T( J, I ) = -TAU( I ) * V( I , J ) |
| END DO |
| J = MIN( LASTV, PREVLASTV ) |
| * |
| * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) |
| * |
| CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ), |
| $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, |
| $ T( 1, I ), 1 ) |
| ELSE |
| * Skip any trailing zeros. |
| DO LASTV = N, I+1, -1 |
| IF( V( I, LASTV ).NE.ZERO ) EXIT |
| END DO |
| DO J = 1, I-1 |
| T( J, I ) = -TAU( I ) * V( J , I ) |
| END DO |
| J = MIN( LASTV, PREVLASTV ) |
| * |
| * T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T |
| * |
| CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ), |
| $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE, |
| $ T( 1, I ), 1 ) |
| END IF |
| * |
| * T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) |
| * |
| CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, |
| $ LDT, T( 1, I ), 1 ) |
| T( I, I ) = TAU( I ) |
| IF( I.GT.1 ) THEN |
| PREVLASTV = MAX( PREVLASTV, LASTV ) |
| ELSE |
| PREVLASTV = LASTV |
| END IF |
| END IF |
| END DO |
| ELSE |
| PREVLASTV = 1 |
| DO I = K, 1, -1 |
| IF( TAU( I ).EQ.ZERO ) THEN |
| * |
| * H(i) = I |
| * |
| DO J = I, K |
| T( J, I ) = ZERO |
| END DO |
| ELSE |
| * |
| * general case |
| * |
| IF( I.LT.K ) THEN |
| IF( LSAME( STOREV, 'C' ) ) THEN |
| * Skip any leading zeros. |
| DO LASTV = 1, I-1 |
| IF( V( LASTV, I ).NE.ZERO ) EXIT |
| END DO |
| DO J = I+1, K |
| T( J, I ) = -TAU( I ) * V( N-K+I , J ) |
| END DO |
| J = MAX( LASTV, PREVLASTV ) |
| * |
| * T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) |
| * |
| CALL DGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ), |
| $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, |
| $ T( I+1, I ), 1 ) |
| ELSE |
| * Skip any leading zeros. |
| DO LASTV = 1, I-1 |
| IF( V( I, LASTV ).NE.ZERO ) EXIT |
| END DO |
| DO J = I+1, K |
| T( J, I ) = -TAU( I ) * V( J, N-K+I ) |
| END DO |
| J = MAX( LASTV, PREVLASTV ) |
| * |
| * T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T |
| * |
| CALL DGEMV( 'No transpose', K-I, N-K+I-J, |
| $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, |
| $ ONE, T( I+1, I ), 1 ) |
| END IF |
| * |
| * T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) |
| * |
| CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, |
| $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) |
| IF( I.GT.1 ) THEN |
| PREVLASTV = MIN( PREVLASTV, LASTV ) |
| ELSE |
| PREVLASTV = LASTV |
| END IF |
| END IF |
| T( I, I ) = TAU( I ) |
| END IF |
| END DO |
| END IF |
| RETURN |
| * |
| * End of DLARFT |
| * |
| END |
