/* sstevr.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__10 = 10;
static integer c__1 = 1;
static integer c__2 = 2;
static integer c__3 = 3;
static integer c__4 = 4;
/* Subroutine */ int sstevr_(char *jobz, char *range, integer *n, real *d__,
real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol,
integer *m, real *w, real *z__, integer *ldz, integer *isuppz, 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 sqrt(doublereal);
/* Local variables */
integer i__, j, jj;
real eps, vll, vuu, tmp1;
integer imax;
real rmin, rmax;
logical test;
real tnrm, sigma;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
char order[1];
integer lwmin;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), sswap_(integer *, real *, integer *, real *, integer *
);
logical wantz, alleig, indeig;
integer iscale, ieeeok, indibl, indifl;
logical valeig;
extern doublereal slamch_(char *);
real safmin;
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
integer indisp, indiwo, liwmin;
logical tryrac;
extern doublereal slanst_(char *, integer *, real *, real *);
extern /* Subroutine */ int sstein_(integer *, real *, real *, integer *,
real *, integer *, integer *, real *, integer *, real *, integer *
, integer *, integer *), ssterf_(integer *, real *, real *,
integer *);
integer nsplit;
extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *,
real *, integer *, integer *, real *, real *, real *, integer *,
integer *, real *, integer *, integer *, real *, integer *,
integer *);
real smlnum;
extern /* Subroutine */ int sstemr_(char *, char *, integer *, real *,
real *, real *, real *, integer *, integer *, integer *, real *,
real *, integer *, integer *, integer *, logical *, real *,
integer *, integer *, integer *, integer *);
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SSTEVR computes selected eigenvalues and, optionally, eigenvectors */
/* of a real symmetric tridiagonal matrix T. Eigenvalues and */
/* eigenvectors can be selected by specifying either a range of values */
/* or a range of indices for the desired eigenvalues. */
/* Whenever possible, SSTEVR calls SSTEMR to compute the */
/* eigenspectrum using Relatively Robust Representations. SSTEMR */
/* computes eigenvalues by the dqds algorithm, while orthogonal */
/* eigenvectors are computed from various "good" L D L^T representations */
/* (also known as Relatively Robust Representations). Gram-Schmidt */
/* orthogonalization is avoided as far as possible. More specifically, */
/* the various steps of the algorithm are as follows. For the i-th */
/* unreduced block of T, */
/* (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T */
/* is a relatively robust representation, */
/* (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high */
/* relative accuracy by the dqds algorithm, */
/* (c) If there is a cluster of close eigenvalues, "choose" sigma_i */
/* close to the cluster, and go to step (a), */
/* (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T, */
/* compute the corresponding eigenvector by forming a */
/* rank-revealing twisted factorization. */
/* The desired accuracy of the output can be specified by the input */
/* parameter ABSTOL. */
/* For more details, see "A new O(n^2) algorithm for the symmetric */
/* tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon, */
/* Computer Science Division Technical Report No. UCB//CSD-97-971, */
/* UC Berkeley, May 1997. */
/* Note 1 : SSTEVR calls SSTEMR when the full spectrum is requested */
/* on machines which conform to the ieee-754 floating point standard. */
/* SSTEVR calls SSTEBZ and SSTEIN on non-ieee machines and */
/* when partial spectrum requests are made. */
/* Normal execution of SSTEMR may create NaNs and infinities and */
/* hence may abort due to a floating point exception in environments */
/* which do not handle NaNs and infinities in the ieee standard default */
/* manner. */
/* Arguments */
/* ========= */
/* JOBZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only; */
/* = 'V': Compute eigenvalues and eigenvectors. */
/* RANGE (input) CHARACTER*1 */
/* = 'A': all eigenvalues will be found. */
/* = 'V': all eigenvalues in the half-open interval (VL,VU] */
/* will be found. */
/* = 'I': the IL-th through IU-th eigenvalues will be found. */
/* ********* For RANGE = 'V' or 'I' and IU - IL < N - 1, SSTEBZ and */
/* ********* SSTEIN are called */
/* 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 */
/* A. */
/* On exit, D may be multiplied by a constant factor chosen */
/* to avoid over/underflow in computing the eigenvalues. */
