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/* ../../../dependencies/lapack/src/zlatrd.f -- translated by f2c (version 20061008).
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
*/
#include "f2c.h"
/* Table of constant values */
static doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb,
doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau,
doublecomplex *w, integer *ldw, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
doublereal d__1;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
static integer i__, iw;
static doublecomplex alpha;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, ftnlen),
zhemv_(char *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, ftnlen), zaxpy_(integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *,
integer *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to */
/* Hermitian tridiagonal form by a unitary similarity */
/* transformation Q' * A * Q, and returns the matrices V and W which are */
/* needed to apply the transformation to the unreduced part of A. */
/* If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a */
/* matrix, of which the upper triangle is supplied; */
/* if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a */
/* matrix, of which the lower triangle is supplied. */
/* This is an auxiliary routine called by ZHETRD. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER */
/* Specifies whether the upper or lower triangular part of the */
/* Hermitian matrix A is stored: */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* N (input) INTEGER */
/* The order of the matrix A. */
/* NB (input) INTEGER */
/* The number of rows and columns to be reduced. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the Hermitian matrix A. If UPLO = 'U', the leading */
/* n-by-n upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading n-by-n lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* On exit: */
/* if UPLO = 'U', the last NB columns have been reduced to */
/* tridiagonal form, with the diagonal elements overwriting */
/* the diagonal elements of A; the elements above the diagonal */
/* with the array TAU, represent the unitary matrix Q as a */
/* product of elementary reflectors; */
/* if UPLO = 'L', the first NB columns have been reduced to */
/* tridiagonal form, with the diagonal elements overwriting */
/* the diagonal elements of A; the elements below the diagonal */
/* 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). */
/* E (output) DOUBLE PRECISION array, dimension (N-1) */
/* If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */
/* elements of the last NB columns of the reduced matrix; */
/* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */
/* the first NB columns of the reduced matrix. */
/* TAU (output) COMPLEX*16 array, dimension (N-1) */
/* The scalar factors of the elementary reflectors, stored in */
/* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */
/* See Further Details. */
/* W (output) COMPLEX*16 array, dimension (LDW,NB) */
/* The n-by-nb matrix W required to update the unreduced part */
/* of A. */
/* LDW (input) INTEGER */
/* The leading dimension of the array W. LDW >= max(1,N). */
/* Further Details */
/* =============== */
/* If UPLO = 'U', the matrix Q is represented as a product of elementary */
/* reflectors */
/* Q = H(n) H(n-1) . . . H(n-nb+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(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */
/* and tau in TAU(i-1). */
/* If UPLO = 'L', the matrix Q is represented as a product of elementary */
/* reflectors */
/* Q = H(1) H(2) . . . H(nb). */
/* 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 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
/* and tau in TAU(i). */
/* The elements of the vectors v together form the n-by-nb matrix V */
/* which is needed, with W, to apply the transformation to the unreduced */
/* part of the matrix, using a Hermitian rank-2k update of the form: */
/* A := A - V*W' - W*V'. */
/* The contents of A on exit are illustrated by the following examples */
/* with n = 5 and nb = 2: */
/* if UPLO = 'U': if UPLO = 'L': */
/* ( a a a v4 v5 ) ( d ) */
/* ( a a v4 v5 ) ( 1 d ) */
/* ( a 1 v5 ) ( v1 1 a ) */
/* ( d 1 ) ( v1 v2 a a ) */
/* ( d ) ( v1 v2 a a a ) */
/* where d denotes a diagonal element of the reduced matrix, a denotes */
/* an element of the original matrix that is unchanged, and vi denotes */
/* an element of the vector defining H(i). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--e;
--tau;
w_dim1 = *ldw;
w_offset = 1 + w_dim1;
w -= w_offset;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
/* Reduce last NB columns of upper triangle */
i__1 = *n - *nb + 1;
for (i__ = *n; i__ >= i__1; --i__) {
iw = i__ - *n + *nb;
if (i__ < *n) {
/* Update A(1:i,i) */
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
