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389 lines
11 KiB
389 lines
11 KiB
/* -- translated by f2c (version 20201020 (for_lapack)). -- */ |
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#include "f2c.h" |
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//> \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH |
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// |
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// =========== DOCUMENTATION =========== |
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// |
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// Online html documentation available at |
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// http://www.netlib.org/lapack/explore-html/ |
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// |
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//> \htmlonly |
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//> Download DLARFT + dependencies |
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//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarft.f"> |
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//> [TGZ]</a> |
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//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarft.f"> |
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//> [ZIP]</a> |
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//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarft.f"> |
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//> [TXT]</a> |
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//> \endhtmlonly |
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// |
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// Definition: |
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// =========== |
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// |
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// SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) |
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// |
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// .. Scalar Arguments .. |
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// CHARACTER DIRECT, STOREV |
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// INTEGER K, LDT, LDV, N |
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// .. |
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// .. Array Arguments .. |
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// DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) |
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// .. |
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// |
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// |
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//> \par Purpose: |
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// ============= |
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//> |
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//> \verbatim |
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//> |
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//> DLARFT forms the triangular factor T of a real block reflector H |
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//> of order n, which is defined as a product of k elementary reflectors. |
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//> |
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//> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; |
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//> |
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//> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. |
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//> |
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//> If STOREV = 'C', the vector which defines the elementary reflector |
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//> H(i) is stored in the i-th column of the array V, and |
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//> |
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//> H = I - V * T * V**T |
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//> |
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//> If STOREV = 'R', the vector which defines the elementary reflector |
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//> H(i) is stored in the i-th row of the array V, and |
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//> |
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//> H = I - V**T * T * V |
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//> \endverbatim |
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// |
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// Arguments: |
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// ========== |
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// |
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//> \param[in] DIRECT |
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//> \verbatim |
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//> DIRECT is CHARACTER*1 |
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//> Specifies the order in which the elementary reflectors are |
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//> multiplied to form the block reflector: |
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//> = 'F': H = H(1) H(2) . . . H(k) (Forward) |
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//> = 'B': H = H(k) . . . H(2) H(1) (Backward) |
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//> \endverbatim |
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//> |
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//> \param[in] STOREV |
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//> \verbatim |
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//> STOREV is CHARACTER*1 |
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//> Specifies how the vectors which define the elementary |
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//> reflectors are stored (see also Further Details): |
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//> = 'C': columnwise |
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//> = 'R': rowwise |
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//> \endverbatim |
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//> |
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//> \param[in] N |
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//> \verbatim |
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//> N is INTEGER |
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//> The order of the block reflector H. N >= 0. |
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//> \endverbatim |
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//> |
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//> \param[in] K |
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//> \verbatim |
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//> K is INTEGER |
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//> The order of the triangular factor T (= the number of |
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//> elementary reflectors). K >= 1. |
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//> \endverbatim |
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//> |
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//> \param[in] V |
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//> \verbatim |
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//> V is DOUBLE PRECISION array, dimension |
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//> (LDV,K) if STOREV = 'C' |
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//> (LDV,N) if STOREV = 'R' |
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//> The matrix V. See further details. |
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//> \endverbatim |
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//> |
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//> \param[in] LDV |
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//> \verbatim |
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//> LDV is INTEGER |
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//> The leading dimension of the array V. |
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//> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. |
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//> \endverbatim |
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//> |
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//> \param[in] TAU |
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//> \verbatim |
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//> TAU is DOUBLE PRECISION array, dimension (K) |
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//> TAU(i) must contain the scalar factor of the elementary |
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//> reflector H(i). |
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//> \endverbatim |
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//> |
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//> \param[out] T |
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//> \verbatim |
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//> T is DOUBLE PRECISION array, dimension (LDT,K) |
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//> The k by k triangular factor T of the block reflector. |
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//> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is |
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//> lower triangular. The rest of the array is not used. |
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//> \endverbatim |
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//> |
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//> \param[in] LDT |
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//> \verbatim |
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//> LDT is INTEGER |
