353 lines
12 KiB
C
353 lines
12 KiB
C
/* slaed7.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 "clapack.h"
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__2 = 2;
|
|
static integer c__1 = 1;
|
|
static real c_b10 = 1.f;
|
|
static real c_b11 = 0.f;
|
|
static integer c_n1 = -1;
|
|
|
|
/* Subroutine */ int slaed7_(integer *icompq, integer *n, integer *qsiz,
|
|
integer *tlvls, integer *curlvl, integer *curpbm, real *d__, real *q,
|
|
integer *ldq, integer *indxq, real *rho, integer *cutpnt, real *
|
|
qstore, integer *qptr, integer *prmptr, integer *perm, integer *
|
|
givptr, integer *givcol, real *givnum, real *work, integer *iwork,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer q_dim1, q_offset, i__1, i__2;
|
|
|
|
/* Builtin functions */
|
|
integer pow_ii(integer *, integer *);
|
|
|
|
/* Local variables */
|
|
integer i__, k, n1, n2, is, iw, iz, iq2, ptr, ldq2, indx, curr, indxc;
|
|
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
|
|
integer *, real *, real *, integer *, real *, integer *, real *,
|
|
real *, integer *);
|
|
integer indxp;
|
|
extern /* Subroutine */ int slaed8_(integer *, integer *, integer *,
|
|
integer *, real *, real *, integer *, integer *, real *, integer *
|
|
, real *, real *, real *, integer *, real *, integer *, integer *,
|
|
integer *, real *, integer *, integer *, integer *), slaed9_(
|
|
integer *, integer *, integer *, integer *, real *, real *,
|
|
integer *, real *, real *, real *, real *, integer *, integer *),
|
|
slaeda_(integer *, integer *, integer *, integer *, integer *,
|
|
integer *, integer *, integer *, real *, real *, 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 */
|
|
/* ======= */
|
|
|
|
/* SLAED7 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 optionally eigenvectors of a dense symmetric matrix */
|
|
/* that has been reduced to tridiagonal form. SLAED1 handles */
|
|
/* the case in which all eigenvalues and eigenvectors of a symmetric */
|
|
/* tridiagonal matrix 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 SLAED8. */
|
|
|
|
/* 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 SLAED9). */
|
|
/* 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 */
|
|
/* ========= */
|
|
|
|
/* ICOMPQ (input) INTEGER */
|
|
/* = 0: Compute eigenvalues only. */
|
|
/* = 1: Compute eigenvectors of original dense symmetric matrix */
|
|
/* also. On entry, Q 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. */
|
|
|
|
/* QSIZ (input) INTEGER */
|
|
/* The dimension of the orthogonal matrix used to reduce */
|
|
/* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
|
|
|
|
/* TLVLS (input) INTEGER */
|
|
/* The total number of merging levels in the overall divide and */
|
|
/* conquer tree. */
|
|
|
|
/* CURLVL (input) INTEGER */
|
|
/* The current level in the overall merge routine, */
|
|
/* 0 <= CURLVL <= TLVLS. */
|
|
|
|
/* CURPBM (input) INTEGER */
|
|
/* The current problem in the current level in the overall */
|
|
/* merge routine (counting from upper left to lower right). */
|
|
|
|
/* 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 (output) INTEGER array, dimension (N) */
|
|
/* The permutation which will reintegrate the subproblem just */
|
|
/* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) */
|
|
/* will be in ascending order. */
|
|
|
|
/* RHO (input) REAL */
|
|
/* The subdiagonal element used to create the rank-1 */
|
|
/* modification. */
|
|
|
|
/* CUTPNT (input) INTEGER */
|
|
/* Contains the location of the last eigenvalue in the leading */
|
|
/* sub-matrix. min(1,N) <= CUTPNT <= N. */
|
|
|
|
/* QSTORE (input/output) REAL array, dimension (N**2+1) */
|
|
/* Stores eigenvectors of submatrices encountered during */
|
|
/* divide and conquer, packed together. QPTR points to */
|
|
/* beginning of the submatrices. */
|
|
|
|
/* QPTR (input/output) INTEGER array, dimension (N+2) */
|
|
/* List of indices pointing to beginning of submatrices stored */
|
|
/* in QSTORE. The submatrices are numbered starting at the */
|
|
/* bottom left of the divide and conquer tree, from left to */
|
|
/* right and bottom to top. */
|
|
|
|
/* PRMPTR (input) INTEGER array, dimension (N lg N) */
