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/* zpbstf.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 integer c__1 = 1;
static doublereal c_b9 = -1.;
/* Subroutine */ int zpbstf_(char *uplo, integer *n, integer *kd,
doublecomplex *ab, integer *ldab, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer j, m, km;
doublereal ajj;
integer kld;
extern /* Subroutine */ int zher_(char *, integer *, doublereal *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern logical lsame_(char *, char *);
logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
integer *, doublereal *, doublecomplex *, integer *), zlacgv_(
integer *, doublecomplex *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZPBSTF computes a split Cholesky factorization of a complex */
/* Hermitian positive definite band matrix A. */
/* This routine is designed to be used in conjunction with ZHBGST. */
/* The factorization has the form A = S**H*S where S is a band matrix */
/* of the same bandwidth as A and the following structure: */
/* S = ( U ) */
/* ( M L ) */
/* where U is upper triangular of order m = (n+kd)/2, and L is lower */
/* triangular of order n-m. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* AB (input/output) COMPLEX*16 array, dimension (LDAB,N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first kd+1 rows of the array. The */
/* j-th column of A is stored in the j-th column of the array AB */
/* as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* On exit, if INFO = 0, the factor S from the split Cholesky */
/* factorization A = S**H*S. See Further Details. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the factorization could not be completed, */
/* because the updated element a(i,i) was negative; the */
/* matrix A is not positive definite. */
/* Further Details */
/* =============== */
/* The band storage scheme is illustrated by the following example, when */
/* N = 7, KD = 2: */
/* S = ( s11 s12 s13 ) */
/* ( s22 s23 s24 ) */
/* ( s33 s34 ) */
/* ( s44 ) */
/* ( s53 s54 s55 ) */
/* ( s64 s65 s66 ) */
/* ( s75 s76 s77 ) */
/* If UPLO = 'U', the array AB holds: */
/* on entry: on exit: */
/* * * a13 a24 a35 a46 a57 * * s13 s24 s53' s64' s75' */
/* * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54' s65' s76' */
/* a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 */
/* If UPLO = 'L', the array AB holds: */
/* on entry: on exit: */
/* a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 */
/* a21 a32 a43 a54 a65 a76 * s12' s23' s34' s54 s65 s76 * */
/* a31 a42 a53 a64 a64 * * s13' s24' s53 s64 s75 * * */
/* Array elements marked * are not used by the routine; s12' denotes */
/* conjg(s12); the diagonal elements of S are real. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*ldab < *kd + 1) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPBSTF", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Computing MAX */
i__1 = 1, i__2 = *ldab - 1;
kld = max(i__1,i__2);
/* Set the splitting point m. */
m = (*n + *kd) / 2;
if (upper) {
/* Factorize A(m+1:n,m+1:n) as L**H*L, and update A(1:m,1:m). */
i__1 = m + 1;
for (j = *n; j >= i__1; --j) {