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//> The leading dimension of the array T. LDT >= K. |
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//> \endverbatim |
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// |
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// Authors: |
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// ======== |
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// |
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//> \author Univ. of Tennessee |
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//> \author Univ. of California Berkeley |
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//> \author Univ. of Colorado Denver |
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//> \author NAG Ltd. |
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// |
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//> \date December 2016 |
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// |
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//> \ingroup doubleOTHERauxiliary |
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// |
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//> \par Further Details: |
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// ===================== |
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//> |
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//> \verbatim |
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//> |
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//> The shape of the matrix V and the storage of the vectors which define |
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//> the H(i) is best illustrated by the following example with n = 5 and |
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//> k = 3. The elements equal to 1 are not stored. |
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//> |
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//> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': |
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//> |
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//> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) |
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//> ( v1 1 ) ( 1 v2 v2 v2 ) |
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//> ( v1 v2 1 ) ( 1 v3 v3 ) |
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//> ( v1 v2 v3 ) |
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//> ( v1 v2 v3 ) |
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//> |
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//> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': |
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//> |
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//> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) |
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//> ( v1 v2 v3 ) ( v2 v2 v2 1 ) |
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//> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) |
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//> ( 1 v3 ) |
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//> ( 1 ) |
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//> \endverbatim |
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//> |
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// ===================================================================== |
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/* Subroutine */ int dlarft_(char *direct, char *storev, int *n, int *k, |
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double *v, int *ldv, double *tau, double *t, int *ldt) |
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{ |
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// Table of constant values |
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int c__1 = 1; |
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double c_b7 = 1.; |
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// System generated locals |
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int t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3; |
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double d__1; |
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// Local variables |
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int i__, j, prevlastv; |
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extern int lsame_(char *, char *); |
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extern /* Subroutine */ int dgemv_(char *, int *, int *, double *, double |
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*, int *, double *, int *, double *, double *, int *); |
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int lastv; |
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extern /* Subroutine */ int dtrmv_(char *, char *, char *, int *, double * |
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, int *, double *, int *); |
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// |
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// -- LAPACK auxiliary routine (version 3.7.0) -- |
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// -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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// -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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// December 2016 |
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// |
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// .. Scalar Arguments .. |
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// .. |
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// .. Array Arguments .. |
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// .. |
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// |
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// ===================================================================== |
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// |
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// .. Parameters .. |
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// .. |
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// .. Local Scalars .. |
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// .. |
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// .. External Subroutines .. |
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// .. |
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// .. External Functions .. |
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// .. |
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// .. Executable Statements .. |
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// |
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// Quick return if possible |
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// |
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// Parameter adjustments |
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v_dim1 = *ldv; |
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v_offset = 1 + v_dim1; |
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v -= v_offset; |
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--tau; |
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t_dim1 = *ldt; |
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t_offset = 1 + t_dim1; |
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t -= t_offset; |
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// Function Body |
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if (*n == 0) { |
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return 0; |
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} |
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if (lsame_(direct, "F")) { |
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prevlastv = *n; |
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i__1 = *k; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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prevlastv = max(i__,prevlastv); |
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if (tau[i__] == 0.) { |
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// |
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// H(i) = I |
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// |
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i__2 = i__; |
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for (j = 1; j <= i__2; ++j) { |
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t[j + i__ * t_dim1] = 0.; |
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} |
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} else { |
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// |
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// general case |
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// |
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if (lsame_(storev, "C")) { |
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// Skip any trailing zeros. |
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i__2 = i__ + 1; |
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for (lastv = *n; lastv >= i__2; --lastv) { |
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if (v[lastv + i__ * v_dim1] != 0.) { |
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break; |
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} |
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} |
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i__2 = i__ - 1; |
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for (j = 1; j <= i__2; ++j) { |
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t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1]; |
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} |
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j = min(lastv,prevlastv); |
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// |
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// T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) |
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// |