/* E (input/output) REAL array, dimension (max(1,N-1)) */
/* On entry, the (n-1) subdiagonal elements of the tridiagonal */
/* matrix A in elements 1 to N-1 of E. */
/* On exit, E may be multiplied by a constant factor chosen */
/* to avoid over/underflow in computing the eigenvalues. */
/* VL (input) REAL */
/* VU (input) REAL */
/* If RANGE='V', the lower and upper bounds of the interval to */
/* be searched for eigenvalues. VL < VU. */
/* Not referenced if RANGE = 'A' or 'I'. */
/* IL (input) INTEGER */
/* IU (input) INTEGER */
/* If RANGE='I', the indices (in ascending order) of the */
/* smallest and largest eigenvalues to be returned. */
/* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* Not referenced if RANGE = 'A' or 'V'. */
/* ABSTOL (input) REAL */
/* The absolute error tolerance for the eigenvalues. */
/* An approximate eigenvalue is accepted as converged */
/* when it is determined to lie in an interval [a,b] */
/* of width less than or equal to */
/* ABSTOL + EPS * max( |a|,|b| ) , */
/* where EPS is the machine precision. If ABSTOL is less than */
/* or equal to zero, then EPS*|T| will be used in its place, */
/* where |T| is the 1-norm of the tridiagonal matrix obtained */
/* by reducing A to tridiagonal form. */
/* See "Computing Small Singular Values of Bidiagonal Matrices */
/* with Guaranteed High Relative Accuracy," by Demmel and */
/* Kahan, LAPACK Working Note #3. */
/* If high relative accuracy is important, set ABSTOL to */
/* SLAMCH( 'Safe minimum' ). Doing so will guarantee that */
/* eigenvalues are computed to high relative accuracy when */
/* possible in future releases. The current code does not */
/* make any guarantees about high relative accuracy, but */
/* future releases will. See J. Barlow and J. Demmel, */
/* "Computing Accurate Eigensystems of Scaled Diagonally */
/* Dominant Matrices", LAPACK Working Note #7, for a discussion */
/* of which matrices define their eigenvalues to high relative */
/* accuracy. */
/* M (output) INTEGER */
/* The total number of eigenvalues found. 0 <= M <= N. */
/* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
/* W (output) REAL array, dimension (N) */
/* The first M elements contain the selected eigenvalues in */
/* ascending order. */
/* Z (output) REAL array, dimension (LDZ, max(1,M) ) */
/* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
/* contain the orthonormal eigenvectors of the matrix A */
/* corresponding to the selected eigenvalues, with the i-th */
/* column of Z holding the eigenvector associated with W(i). */
/* Note: the user must ensure that at least max(1,M) columns are */
/* supplied in the array Z; if RANGE = 'V', the exact value of M */
/* is not known in advance and an upper bound must be used. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1, and if */
/* JOBZ = 'V', LDZ >= max(1,N). */
/* ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) ) */
/* The support of the eigenvectors in Z, i.e., the indices */
/* indicating the nonzero elements in Z. The i-th eigenvector */
/* is nonzero only in elements ISUPPZ( 2*i-1 ) through */
/* ISUPPZ( 2*i ). */
/* ********* Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal (and */
/* minimal) LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 20*N. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal sizes of the WORK and IWORK */
/* arrays, returns these values as the first entries of the WORK */
/* and IWORK arrays, and no error message related to LWORK or */
/* LIWORK is issued by XERBLA. */
/* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/* On exit, if INFO = 0, IWORK(1) returns the optimal (and */
/* minimal) LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. LIWORK >= 10*N. */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the optimal sizes of the WORK and */
/* IWORK arrays, returns these values as the first entries of */
/* the WORK and IWORK arrays, and no error message related to */
/* LWORK or LIWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: Internal error */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Inderjit Dhillon, IBM Almaden, USA */
/* Osni Marques, LBNL/NERSC, USA */
/* Ken Stanley, Computer Science Division, University of */
/* California at Berkeley, USA */
/* Jason Riedy, Computer Science Division, University of */
/* California at Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
--e;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--isuppz;
--work;
--iwork;
/* Function Body */
ieeeok = ilaenv_(&c__10, "SSTEVR", "N", &c__1, &c__2, &c__3, &c__4);
