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/* slaed1.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 integer c_n1 = -1;
/* Subroutine */ int slaed1_(integer *n, real *d__, real *q, integer *ldq,
integer *indxq, real *rho, integer *cutpnt, real *work, integer *
iwork, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, i__1, i__2;
/* Local variables */
integer i__, k, n1, n2, is, iw, iz, iq2, cpp1, indx, indxc, indxp;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), slaed2_(integer *, integer *, integer *, real *, real
*, integer *, integer *, real *, real *, real *, real *, real *,
integer *, integer *, integer *, integer *, integer *), slaed3_(
integer *, integer *, integer *, real *, real *, integer *, real *
, real *, real *, integer *, integer *, real *, real *, integer *)
;
integer idlmda;
extern /* Subroutine */ int xerbla_(char *, integer *), slamrg_(
integer *, integer *, real *, integer *, integer *, integer *);
integer coltyp;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAED1 computes the updated eigensystem of a diagonal */
/* matrix after modification by a rank-one symmetric matrix. This */
/* routine is used only for the eigenproblem which requires all */
/* eigenvalues and eigenvectors of a tridiagonal matrix. SLAED7 handles */
/* the case in which eigenvalues only or eigenvalues and eigenvectors */
/* of a full symmetric matrix (which was reduced to tridiagonal form) */
/* are desired. */
/* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) */
/* where Z = Q'u, u is a vector of length N with ones in the */
/* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */
/* The eigenvectors of the original matrix are stored in Q, and the */
/* eigenvalues are in D. The algorithm consists of three stages: */
/* The first stage consists of deflating the size of the problem */
/* when there are multiple eigenvalues or if there is a zero in */
/* the Z vector. For each such occurence the dimension of the */
/* secular equation problem is reduced by one. This stage is */
/* performed by the routine SLAED2. */
/* The second stage consists of calculating the updated */
/* eigenvalues. This is done by finding the roots of the secular */
/* equation via the routine SLAED4 (as called by SLAED3). */
/* This routine also calculates the eigenvectors of the current */
/* problem. */
/* The final stage consists of computing the updated eigenvectors */
/* directly using the updated eigenvalues. The eigenvectors for */
/* the current problem are multiplied with the eigenvectors from */
/* the overall problem. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The dimension of the symmetric tridiagonal matrix. N >= 0. */
/* D (input/output) REAL array, dimension (N) */
/* On entry, the eigenvalues of the rank-1-perturbed matrix. */
/* On exit, the eigenvalues of the repaired matrix. */
/* Q (input/output) REAL array, dimension (LDQ,N) */
/* On entry, the eigenvectors of the rank-1-perturbed matrix. */
/* On exit, the eigenvectors of the repaired tridiagonal matrix. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,N). */
/* INDXQ (input/output) INTEGER array, dimension (N) */
/* On entry, the permutation which separately sorts the two */
/* subproblems in D into ascending order. */
/* On exit, the permutation which will reintegrate the */
/* subproblems back into sorted order, */
/* i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. */
/* RHO (input) REAL */
/* The subdiagonal entry used to create the rank-1 modification. */
/* CUTPNT (input) INTEGER */
/* The location of the last eigenvalue in the leading sub-matrix. */
/* min(1,N) <= CUTPNT <= N/2. */
/* WORK (workspace) REAL array, dimension (4*N + N**2) */
/* IWORK (workspace) INTEGER 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 = 1, an eigenvalue did not converge */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Jeff Rutter, Computer Science Division, University of California */
/* at Berkeley, USA */
/* Modified by Francoise Tisseur, University of Tennessee. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--indxq;
--work;
--iwork;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*ldq < max(1,*n)) {
*info = -4;
} else /* if(complicated condition) */ {
/* Computing MIN */
i__1 = 1, i__2 = *n / 2;
if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SLAED1", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* The following values are integer pointers which indicate */
/* the portion of the workspace */
/* used by a particular array in SLAED2 and SLAED3. */
iz = 1;
idlmda = iz + *n;
iw = idlmda + *n;
iq2 = iw + *n;
indx = 1;
indxc = indx + *n;
coltyp = indxc + *n;
indxp = coltyp + *n;
/* Form the z-vector which consists of the last row of Q_1 and the */
/* first row of Q_2. */
scopy_(cutpnt, &q[*cutpnt + q_dim1], ldq, &work[iz], &c__1);
cpp1 = *cutpnt + 1;
i__1 = *n - *cutpnt;
scopy_(&i__1, &q[cpp1 + cpp1 * q_dim1], ldq, &work[iz + *cutpnt], &c__1);
/* Deflate eigenvalues. */
slaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[
iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[
indxc], &iwork[indxp], &iwork[coltyp], info);
if (*info != 0) {
goto L20;
}
/* Solve Secular Equation. */
if (k != 0) {
is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp +
1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2;
slaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda],
&work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[
is], info);
if (*info != 0) {
goto L20;
}
/* Prepare the INDXQ sorting permutation. */
n1 = k;
n2 = *n - k;
slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
indxq[i__] = i__;
/* L10: */
}
}
L20:
return 0;
/* End of SLAED1 */
} /* slaed1_ */
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