i__2 = *n - i__;
zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw);
i__2 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__, &i__2, &z__1, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12);
i__2 = *n - i__;
zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw);
i__2 = *n - i__;
zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__, &i__2, &z__1, &w[(iw + 1) *
w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12);
i__2 = *n - i__;
zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
}
if (i__ > 1) {
/* Generate elementary reflector H(i) to annihilate */
/* A(1:i-2,i) */
i__2 = i__ - 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = i__ - 1;
zlarfg_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &tau[i__
- 1]);
i__2 = i__ - 1;
e[i__2] = alpha.r;
i__2 = i__ - 1 + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute W(1:i-1,i) */
i__2 = i__ - 1;
zhemv_("Upper", &i__2, &c_b2, &a[a_offset], lda, &a[i__ *
a_dim1 + 1], &c__1, &c_b1, &w[iw * w_dim1 + 1], &c__1,
(ftnlen)5);
if (i__ < *n) {
i__2 = i__ - 1;
i__3 = *n - i__;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &w[(iw
+ 1) * w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &
c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, (
ftnlen)19);
i__2 = i__ - 1;
i__3 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &
c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen)
12);
i__2 = i__ - 1;
i__3 = *n - i__;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[(
i__ + 1) * a_dim1 + 1], lda, &a[i__ * a_dim1 + 1],
&c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, (
ftnlen)19);
i__2 = i__ - 1;
i__3 = *n - i__;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &w[(iw + 1) *
w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &
c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen)
12);
}
i__2 = i__ - 1;
zscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
z__3.r = -.5, z__3.i = -0.;
i__2 = i__ - 1;
z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i =
z__3.r * tau[i__2].i + z__3.i * tau[i__2].r;
i__3 = i__ - 1;
zdotc_(&z__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ *
a_dim1 + 1], &c__1);
z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r *
z__4.i + z__2.i * z__4.r;
alpha.r = z__1.r, alpha.i = z__1.i;
i__2 = i__ - 1;
zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw *
w_dim1 + 1], &c__1);
}
/* L10: */
}
} else {
/* Reduce first NB columns of lower triangle */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i:n,i) */
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
i__2 = i__ - 1;
zlacgv_(&i__2, &w[i__ + w_dim1], ldw);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda,
&w[i__ + w_dim1], ldw, &c_b2, &a[i__ + i__ * a_dim1], &
c__1, (ftnlen)12);
i__2 = i__ - 1;
zlacgv_(&i__2, &w[i__ + w_dim1], ldw);
i__2 = i__ - 1;
zlacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &w[i__ + w_dim1], ldw,
&a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1], &
c__1, (ftnlen)12);
i__2 = i__ - 1;
zlacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
if (i__ < *n) {
/* Generate elementary reflector H(i) to annihilate */
/* A(i+2:n,i) */
i__2 = i__ + 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1,
&tau[i__]);
i__2 = i__;
e[i__2] = alpha.r;
i__2 = i__ + 1 + i__ * a_dim1;
a[i__2].r = 1., a[i__2].i = 0.;
/* Compute W(i+1:n,i) */
i__2 = *n - i__;
zhemv_("Lower", &i__2, &c_b2, &a[i__ + 1 + (i__ + 1) * a_dim1]
, lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[
i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5);
i__2 = *n - i__;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &w[i__ + 1
+ w_dim1], ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19);
i__2 = *n - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 +
a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[
i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12);
i__2 = *n - i__;
i__3 = i__ - 1;
zgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1
+ a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19);
i__2 = *n - i__;
i__3 = i__ - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__2, &i__3, &z__1, &w[i__ + 1 +
w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[
i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12);
i__2 = *n - i__;
zscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
z__3.r = -.5, z__3.i = -0.;
i__2 = i__;
z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i =
z__3.r * tau[i__2].i + z__3.i * tau[i__2].r;
i__3 = *n - i__;
zdotc_(&z__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[
i__ + 1 + i__ * a_dim1], &c__1);
z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r *
z__4.i + z__2.i * z__4.r;
alpha.r = z__1.r, alpha.i = z__1.i;
i__2 = *n - i__;
zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
i__ + 1 + i__ * w_dim1], &c__1);
}
/* L20: */
}
}
return 0;
/* End of ZLATRD */
} /* zlatrd_ */
|
