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/* clatrd.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"
#include "blaswrap.h"
/* Table of constant values */
static complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__1 = 1;
/* Subroutine */ int clatrd_(char *uplo, integer *n, integer *nb, complex *a,
integer *lda, real *e, complex *tau, complex *w, integer *ldw)
{
/* System generated locals */
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
real r__1;
complex q__1, q__2, q__3, q__4;
/* Local variables */
integer i__, iw;
complex alpha;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *), chemv_(char *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, complex *,
integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), clarfg_(integer *, complex *,
complex *, integer *, complex *), clacgv_(integer *, complex *,
integer *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLATRD 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', CLATRD reduces the last NB rows and columns of a */
/* matrix, of which the upper triangle is supplied; */
/* if UPLO = 'L', CLATRD reduces the first NB rows and columns of a */
/* matrix, of which the lower triangle is supplied. */
/* This is an auxiliary routine called by CHETRD. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* 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 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) REAL 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 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 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")) {
/* 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;
r__1 = a[i__3].r;
a[i__2].r = r__1, a[i__2].i = 0.f;
i__2 = *n - i__;
clacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw);
i__2 = *n - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__, &i__2, &q__1, &a[(i__ + 1) *
a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
c_b2, &a[i__ * a_dim1 + 1], &c__1);
i__2 = *n - i__;
clacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw);
i__2 = *n - i__;
clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = *n - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__, &i__2, &q__1, &w[(iw + 1) *
w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b2, &a[i__ * a_dim1 + 1], &c__1);
i__2 = *n - i__;
clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
r__1 = a[i__3].r;
a[i__2].r = r__1, a[i__2].i = 0.f;
}
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;
clarfg_(&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.f, a[i__2].i = 0.f;
/* Compute W(1:i-1,i) */
i__2 = i__ - 1;
chemv_("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);
if (i__ < *n) {
i__2 = i__ - 1;
i__3 = *n - i__;
cgemv_("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);
i__2 = i__ - 1;
i__3 = *n - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__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);
i__2 = i__ - 1;
i__3 = *n - i__;
cgemv_("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);
i__2 = i__ - 1;
i__3 = *n - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__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);
}
i__2 = i__ - 1;
cscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
q__3.r = -.5f, q__3.i = -0.f;
i__2 = i__ - 1;
q__2.r = q__3.r * tau[i__2].r - q__3.i * tau[i__2].i, q__2.i =
q__3.r * tau[i__2].i + q__3.i * tau[i__2].r;
i__3 = i__ - 1;
cdotc_(&q__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ *
a_dim1 + 1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r *
q__4.i + q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = i__ - 1;
caxpy_(&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;
r__1 = a[i__3].r;
a[i__2].r = r__1, a[i__2].i = 0.f;
i__2 = i__ - 1;
clacgv_(&i__2, &w[i__ + w_dim1], ldw);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &a[i__ + a_dim1], lda,
&w[i__ + w_dim1], ldw, &c_b2, &a[i__ + i__ * a_dim1], &
c__1);
i__2 = i__ - 1;
clacgv_(&i__2, &w[i__ + w_dim1], ldw);
i__2 = i__ - 1;
clacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &w[i__ + w_dim1], ldw,
&a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1], &
c__1);
i__2 = i__ - 1;
clacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
i__3 = i__ + i__ * a_dim1;
r__1 = a[i__3].r;
a[i__2].r = r__1, a[i__2].i = 0.f;
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;
clarfg_(&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.f, a[i__2].i = 0.f;
/* Compute W(i+1:n,i) */
i__2 = *n - i__;
chemv_("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);
i__2 = *n - i__;
i__3 = i__ - 1;
cgemv_("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);
i__2 = *n - i__;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &a[i__ + 1 +
a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[
i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
cgemv_("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);
i__2 = *n - i__;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &w[i__ + 1 +
w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[
i__ + 1 + i__ * w_dim1], &c__1);
i__2 = *n - i__;
cscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
q__3.r = -.5f, q__3.i = -0.f;
i__2 = i__;
q__2.r = q__3.r * tau[i__2].r - q__3.i * tau[i__2].i, q__2.i =
q__3.r * tau[i__2].i + q__3.i * tau[i__2].r;
i__3 = *n - i__;
cdotc_(&q__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[
i__ + 1 + i__ * a_dim1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r *
q__4.i + q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = *n - i__;
caxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
i__ + 1 + i__ * w_dim1], &c__1);
}
/* L20: */
}
}
return 0;
/* End of CLATRD */
} /* clatrd_ */
|
