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/* lapack/complex16/zgehrd.f -- translated by f2c (version 20050501).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static integer c__65 = 65;
/*< SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) >*/
/* Subroutine */ int zgehrd_(integer *n, integer *ilo, integer *ihi,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Local variables */
integer i__;
doublecomplex t[4160] /* was [65][64] */;
integer ib;
doublecomplex ei;
integer nb, nh, nx=0, iws, nbmin, iinfo;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, ftnlen, ftnlen), zgehd2_(integer *, integer *, integer
*, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen),
zlahrd_(integer *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< INTEGER IHI, ILO, INFO, LDA, LWORK, N >*/
/* .. */
/* .. Array Arguments .. */
/*< COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZGEHRD reduces a complex general matrix A to upper Hessenberg form H */
/* by a unitary similarity transformation: Q' * A * Q = H . */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* It is assumed that A is already upper triangular in rows */
/* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* set by a previous call to ZGEBAL; otherwise they should be */
/* set to 1 and N respectively. See Further Details. */
/* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N general matrix to be reduced. */
/* On exit, the upper triangle and the first subdiagonal of A */
/* are overwritten with the upper Hessenberg matrix H, and the */
/* elements below the first subdiagonal, with the array TAU, */
/* represent the unitary matrix Q as a product of elementary */
/* reflectors. See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* TAU (output) COMPLEX*16 array, dimension (N-1) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to */
/* zero. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length of the array WORK. LWORK >= max(1,N). */
/* For optimum performance LWORK >= N*NB, where NB is the */
/* optimal blocksize. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of (ihi-ilo) elementary */
/* reflectors */
/* Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a complex scalar, and v is a complex vector with */
/* v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on */
/* exit in A(i+2:ihi,i), and tau in TAU(i). */
/* The contents of A are illustrated by the following example, with */
/* n = 7, ilo = 2 and ihi = 6: */
/* on entry, on exit, */
/* ( a a a a a a a ) ( a a h h h h a ) */
/* ( a a a a a a ) ( a h h h h a ) */
/* ( a a a a a a ) ( h h h h h h ) */
/* ( a a a a a a ) ( v2 h h h h h ) */
/* ( a a a a a a ) ( v2 v3 h h h h ) */
/* ( a a a a a a ) ( v2 v3 v4 h h h ) */
/* ( a ) ( a ) */
/* where a denotes an element of the original matrix A, h denotes a */
/* modified element of the upper Hessenberg matrix H, and vi denotes an */
/* element of the vector defining H(i). */
/* ===================================================================== */
/* .. Parameters .. */
/*< INTEGER NBMAX, LDT >*/
/*< PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) >*/
/*< COMPLEX*16 ZERO, ONE >*/
/*< >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY >*/
/*< >*/
/*< COMPLEX*16 EI >*/
/* .. */
/* .. Local Arrays .. */
/*< COMPLEX*16 T( LDT, NBMAX ) >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL XERBLA, ZGEHD2, ZGEMM, ZLAHRD, ZLARFB >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ILAENV >*/
/*< EXTERNAL ILAENV >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) >*/
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "ZGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nb = min(i__1,i__2);
/*< LWKOPT = N*NB >*/
lwkopt = *n * nb;
/*< WORK( 1 ) = LWKOPT >*/
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( N.LT.0 ) THEN >*/
if (*n < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN >*/
} else if (*ilo < 1 || *ilo > max(1,*n)) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN >*/
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( LDA.LT.MAX( 1, N ) ) THEN >*/
} else if (*lda < max(1,*n)) {
