octave-nkf: libcruft/lapack/cgehrd.f annotate

annotate libcruft/lapack/cgehrd.f @ 8203:a9da991c77aa

update contrib.txi

author	John W. Eaton <jwe@octave.org>
date	Wed, 08 Oct 2008 14:29:51 -0400
parents	82be108cc558
children

rev	line source
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	1 SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	2 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	3 * -- LAPACK routine (version 3.1) --
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	5 * November 2006
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	6 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	7 * .. Scalar Arguments ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	8 INTEGER IHI, ILO, INFO, LDA, LWORK, N
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	9 * ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	10 * .. Array Arguments ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	11 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	12 * ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	13 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	14 * Purpose
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	15 * =======
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	16 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	17 * CGEHRD reduces a complex general matrix A to upper Hessenberg form H by
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	18 * an unitary similarity transformation: Q' * A * Q = H .
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	19 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	20 * Arguments
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	21 * =========
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	22 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	23 * N (input) INTEGER
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	24 * The order of the matrix A. N >= 0.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	25 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	26 * ILO (input) INTEGER
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	27 * IHI (input) INTEGER
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	28 * It is assumed that A is already upper triangular in rows
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	29 * and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	30 * set by a previous call to CGEBAL; otherwise they should be
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	31 * set to 1 and N respectively. See Further Details.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	32 * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	33 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	34 * A (input/output) COMPLEX array, dimension (LDA,N)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	35 * On entry, the N-by-N general matrix to be reduced.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	36 * On exit, the upper triangle and the first subdiagonal of A
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	37 * are overwritten with the upper Hessenberg matrix H, and the
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	38 * elements below the first subdiagonal, with the array TAU,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	39 * represent the unitary matrix Q as a product of elementary
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	40 * reflectors. See Further Details.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	41 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	42 * LDA (input) INTEGER
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	43 * The leading dimension of the array A. LDA >= max(1,N).
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	44 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	45 * TAU (output) COMPLEX array, dimension (N-1)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	46 * The scalar factors of the elementary reflectors (see Further
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	47 * Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	48 * zero.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	49 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	50 * WORK (workspace/output) COMPLEX array, dimension (LWORK)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	51 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	52 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	53 * LWORK (input) INTEGER
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	54 * The length of the array WORK. LWORK >= max(1,N).
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	55 * For optimum performance LWORK >= N*NB, where NB is the
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	56 * optimal blocksize.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	57 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	58 * If LWORK = -1, then a workspace query is assumed; the routine
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	59 * only calculates the optimal size of the WORK array, returns
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	60 * this value as the first entry of the WORK array, and no error
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	61 * message related to LWORK is issued by XERBLA.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	62 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	63 * INFO (output) INTEGER
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	64 * = 0: successful exit
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	65 * < 0: if INFO = -i, the i-th argument had an illegal value.
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	66 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	67 * Further Details
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	68 * ===============
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	69 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	70 * The matrix Q is represented as a product of (ihi-ilo) elementary
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	71 * reflectors
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	72 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	73 * Q = H(ilo) H(ilo+1) . . . H(ihi-1).
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	74 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	75 * Each H(i) has the form
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	76 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	77 * H(i) = I - tau * v * v'
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	78 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	79 * where tau is a complex scalar, and v is a complex vector with
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	80 * v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	81 * exit in A(i+2:ihi,i), and tau in TAU(i).
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	82 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	83 * The contents of A are illustrated by the following example, with
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	84 * n = 7, ilo = 2 and ihi = 6:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	85 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	86 * on entry, on exit,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	87 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	88 * ( a a a a a a a ) ( a a h h h h a )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	89 * ( a a a a a a ) ( a h h h h a )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	90 * ( a a a a a a ) ( h h h h h h )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	91 * ( a a a a a a ) ( v2 h h h h h )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	92 * ( a a a a a a ) ( v2 v3 h h h h )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	93 * ( a a a a a a ) ( v2 v3 v4 h h h )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	94 * ( a ) ( a )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	95 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	96 * where a denotes an element of the original matrix A, h denotes a
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	97 * modified element of the upper Hessenberg matrix H, and vi denotes an
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	98 * element of the vector defining H(i).
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	99 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	100 * This file is a slight modification of LAPACK-3.0's CGEHRD
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	101 * subroutine incorporating improvements proposed by Quintana-Orti and
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	102 * Van de Geijn (2005).
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	103 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	104 * =====================================================================
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	105 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	106 * .. Parameters ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	107 INTEGER NBMAX, LDT
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	108 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	109 COMPLEX ZERO, ONE
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	110 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	111 $ ONE = ( 1.0E+0, 0.0E+0 ) )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	112 * ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	113 * .. Local Scalars ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	114 LOGICAL LQUERY
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	115 INTEGER I, IB, IINFO, IWS, J, LDWORK, LWKOPT, NB,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	116 $ NBMIN, NH, NX
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	117 COMPLEX EI
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	118 * ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	119 * .. Local Arrays ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	120 COMPLEX T( LDT, NBMAX )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	121 * ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	122 * .. External Subroutines ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	123 EXTERNAL CAXPY, CGEHD2, CGEMM, CLAHR2, CLARFB, CTRMM,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	124 $ XERBLA
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	125 * ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	126 * .. Intrinsic Functions ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	127 INTRINSIC MAX, MIN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	128 * ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	129 * .. External Functions ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	130 INTEGER ILAENV
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	131 EXTERNAL ILAENV
