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/* zhegst.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 doublecomplex c_b1 = {1.,0.};
static doublecomplex c_b2 = {.5,0.};
static integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b18 = 1.;
/* Subroutine */ int zhegst_(integer *itype, char *uplo, integer *n,
doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
doublecomplex z__1;
/* Local variables */
integer k, kb, nb;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zhemm_(char *, char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
logical upper;
extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *),
ztrsm_(char *, char *, char *, char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *), zhegs2_(integer *,
char *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *), zher2k_(char *, char *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *,
integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZHEGST reduces a complex Hermitian-definite generalized */
/* eigenproblem to standard form. */
/* If ITYPE = 1, the problem is A*x = lambda*B*x, */
/* and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) */
/* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */
/* B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. */
/* B must have been previously factorized as U**H*U or L*L**H by ZPOTRF. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); */
/* = 2 or 3: compute U*A*U**H or L**H*A*L. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored and B is factored as */
/* U**H*U; */
/* = 'L': Lower triangle of A is stored and B is factored as */
/* L*L**H. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* 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 INFO = 0, the transformed matrix, stored in the */
/* same format as A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input) COMPLEX*16 array, dimension (LDB,N) */
/* The triangular factor from the Cholesky factorization of B, */
/* as returned by ZPOTRF. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHEGST", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine the block size for this environment. */
nb = ilaenv_(&c__1, "ZHEGST", uplo, n, &c_n1, &c_n1, &c_n1);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code */
zhegs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
} else {
/* Use blocked code */
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the upper triangle of A(k:n,k:n) */
zhegs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
ztrsm_("Left", uplo, "Conjugate transpose", "Non-unit"
, &kb, &i__3, &c_b1, &b[k + k * b_dim1], ldb,
&a[k + (k + kb) * a_dim1], lda);
i__3 = *n - k - kb + 1;
z__1.r = -.5, z__1.i = -0.;
zhemm_("Left", uplo, &kb, &i__3, &z__1, &a[k + k *
a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb,
&c_b1, &a[k + (k + kb) * a_dim1], lda);
i__3 = *n - k - kb + 1;
z__1.r = -1., z__1.i = -0.;
zher2k_(uplo, "Conjugate transpose", &i__3, &kb, &
z__1, &a[k + (k + kb) * a_dim1], lda, &b[k + (
k + kb) * b_dim1], ldb, &c_b18, &a[k + kb + (
k + kb) * a_dim1], lda)
;
i__3 = *n - k - kb + 1;
z__1.r = -.5, z__1.i = -0.;
zhemm_("Left", uplo, &kb, &i__3, &z__1, &a[k + k *
a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb,
&c_b1, &a[k + (k + kb) * a_dim1], lda);
i__3 = *n - k - kb + 1;
ztrsm_("Right", uplo, "No transpose", "Non-unit", &kb,
&i__3, &c_b1, &b[k + kb + (k + kb) * b_dim1],
ldb, &a[k + (k + kb) * a_dim1], lda);
}
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L') */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the lower triangle of A(k:n,k:n) */
zhegs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
ztrsm_("Right", uplo, "Conjugate transpose", "Non-un"
"it", &i__3, &kb, &c_b1, &b[k + k * b_dim1],
ldb, &a[k + kb + k * a_dim1], lda);
i__3 = *n - k - kb + 1;
z__1.r = -.5, z__1.i = -0.;
zhemm_("Right", uplo, &i__3, &kb, &z__1, &a[k + k *
a_dim1], lda, &b[k + kb + k * b_dim1], ldb, &
c_b1, &a[k + kb + k * a_dim1], lda);
i__3 = *n - k - kb + 1;
z__1.r = -1., z__1.i = -0.;
zher2k_(uplo, "No transpose", &i__3, &kb, &z__1, &a[k
+ kb + k * a_dim1], lda, &b[k + kb + k *
b_dim1], ldb, &c_b18, &a[k + kb + (k + kb) *
a_dim1], lda);
i__3 = *n - k - kb + 1;
z__1.r = -.5, z__1.i = -0.;
zhemm_("Right", uplo, &i__3, &kb, &z__1, &a[k + k *
a_dim1], lda, &b[k + kb + k * b_dim1], ldb, &
c_b1, &a[k + kb + k * a_dim1], lda);
i__3 = *n - k - kb + 1;
ztrsm_("Left", uplo, "No transpose", "Non-unit", &
i__3, &kb, &c_b1, &b[k + kb + (k + kb) *
b_dim1], ldb, &a[k + kb + k * a_dim1], lda);
}
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U' */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
ztrmm_("Left", uplo, "No transpose", "Non-unit", &i__3, &
kb, &c_b1, &b[b_offset], ldb, &a[k * a_dim1 + 1],
lda);
i__3 = k - 1;
zhemm_("Right", uplo, &i__3, &kb, &c_b2, &a[k + k *
a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b1, &a[
k * a_dim1 + 1], lda);
i__3 = k - 1;
zher2k_(uplo, "No transpose", &i__3, &kb, &c_b1, &a[k *
a_dim1 + 1], lda, &b[k * b_dim1 + 1], ldb, &c_b18,
&a[a_offset], lda);
i__3 = k - 1;
zhemm_("Right", uplo, &i__3, &kb, &c_b2, &a[k + k *
a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b1, &a[
k * a_dim1 + 1], lda);
i__3 = k - 1;
ztrmm_("Right", uplo, "Conjugate transpose", "Non-unit", &
i__3, &kb, &c_b1, &b[k + k * b_dim1], ldb, &a[k *
a_dim1 + 1], lda);
zhegs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info);
/* L30: */
}
} else {
/* Compute L'*A*L */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
ztrmm_("Right", uplo, "No transpose", "Non-unit", &kb, &
i__3, &c_b1, &b[b_offset], ldb, &a[k + a_dim1],
lda);
i__3 = k - 1;
zhemm_("Left", uplo, &kb, &i__3, &c_b2, &a[k + k * a_dim1]
, lda, &b[k + b_dim1], ldb, &c_b1, &a[k + a_dim1],
lda);
i__3 = k - 1;
zher2k_(uplo, "Conjugate transpose", &i__3, &kb, &c_b1, &
a[k + a_dim1], lda, &b[k + b_dim1], ldb, &c_b18, &
a[a_offset], lda);
i__3 = k - 1;
zhemm_("Left", uplo, &kb, &i__3, &c_b2, &a[k + k * a_dim1]
, lda, &b[k + b_dim1], ldb, &c_b1, &a[k + a_dim1],
lda);
i__3 = k - 1;
ztrmm_("Left", uplo, "Conjugate transpose", "Non-unit", &
kb, &i__3, &c_b1, &b[k + k * b_dim1], ldb, &a[k +
a_dim1], lda);
zhegs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info);
/* L40: */
}
}
}
}
return 0;
/* End of ZHEGST */
} /* zhegst_ */
|