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i__2 = j - i__; |
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i__3 = i__ - 1; |
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d__1 = -tau[i__]; |
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dgemv_("Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 + |
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v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, & |
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c_b7, &t[i__ * t_dim1 + 1], &c__1); |
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} else { |
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// Skip any trailing zeros. |
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i__2 = i__ + 1; |
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for (lastv = *n; lastv >= i__2; --lastv) { |
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if (v[i__ + lastv * v_dim1] != 0.) { |
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break; |
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} |
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} |
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i__2 = i__ - 1; |
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for (j = 1; j <= i__2; ++j) { |
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t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1]; |
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} |
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j = min(lastv,prevlastv); |
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// |
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// T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T |
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// |
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i__2 = i__ - 1; |
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i__3 = j - i__; |
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d__1 = -tau[i__]; |
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dgemv_("No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) * |
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v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], |
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ldv, &c_b7, &t[i__ * t_dim1 + 1], &c__1); |
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} |
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// |
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// T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) |
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// |
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i__2 = i__ - 1; |
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dtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[ |
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t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1); |
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t[i__ + i__ * t_dim1] = tau[i__]; |
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if (i__ > 1) { |
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prevlastv = max(prevlastv,lastv); |
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} else { |
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prevlastv = lastv; |
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} |
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} |
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} |
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} else { |
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prevlastv = 1; |
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for (i__ = *k; i__ >= 1; --i__) { |
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if (tau[i__] == 0.) { |
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// |
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// H(i) = I |
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// |
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i__1 = *k; |
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for (j = i__; j <= i__1; ++j) { |
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t[j + i__ * t_dim1] = 0.; |
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} |
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} else { |
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// |
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// general case |
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// |
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if (i__ < *k) { |
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if (lsame_(storev, "C")) { |
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// Skip any leading zeros. |
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i__1 = i__ - 1; |
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for (lastv = 1; lastv <= i__1; ++lastv) { |
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if (v[lastv + i__ * v_dim1] != 0.) { |
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break; |
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} |
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} |
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i__1 = *k; |
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for (j = i__ + 1; j <= i__1; ++j) { |
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t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__ |
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+ j * v_dim1]; |
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} |
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j = max(lastv,prevlastv); |
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// |
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// T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) |
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// |
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i__1 = *n - *k + i__ - j; |
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i__2 = *k - i__; |
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d__1 = -tau[i__]; |
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dgemv_("Transpose", &i__1, &i__2, &d__1, &v[j + (i__ |
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+ 1) * v_dim1], ldv, &v[j + i__ * v_dim1], & |
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c__1, &c_b7, &t[i__ + 1 + i__ * t_dim1], & |
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c__1); |
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} else { |
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// Skip any leading zeros. |
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i__1 = i__ - 1; |
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for (lastv = 1; lastv <= i__1; ++lastv) { |
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if (v[i__ + lastv * v_dim1] != 0.) { |
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break; |
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} |
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} |
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i__1 = *k; |
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for (j = i__ + 1; j <= i__1; ++j) { |
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t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k |
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+ i__) * v_dim1]; |
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} |
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j = max(lastv,prevlastv); |
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// |
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// T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T |
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// |
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i__1 = *k - i__; |
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i__2 = *n - *k + i__ - j; |
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d__1 = -tau[i__]; |
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dgemv_("No transpose", &i__1, &i__2, &d__1, &v[i__ + |
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1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], |
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ldv, &c_b7, &t[i__ + 1 + i__ * t_dim1], &c__1) |
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; |
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} |
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// |
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// T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) |
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// |
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i__1 = *k - i__; |
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dtrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__ |
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+ 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * |
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t_dim1], &c__1); |
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if (i__ > 1) { |
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prevlastv = min(prevlastv,lastv); |
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} else { |
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prevlastv = lastv; |
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} |
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} |
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t[i__ + i__ * t_dim1] = tau[i__]; |
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} |
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} |
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} |
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return 0; |
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// |
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// End of DLARFT |
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// |
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} // dlarft_ |
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