/* sstedc.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__9 = 9;
static integer c__0 = 0;
static integer c__2 = 2;
static real c_b17 = 0.f;
static real c_b18 = 1.f;
static integer c__1 = 1;
/* Subroutine */ int sstedc_(char *compz, integer *n, real *d__, real *e,
real *z__, integer *ldz, real *work, integer *lwork, integer *iwork,
integer *liwork, integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
real r__1, r__2;
/* Builtin functions */
double log(doublereal);
integer pow_ii(integer *, integer *);
double sqrt(doublereal);
/* Local variables */
integer i__, j, k, m;
real p;
integer ii, lgn;
real eps, tiny;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
integer lwmin, start;
extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *,
integer *), slaed0_(integer *, integer *, integer *, real *, real
*, real *, integer *, real *, integer *, real *, integer *,
integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer finish;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *,
real *, integer *), slaset_(char *, integer *, integer *,
real *, real *, real *, integer *);
integer liwmin, icompz;
real orgnrm;
extern doublereal slanst_(char *, integer *, real *, real *);
extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *),
slasrt_(char *, integer *, real *, integer *);
logical lquery;
integer smlsiz;
extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *,
real *, integer *, real *, integer *);
integer storez, strtrw;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SSTEDC computes all eigenvalues and, optionally, eigenvectors of a */
/* symmetric tridiagonal matrix using the divide and conquer method. */
/* The eigenvectors of a full or band real symmetric matrix can also be */
/* found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this */
/* matrix to tridiagonal form. */
/* This code makes very mild assumptions about floating point */
/* arithmetic. It will work on machines with a guard digit in */
/* add/subtract, or on those binary machines without guard digits */
/* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
/* It could conceivably fail on hexadecimal or decimal machines */
/* without guard digits, but we know of none. See SLAED3 for details. */
/* Arguments */
/* ========= */
/* COMPZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only. */
/* = 'I': Compute eigenvectors of tridiagonal matrix also. */
/* = 'V': Compute eigenvectors of original dense symmetric */
/* matrix also. On entry, Z contains the orthogonal */
/* matrix used to reduce the original matrix to */
/* tridiagonal form. */
/* N (input) INTEGER */
/* The dimension of the symmetric tridiagonal matrix. N >= 0. */
/* D (input/output) REAL array, dimension (N) */
/* On entry, the diagonal elements of the tridiagonal matrix. */
/* On exit, if INFO = 0, the eigenvalues in ascending order. */
/* E (input/output) REAL array, dimension (N-1) */
/* On entry, the 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', then Z contains the orthogonal */
/* matrix used in the reduction to tridiagonal form. */
/* On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */
/* orthonormal eigenvectors of the original symmetric matrix, */
/* and if COMPZ = 'I', Z contains the orthonormal eigenvectors */
/* of the symmetric tridiagonal matrix. */
/* If COMPZ = 'N', then Z is not referenced. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1. */
/* If eigenvectors are desired, then LDZ >= max(1,N). */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. */
/* If COMPZ = 'V' and N > 1 then LWORK must be at least */
/* ( 1 + 3*N + 2*N*lg N + 3*N**2 ), */
/* where lg( N ) = smallest integer k such */
/* that 2**k >= N. */
/* If COMPZ = 'I' and N > 1 then LWORK must be at least */
/* ( 1 + 4*N + N**2 ). */
/* Note that for COMPZ = 'I' or 'V', then if N is less than or */
/* equal to the minimum divide size, usually 25, then LWORK need */
/* only be max(1,2*(N-1)). */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. */
/* If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. */
/* If COMPZ = 'V' and N > 1 then LIWORK must be at least */
/* ( 6 + 6*N + 5*N*lg N ). */
/* If COMPZ = 'I' and N > 1 then LIWORK must be at least */
/* ( 3 + 5*N ). */
/* Note that for COMPZ = 'I' or 'V', then if N is less than or */
/* equal to the minimum divide size, usually 25, then LIWORK */
/* need only be 1. */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the optimal size of the IWORK array, */
/* returns this value as the first entry of the IWORK array, and */
/* no error message related to LIWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: The algorithm failed to compute an eigenvalue while */
/* working on the submatrix lying in rows and columns */
/* INFO/(N+1) through mod(INFO,N+1). */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Jeff Rutter, Computer Science Division, University of California */
/* at Berkeley, USA */
/* Modified by Francoise Tisseur, University of Tennessee. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