/*< INFO = -5 >*/
*info = -5;
/*< ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < max(1,*n) && ! lquery) {
/*< INFO = -8 >*/
*info = -8;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'ZGEHRD', -INFO ) >*/
i__1 = -(*info);
xerbla_("ZGEHRD", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
/*< DO 10 I = 1, ILO - 1 >*/
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< TAU( I ) = ZERO >*/
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< DO 20 I = MAX( 1, IHI ), N - 1 >*/
i__1 = *n - 1;
for (i__ = max(1,*ihi); i__ <= i__1; ++i__) {
/*< TAU( I ) = ZERO >*/
i__2 = i__;
tau[i__2].r = 0., tau[i__2].i = 0.;
/*< 20 CONTINUE >*/
/* L20: */
}
/* Quick return if possible */
/*< NH = IHI - ILO + 1 >*/
nh = *ihi - *ilo + 1;
/*< IF( NH.LE.1 ) THEN >*/
if (nh <= 1) {
/*< WORK( 1 ) = 1 >*/
work[1].r = 1., work[1].i = 0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< NBMIN = 2 >*/
nbmin = 2;
/*< IWS = 1 >*/
iws = 1;
/*< IF( NB.GT.1 .AND. NB.LT.NH ) THEN >*/
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code */
/* (last block is always handled by unblocked code). */
/*< NX = MAX( NB, ILAENV( 3, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) >*/
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__3, "ZGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
/*< IF( NX.LT.NH ) THEN >*/
if (nx < nh) {
/* Determine if workspace is large enough for blocked code. */
/*< IWS = N*NB >*/
iws = *n * nb;
/*< IF( LWORK.LT.IWS ) THEN >*/
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: determine the */
/* minimum value of NB, and reduce NB or force use of */
/* unblocked code. */
/*< >*/
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEHRD", " ", n, ilo, ihi, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
/*< IF( LWORK.GE.N*NBMIN ) THEN >*/
if (*lwork >= *n * nbmin) {
/*< NB = LWORK / N >*/
nb = *lwork / *n;
/*< ELSE >*/
} else {
/*< NB = 1 >*/
nb = 1;
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< LDWORK = N >*/
ldwork = *n;
/*< IF( NB.LT.NBMIN .OR. NB.GE.NH ) THEN >*/
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
/*< I = ILO >*/
i__ = *ilo;
/*< ELSE >*/
} else {
/* Use blocked code */
/*< DO 30 I = ILO, IHI - 1 - NX, NB >*/
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/*< IB = MIN( NB, IHI-I ) >*/
/* Computing MIN */
i__3 = nb, i__4 = *ihi - i__;
ib = min(i__3,i__4);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the */
/* matrices V and T of the block reflector H = I - V*T*V' */
/* which performs the reduction, and also the matrix Y = A*V*T */
/*< >*/
zlahrd_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, &
c__65, &work[1], &ldwork);
/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the */
/* right, computing A := A - Y * V'. V(i+ib,ib-1) must be set */
/* to 1. */
/*< EI = A( I+IB, I+IB-1 ) >*/
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
ei.r = a[i__3].r, ei.i = a[i__3].i;
/*< A( I+IB, I+IB-1 ) = ONE >*/
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = 1., a[i__3].i = 0.;
/*< >*/
i__3 = *ihi - i__ - ib + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", ihi, &i__3, &ib, &
z__1, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda,
&c_b2, &a[(i__ + ib) * a_dim1 + 1], lda, (ftnlen)12, (
ftnlen)19);
/*< A( I+IB, I+IB-1 ) = EI >*/
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = ei.r, a[i__3].i = ei.i;
/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the */
/* left */
/*< >*/
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise", &
i__3, &i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &
c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &
ldwork, (ftnlen)4, (ftnlen)19, (ftnlen)7, (ftnlen)10);
/*< 30 CONTINUE >*/
/* L30: */
}
/*< END IF >*/
}
/* Use unblocked code to reduce the rest of the matrix */
/*< CALL ZGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO ) >*/
zgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
/*< WORK( 1 ) = IWS >*/
work[1].r = (doublereal) iws, work[1].i = 0.;
/*< RETURN >*/
return 0;
/* End of ZGEHRD */
/*< END >*/
} /* zgehrd_ */
#ifdef __cplusplus
}
#endif
|