/* Compute s(j,j) and test for non-positive-definiteness. */
i__2 = *kd + 1 + j * ab_dim1;
ajj = ab[i__2].r;
if (ajj <= 0.) {
i__2 = *kd + 1 + j * ab_dim1;
ab[i__2].r = ajj, ab[i__2].i = 0.;
goto L50;
}
ajj = sqrt(ajj);
i__2 = *kd + 1 + j * ab_dim1;
ab[i__2].r = ajj, ab[i__2].i = 0.;
/* Computing MIN */
i__2 = j - 1;
km = min(i__2,*kd);
/* Compute elements j-km:j-1 of the j-th column and update the */
/* the leading submatrix within the band. */
d__1 = 1. / ajj;
zdscal_(&km, &d__1, &ab[*kd + 1 - km + j * ab_dim1], &c__1);
zher_("Upper", &km, &c_b9, &ab[*kd + 1 - km + j * ab_dim1], &c__1,
&ab[*kd + 1 + (j - km) * ab_dim1], &kld);
/* L10: */
}
/* Factorize the updated submatrix A(1:m,1:m) as U**H*U. */
i__1 = m;
for (j = 1; j <= i__1; ++j) {
/* Compute s(j,j) and test for non-positive-definiteness. */
i__2 = *kd + 1 + j * ab_dim1;
ajj = ab[i__2].r;
if (ajj <= 0.) {
i__2 = *kd + 1 + j * ab_dim1;
ab[i__2].r = ajj, ab[i__2].i = 0.;
goto L50;
}
ajj = sqrt(ajj);
i__2 = *kd + 1 + j * ab_dim1;
ab[i__2].r = ajj, ab[i__2].i = 0.;
/* Computing MIN */
i__2 = *kd, i__3 = m - j;
km = min(i__2,i__3);
/* Compute elements j+1:j+km of the j-th row and update the */
/* trailing submatrix within the band. */
if (km > 0) {
d__1 = 1. / ajj;
zdscal_(&km, &d__1, &ab[*kd + (j + 1) * ab_dim1], &kld);
zlacgv_(&km, &ab[*kd + (j + 1) * ab_dim1], &kld);
zher_("Upper", &km, &c_b9, &ab[*kd + (j + 1) * ab_dim1], &kld,
&ab[*kd + 1 + (j + 1) * ab_dim1], &kld);
zlacgv_(&km, &ab[*kd + (j + 1) * ab_dim1], &kld);
}
/* L20: */
}
} else {
/* Factorize A(m+1:n,m+1:n) as L**H*L, and update A(1:m,1:m). */
i__1 = m + 1;
for (j = *n; j >= i__1; --j) {
/* Compute s(j,j) and test for non-positive-definiteness. */
i__2 = j * ab_dim1 + 1;
ajj = ab[i__2].r;
if (ajj <= 0.) {
i__2 = j * ab_dim1 + 1;
ab[i__2].r = ajj, ab[i__2].i = 0.;
goto L50;
}
ajj = sqrt(ajj);
i__2 = j * ab_dim1 + 1;
ab[i__2].r = ajj, ab[i__2].i = 0.;
/* Computing MIN */
i__2 = j - 1;
km = min(i__2,*kd);
/* Compute elements j-km:j-1 of the j-th row and update the */
/* trailing submatrix within the band. */
d__1 = 1. / ajj;
zdscal_(&km, &d__1, &ab[km + 1 + (j - km) * ab_dim1], &kld);
zlacgv_(&km, &ab[km + 1 + (j - km) * ab_dim1], &kld);
zher_("Lower", &km, &c_b9, &ab[km + 1 + (j - km) * ab_dim1], &kld,
&ab[(j - km) * ab_dim1 + 1], &kld);
zlacgv_(&km, &ab[km + 1 + (j - km) * ab_dim1], &kld);
/* L30: */
}
/* Factorize the updated submatrix A(1:m,1:m) as U**H*U. */
i__1 = m;
for (j = 1; j <= i__1; ++j) {
/* Compute s(j,j) and test for non-positive-definiteness. */
i__2 = j * ab_dim1 + 1;
ajj = ab[i__2].r;
if (ajj <= 0.) {
i__2 = j * ab_dim1 + 1;
ab[i__2].r = ajj, ab[i__2].i = 0.;
goto L50;
}
ajj = sqrt(ajj);
i__2 = j * ab_dim1 + 1;
ab[i__2].r = ajj, ab[i__2].i = 0.;
/* Computing MIN */
i__2 = *kd, i__3 = m - j;
km = min(i__2,i__3);
/* Compute elements j+1:j+km of the j-th column and update the */
/* trailing submatrix within the band. */
if (km > 0) {
d__1 = 1. / ajj;
zdscal_(&km, &d__1, &ab[j * ab_dim1 + 2], &c__1);
zher_("Lower", &km, &c_b9, &ab[j * ab_dim1 + 2], &c__1, &ab[(
j + 1) * ab_dim1 + 1], &kld);
}
/* L40: */
}
}
return 0;
L50:
*info = j;
return 0;
/* End of ZPBSTF */
} /* zpbstf_ */
|