--e;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1 || *liwork == -1;
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) {
/* Compute the workspace requirements */
smlsiz = ilaenv_(&c__9, "SSTEDC", " ", &c__0, &c__0, &c__0, &c__0);
if (*n <= 1 || icompz == 0) {
liwmin = 1;
lwmin = 1;
} else if (*n <= smlsiz) {
liwmin = 1;
lwmin = *n - 1 << 1;
} else {
lgn = (integer) (log((real) (*n)) / log(2.f));
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (icompz == 1) {
/* Computing 2nd power */
i__1 = *n;
lwmin = *n * 3 + 1 + (*n << 1) * lgn + i__1 * i__1 * 3;
liwmin = *n * 6 + 6 + *n * 5 * lgn;
} else if (icompz == 2) {
/* Computing 2nd power */
i__1 = *n;
lwmin = (*n << 2) + 1 + i__1 * i__1;
liwmin = *n * 5 + 3;
}
}
work[1] = (real) lwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -8;
} else if (*liwork < liwmin && ! lquery) {
*info = -10;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSTEDC", &i__1);
return 0;
} else if (lquery) {
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 the following conditional clause is removed, then the routine */
/* will use the Divide and Conquer routine to compute only the */
/* eigenvalues, which requires (3N + 3N**2) real workspace and */
/* (2 + 5N + 2N lg(N)) integer workspace. */
/* Since on many architectures SSTERF is much faster than any other */
/* algorithm for finding eigenvalues only, it is used here */
/* as the default. If the conditional clause is removed, then */
/* information on the size of workspace needs to be changed. */
/* If COMPZ = 'N', use SSTERF to compute the eigenvalues. */
if (icompz == 0) {
ssterf_(n, &d__[1], &e[1], info);
goto L50;
}
/* If N is smaller than the minimum divide size (SMLSIZ+1), then */
/* solve the problem with another solver. */
if (*n <= smlsiz) {
ssteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info);
} else {
/* If COMPZ = 'V', the Z matrix must be stored elsewhere for later */
/* use. */
if (icompz == 1) {
storez = *n * *n + 1;
} else {
storez = 1;
}
if (icompz == 2) {
slaset_("Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz);
}
/* Scale. */
orgnrm = slanst_("M", n, &d__[1], &e[1]);
if (orgnrm == 0.f) {
goto L50;
}
eps = slamch_("Epsilon");
start = 1;
/* while ( START <= N ) */
L10:
if (start <= *n) {
/* Let FINISH be the position of the next subdiagonal entry */
/* such that E( FINISH ) <= TINY or FINISH = N if no such */
/* subdiagonal exists. The matrix identified by the elements */
/* between START and FINISH constitutes an independent */
/* sub-problem. */
finish = start;
L20:
if (finish < *n) {
tiny = eps * sqrt((r__1 = d__[finish], dabs(r__1))) * sqrt((
r__2 = d__[finish + 1], dabs(r__2)));
if ((r__1 = e[finish], dabs(r__1)) > tiny) {
++finish;
goto L20;
}
}
/* (Sub) Problem determined. Compute its size and solve it. */
m = finish - start + 1;
if (m == 1) {
start = finish + 1;
goto L10;
}
if (m > smlsiz) {
/* Scale. */
orgnrm = slanst_("M", &m, &d__[start], &e[start]);
slascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[
start], &m, info);
i__1 = m - 1;
i__2 = m - 1;
slascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[
start], &i__2, info);
if (icompz == 1) {
strtrw = 1;
} else {
strtrw = start;
}
slaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw +
start * z_dim1], ldz, &work[1], n, &work[storez], &
iwork[1], info);
if (*info != 0) {
*info = (*info / (m + 1) + start - 1) * (*n + 1) + *info %
(m + 1) + start - 1;
goto L50;
}
/* Scale back. */
slascl_("G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[
start], &m, info);
} else {
if (icompz == 1) {
/* Since QR won't update a Z matrix which is larger than */
/* the length of D, we must solve the sub-problem in a */
/* workspace and then multiply back into Z. */
ssteqr_("I", &m, &d__[start], &e[start], &work[1], &m, &
work[m * m + 1], info);
slacpy_("A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[
storez], n);
sgemm_("N", "N", n, &m, &m, &c_b18, &work[storez], n, &
work[1], &m, &c_b17, &z__[start * z_dim1 + 1],
ldz);
} else if (icompz == 2) {
ssteqr_("I", &m, &d__[start], &e[start], &z__[start +
start * z_dim1], ldz, &work[1], info);
} else {
ssterf_(&m, &d__[start], &e[start], info);
}
if (*info != 0) {
*info = start * (*n + 1) + finish;
goto L50;
}
}
start = finish + 1;
goto L10;
}
/* endwhile */
/* If the problem split any number of times, then the eigenvalues */
/* will not be properly ordered. Here we permute the eigenvalues */
/* (and the associated eigenvectors) into ascending order. */
if (m != *n) {
if (icompz == 0) {
/* Use Quick Sort */
slasrt_("I", n, &d__[1], info);
} else {
/* Use Selection Sort to minimize swaps of eigenvectors */
i__1 = *n;
for (ii = 2; ii <= i__1; ++ii) {
i__ = ii - 1;
k = i__;
p = d__[i__];
i__2 = *n;
for (j = ii; j <= i__2; ++j) {
if (d__[j] < p) {
k = j;
p = d__[j];
}
/* L30: */
}
if (k != i__) {
d__[k] = d__[i__];
d__[i__] = p;
sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k *
z_dim1 + 1], &c__1);
}
/* L40: */
}
}
}
}
L50:
work[1] = (real) lwmin;
iwork[1] = liwmin;
return 0;
/* End of SSTEDC */
} /* sstedc_ */