wantz = lsame_(jobz, "V");
alleig = lsame_(range, "A");
valeig = lsame_(range, "V");
indeig = lsame_(range, "I");
lquery = *lwork == -1 || *liwork == -1;
/* Computing MAX */
i__1 = 1, i__2 = *n * 20;
lwmin = max(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = *n * 10;
liwmin = max(i__1,i__2);
*info = 0;
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else {
if (valeig) {
if (*n > 0 && *vu <= *vl) {
*info = -7;
}
} else if (indeig) {
if (*il < 1 || *il > max(1,*n)) {
*info = -8;
} else if (*iu < min(*n,*il) || *iu > *n) {
*info = -9;
}
}
}
if (*info == 0) {
if (*ldz < 1 || wantz && *ldz < *n) {
*info = -14;
}
}
if (*info == 0) {
work[1] = (real) lwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -17;
} else if (*liwork < liwmin && ! lquery) {
*info = -19;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSTEVR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
*m = 0;
if (*n == 0) {
return 0;
}
if (*n == 1) {
if (alleig || indeig) {
*m = 1;
w[1] = d__[1];
} else {
if (*vl < d__[1] && *vu >= d__[1]) {
*m = 1;
w[1] = d__[1];
}
}
if (wantz) {
z__[z_dim1 + 1] = 1.f;
}
return 0;
}
/* Get machine constants. */
safmin = slamch_("Safe minimum");
eps = slamch_("Precision");
smlnum = safmin / eps;
bignum = 1.f / smlnum;
rmin = sqrt(smlnum);
/* Computing MIN */
r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin));
rmax = dmin(r__1,r__2);
/* Scale matrix to allowable range, if necessary. */
iscale = 0;
vll = *vl;
vuu = *vu;
tnrm = slanst_("M", n, &d__[1], &e[1]);
if (tnrm > 0.f && tnrm < rmin) {
iscale = 1;
sigma = rmin / tnrm;
} else if (tnrm > rmax) {
iscale = 1;
sigma = rmax / tnrm;
}
if (iscale == 1) {
sscal_(n, &sigma, &d__[1], &c__1);
i__1 = *n - 1;
sscal_(&i__1, &sigma, &e[1], &c__1);
if (valeig) {
vll = *vl * sigma;
vuu = *vu * sigma;
}
}
/* Initialize indices into workspaces. Note: These indices are used only */
/* if SSTERF or SSTEMR fail. */
/* IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and */
/* stores the block indices of each of the M<=N eigenvalues. */
indibl = 1;
/* IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ and */
/* stores the starting and finishing indices of each block. */
indisp = indibl + *n;
/* IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors */
/* that corresponding to eigenvectors that fail to converge in */
/* SSTEIN. This information is discarded; if any fail, the driver */
/* returns INFO > 0. */
indifl = indisp + *n;
/* INDIWO is the offset of the remaining integer workspace. */
indiwo = indisp + *n;
/* If all eigenvalues are desired, then */
/* call SSTERF or SSTEMR. If this fails for some eigenvalue, then */
/* try SSTEBZ. */
test = FALSE_;
if (indeig) {
if (*il == 1 && *iu == *n) {
test = TRUE_;
}
}
if ((alleig || test) && ieeeok == 1) {
i__1 = *n - 1;
scopy_(&i__1, &e[1], &c__1, &work[1], &c__1);
if (! wantz) {
scopy_(n, &d__[1], &c__1, &w[1], &c__1);
ssterf_(n, &w[1], &work[1], info);
} else {
scopy_(n, &d__[1], &c__1, &work[*n + 1], &c__1);
if (*abstol <= *n * 2.f * eps) {
tryrac = TRUE_;
} else {
tryrac = FALSE_;
}
i__1 = *lwork - (*n << 1);
sstemr_(jobz, "A", n, &work[*n + 1], &work[1], vl, vu, il, iu, m,
&w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac, &work[
(*n << 1) + 1], &i__1, &iwork[1], liwork, info);
}
if (*info == 0) {
*m = *n;
goto L10;
}
*info = 0;
}
/* Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */
if (wantz) {
*(unsigned char *)order = 'B';
} else {
*(unsigned char *)order = 'E';
}
sstebz_(range, order, n, &vll, &vuu, il, iu, abstol, &d__[1], &e[1], m, &
nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[1], &iwork[
indiwo], info);
if (wantz) {
sstein_(n, &d__[1], &e[1], m, &w[1], &iwork[indibl], &iwork[indisp], &
z__[z_offset], ldz, &work[1], &iwork[indiwo], &iwork[indifl],
info);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
L10:
if (iscale == 1) {
if (*info == 0) {
imax = *m;
} else {
imax = *info - 1;
}
r__1 = 1.f / sigma;
sscal_(&imax, &r__1, &w[1], &c__1);
}
/* If eigenvalues are not in order, then sort them, along with */
/* eigenvectors. */
if (wantz) {
i__1 = *m - 1;
for (j = 1; j <= i__1; ++j) {
i__ = 0;
tmp1 = w[j];
i__2 = *m;
for (jj = j + 1; jj <= i__2; ++jj) {
if (w[jj] < tmp1) {
i__ = jj;
tmp1 = w[jj];
}
/* L20: */
}
if (i__ != 0) {
w[i__] = w[j];
w[j] = tmp1;
sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1],
&c__1);
}
/* L30: */
}
}
/* Causes problems with tests 19 & 20: */
/* IF (wantz .and. INDEIG ) Z( 1,1) = Z(1,1) / 1.002 + .002 */
work[1] = (real) lwmin;
iwork[1] = liwmin;
return 0;
/* End of SSTEVR */
} /* sstevr_ */