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	132 * ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	133 * .. Executable Statements ..
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	134 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	135 * Test the input parameters
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	136 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	137 INFO = 0
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	138 NB = MIN( NBMAX, ILAENV( 1, 'CGEHRD', ' ', N, ILO, IHI, -1 ) )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	139 LWKOPT = N*NB
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	140 WORK( 1 ) = LWKOPT
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	141 LQUERY = ( LWORK.EQ.-1 )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	142 IF( N.LT.0 ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	143 INFO = -1
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	144 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	145 INFO = -2
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	146 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	147 INFO = -3
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	148 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	149 INFO = -5
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	150 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	151 INFO = -8
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	152 END IF
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	153 IF( INFO.NE.0 ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	154 CALL XERBLA( 'CGEHRD', -INFO )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	155 RETURN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	156 ELSE IF( LQUERY ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	157 RETURN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	158 END IF
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	159 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	160 * Set elements 1:ILO-1 and IHI:N-1 of TAU to zero
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	161 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	162 DO 10 I = 1, ILO - 1
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	163 TAU( I ) = ZERO
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	164 10 CONTINUE
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	165 DO 20 I = MAX( 1, IHI ), N - 1
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	166 TAU( I ) = ZERO
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	167 20 CONTINUE
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	168 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	169 * Quick return if possible
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	170 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	171 NH = IHI - ILO + 1
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	172 IF( NH.LE.1 ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	173 WORK( 1 ) = 1
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	174 RETURN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	175 END IF
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	176 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	177 * Determine the block size
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	178 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	179 NB = MIN( NBMAX, ILAENV( 1, 'CGEHRD', ' ', N, ILO, IHI, -1 ) )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	180 NBMIN = 2
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	181 IWS = 1
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	182 IF( NB.GT.1 .AND. NB.LT.NH ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	183 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	184 * Determine when to cross over from blocked to unblocked code
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	185 * (last block is always handled by unblocked code)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	186 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	187 NX = MAX( NB, ILAENV( 3, 'CGEHRD', ' ', N, ILO, IHI, -1 ) )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	188 IF( NX.LT.NH ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	189 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	190 * Determine if workspace is large enough for blocked code
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	191 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	192 IWS = N*NB
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	193 IF( LWORK.LT.IWS ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	194 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	195 * Not enough workspace to use optimal NB: determine the
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	196 * minimum value of NB, and reduce NB or force use of
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	197 * unblocked code
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	198 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	199 NBMIN = MAX( 2, ILAENV( 2, 'CGEHRD', ' ', N, ILO, IHI,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	200 $ -1 ) )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	201 IF( LWORK.GE.N*NBMIN ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	202 NB = LWORK / N
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	203 ELSE
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	204 NB = 1
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	205 END IF
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	206 END IF
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	207 END IF
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	208 END IF
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	209 LDWORK = N
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	210 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	211 IF( NB.LT.NBMIN .OR. NB.GE.NH ) THEN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	212 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	213 * Use unblocked code below
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	214 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	215 I = ILO
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	216 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	217 ELSE
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	218 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	219 * Use blocked code
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	220 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	221 DO 40 I = ILO, IHI - 1 - NX, NB
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	222 IB = MIN( NB, IHI-I )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	223 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	224 * Reduce columns i:i+ib-1 to Hessenberg form, returning the
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	225 * matrices V and T of the block reflector H = I - VTV'
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	226 * which performs the reduction, and also the matrix Y = AVT
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	227 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	228 CALL CLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	229 $ WORK, LDWORK )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	230 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	231 * Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	232 * right, computing A := A - Y * V'. V(i+ib,ib-1) must be set
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	233 * to 1
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	234 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	235 EI = A( I+IB, I+IB-1 )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	236 A( I+IB, I+IB-1 ) = ONE
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	237 CALL CGEMM( 'No transpose', 'Conjugate transpose',
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	238 $ IHI, IHI-I-IB+1,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	239 $ IB, -ONE, WORK, LDWORK, A( I+IB, I ), LDA, ONE,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	240 $ A( 1, I+IB ), LDA )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	241 A( I+IB, I+IB-1 ) = EI
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	242 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	243 * Apply the block reflector H to A(1:i,i+1:i+ib-1) from the
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	244 * right
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	245 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	246 CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	247 $ 'Unit', I, IB-1,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	248 $ ONE, A( I+1, I ), LDA, WORK, LDWORK )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	249 DO 30 J = 0, IB-2
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	250 CALL CAXPY( I, -ONE, WORK( LDWORK*J+1 ), 1,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	251 $ A( 1, I+J+1 ), 1 )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	252 30 CONTINUE
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	253 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	254 * Apply the block reflector H to A(i+1:ihi,i+ib:n) from the
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	255 * left
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	256 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	257 CALL CLARFB( 'Left', 'Conjugate transpose', 'Forward',
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	258 $ 'Columnwise',
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	259 $ IHI-I, N-I-IB+1, IB, A( I+1, I ), LDA, T, LDT,
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	260 $ A( I+1, I+IB ), LDA, WORK, LDWORK )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	261 40 CONTINUE
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	262 END IF
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	263 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	264 * Use unblocked code to reduce the rest of the matrix
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	265 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	266 CALL CGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO )
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	267 WORK( 1 ) = IWS
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	268 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	269 RETURN
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	270 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	271 * End of CGEHRD
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	272 *
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: diff changeset	273 END

Mercurial > hg > octave-nkf

annotate libcruft/lapack/cgehrd.f @ 8203:a9da991c77aa