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/* spteqr.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 real c_b7 = 0.f;
static real c_b8 = 1.f;
static integer c__0 = 0;
static integer c__1 = 1;
/* Subroutine */ int spteqr_(char *compz, integer *n, real *d__, real *e,
real *z__, integer *ldz, real *work, integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real c__[1] /* was [1][1] */;
integer i__;
real vt[1] /* was [1][1] */;
integer nru;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *), slaset_(
char *, integer *, integer *, real *, real *, real *, integer *), sbdsqr_(char *, integer *, integer *, integer *, integer
*, real *, real *, real *, integer *, real *, integer *, real *,
integer *, real *, integer *);
integer icompz;
extern /* Subroutine */ int spttrf_(integer *, real *, real *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SPTEQR computes all eigenvalues and, optionally, eigenvectors of a */
/* symmetric positive definite tridiagonal matrix by first factoring the */
/* matrix using SPTTRF, and then calling SBDSQR to compute the singular */
/* values of the bidiagonal factor. */
/* This routine computes the eigenvalues of the positive definite */
/* tridiagonal matrix to high relative accuracy. This means that if the */
/* eigenvalues range over many orders of magnitude in size, then the */
/* small eigenvalues and corresponding eigenvectors will be computed */
/* more accurately than, for example, with the standard QR method. */
/* The eigenvectors of a full or band symmetric positive definite matrix */
/* can also be found if SSYTRD, SSPTRD, or SSBTRD has been used to */
/* reduce this matrix to tridiagonal form. (The reduction to tridiagonal */
/* form, however, may preclude the possibility of obtaining high */
/* relative accuracy in the small eigenvalues of the original matrix, if */
/* these eigenvalues range over many orders of magnitude.) */
/* Arguments */
/* ========= */
/* COMPZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only. */
/* = 'V': Compute eigenvectors of original symmetric */
/* matrix also. Array Z contains the orthogonal */
/* matrix used to reduce the original matrix to */
/* tridiagonal form. */
/* = 'I': Compute eigenvectors of tridiagonal matrix also. */
/* N (input) INTEGER */
/* The order of the matrix. N >= 0. */
/* D (input/output) REAL array, dimension (N) */
/* On entry, the n diagonal elements of the tridiagonal */
/* matrix. */
/* On normal exit, D contains the eigenvalues, in descending */
/* order. */
/* E (input/output) REAL array, dimension (N-1) */
/* On entry, the (n-1) subdiagonal elements of the tridiagonal */
/* matrix. */
/* On exit, E has been destroyed. */
/* Z (input/output) REAL array, dimension (LDZ, N) */
/* On entry, if COMPZ = 'V', the orthogonal matrix used in the */
/* reduction to tridiagonal form. */
/* On exit, if COMPZ = 'V', the orthonormal eigenvectors of the */
/* original symmetric matrix; */
/* if COMPZ = 'I', the orthonormal eigenvectors of the */
/* tridiagonal matrix. */
/* If INFO > 0 on exit, Z contains the eigenvectors associated */
/* with only the stored eigenvalues. */
/* If COMPZ = 'N', then Z is not referenced. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1, and if */
/* COMPZ = 'V' or 'I', LDZ >= max(1,N). */
/* WORK (workspace) REAL array, dimension (4*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = i, and i is: */
/* <= N the Cholesky factorization of the matrix could */
/* not be performed because the i-th principal minor */
/* was not positive definite. */
/* > N the SVD algorithm failed to converge; */
/* if INFO = N+i, i off-diagonal elements of the */
/* bidiagonal factor did not converge to zero. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
--e;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
/* Function Body */
*info = 0;
if (lsame_(compz, "N")) {
icompz = 0;
} else if (lsame_(compz, "V")) {
icompz = 1;
} else if (lsame_(compz, "I")) {
icompz = 2;
} else {
icompz = -1;
}
if (icompz < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SPTEQR", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
if (icompz > 0) {
z__[z_dim1 + 1] = 1.f;
}
return 0;
}
if (icompz == 2) {
slaset_("Full", n, n, &c_b7, &c_b8, &z__[z_offset], ldz);
}
/* Call SPTTRF to factor the matrix. */
spttrf_(n, &d__[1], &e[1], info);
if (*info != 0) {
return 0;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = sqrt(d__[i__]);
/* L10: */
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] *= d__[i__];
/* L20: */
}
/* Call SBDSQR to compute the singular values/vectors of the */
/* bidiagonal factor. */
if (icompz > 0) {
nru = *n;
} else {
nru = 0;
}
sbdsqr_("Lower", n, &c__0, &nru, &c__0, &d__[1], &e[1], vt, &c__1, &z__[
z_offset], ldz, c__, &c__1, &work[1], info);
/* Square the singular values. */
if (*info == 0) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] *= d__[i__];
/* L30: */
}
} else {
*info = *n + *info;
}
return 0;
/* End of SPTEQR */
} /* spteqr_ */
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