|
|
/* Contains a list of pointers which indicate where in PERM a */
|
|
/* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */
|
|
/* indicates the size of the permutation and also the size of */
|
|
/* the full, non-deflated problem. */
|
|
|
|
/* PERM (input) INTEGER array, dimension (N lg N) */
|
|
/* Contains the permutations (from deflation and sorting) to be */
|
|
/* applied to each eigenblock. */
|
|
|
|
/* GIVPTR (input) INTEGER array, dimension (N lg N) */
|
|
/* Contains a list of pointers which indicate where in GIVCOL a */
|
|
/* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */
|
|
/* indicates the number of Givens rotations. */
|
|
|
|
/* GIVCOL (input) INTEGER array, dimension (2, N lg N) */
|
|
/* Each pair of numbers indicates a pair of columns to take place */
|
|
/* in a Givens rotation. */
|
|
|
|
/* GIVNUM (input) REAL array, dimension (2, N lg N) */
|
|
/* Each number indicates the S value to be used in the */
|
|
/* corresponding Givens rotation. */
|
|
|
|
/* WORK (workspace) REAL array, dimension (3*N+QSIZ*N) */
|
|
|
|
/* 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 */
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* .. Parameters .. */
|
|
/* .. */
|
|
/* .. 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;
|
|
--qstore;
|
|
--qptr;
|
|
--prmptr;
|
|
--perm;
|
|
--givptr;
|
|
givcol -= 3;
|
|
givnum -= 3;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
if (*icompq < 0 || *icompq > 1) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*icompq == 1 && *qsiz < *n) {
|
|
*info = -4;
|
|
} else if (*ldq < max(1,*n)) {
|
|
*info = -9;
|
|
} else if (min(1,*n) > *cutpnt || *n < *cutpnt) {
|
|
*info = -12;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SLAED7", &i__1);
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return 0;
|
|
}
|
|
|
|
/* The following values are for bookkeeping purposes only. They are */
|
|
/* integer pointers which indicate the portion of the workspace */
|
|
/* used by a particular array in SLAED8 and SLAED9. */
|
|
|
|
if (*icompq == 1) {
|
|
ldq2 = *qsiz;
|
|
} else {
|
|
ldq2 = *n;
|
|
}
|
|
|
|
iz = 1;
|
|
idlmda = iz + *n;
|
|
iw = idlmda + *n;
|
|
iq2 = iw + *n;
|
|
is = iq2 + *n * ldq2;
|
|
|
|
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. */
|
|
|
|
ptr = pow_ii(&c__2, tlvls) + 1;
|
|
i__1 = *curlvl - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *tlvls - i__;
|
|
ptr += pow_ii(&c__2, &i__2);
|
|
/* L10: */
|
|
}
|
|
curr = ptr + *curpbm;
|
|
slaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &
|
|
givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz
|
|
+ *n], info);
|
|
|
|
/* When solving the final problem, we no longer need the stored data, */
|
|
/* so we will overwrite the data from this level onto the previously */
|
|
/* used storage space. */
|
|
|
|
if (*curlvl == *tlvls) {
|
|
qptr[curr] = 1;
|
|
prmptr[curr] = 1;
|
|
givptr[curr] = 1;
|
|
}
|
|
|
|
/* Sort and Deflate eigenvalues. */
|
|
|
|
slaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho,
|
|
cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], &
|
|
perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1)
|
|
+ 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[
|
|
indx], info);
|
|
prmptr[curr + 1] = prmptr[curr] + *n;
|
|
givptr[curr + 1] += givptr[curr];
|
|
|
|
/* Solve Secular Equation. */
|
|
|
|
if (k != 0) {
|
|
slaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda],
|
|
&work[iw], &qstore[qptr[curr]], &k, info);
|
|
if (*info != 0) {
|
|
goto L30;
|
|
}
|
|
if (*icompq == 1) {
|
|
sgemm_("N", "N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[
|
|
qptr[curr]], &k, &c_b11, &q[q_offset], ldq);
|
|
}
|
|
/* Computing 2nd power */
|
|
i__1 = k;
|
|
qptr[curr + 1] = qptr[curr] + i__1 * i__1;
|
|
|
|
/* Prepare the INDXQ sorting permutation. */
|
|
|
|
n1 = k;
|
|
n2 = *n - k;
|
|
slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
|
|
} else {
|
|
qptr[curr + 1] = qptr[curr];
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
indxq[i__] = i__;
|
|
/* L20: */
|
|
}
|
|
}
|
|
|
|
L30:
|
|
return 0;
|
|
|
|
/* End of SLAED7 */
|
|
|
|
} /* slaed7_ */
|