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/* dlaed7.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__2 = 2;
static integer c__1 = 1;
static doublereal c_b10 = 1.;
static doublereal c_b11 = 0.;
static integer c_n1 = -1;
/* Subroutine */ int dlaed7_(integer *icompq, integer *n, integer *qsiz,
integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__,
doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer
*cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer *
perm, integer *givptr, integer *givcol, doublereal *givnum,
doublereal *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;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
integer indxc, indxp;
extern /* Subroutine */ int dlaed8_(integer *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *, integer *,
doublereal *, integer *, integer *, integer *), dlaed9_(integer *,
integer *, integer *, integer *, doublereal *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
integer *, integer *), dlaeda_(integer *, integer *, integer *,
integer *, integer *, integer *, integer *, integer *, doublereal
*, doublereal *, integer *, doublereal *, doublereal *, integer *)
;
integer idlmda;
extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
integer *, integer *, integer *), xerbla_(char *, 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 */
/* ======= */
/* DLAED7 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. DLAED1 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 DLAED8. */
/* The second stage consists of calculating the updated */
/* eigenvalues. This is done by finding the roots of the secular */
/* equation via the routine DLAED4 (as called by DLAED9). */
/* 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) DOUBLE PRECISION array, dimension (N) */
/* On entry, the eigenvalues of the rank-1-perturbed matrix. */
/* On exit, the eigenvalues of the repaired matrix. */
/* Q (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION */
/* 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2, N lg N) */
/* Each number indicates the S value to be used in the */
/* corresponding Givens rotation. */
/* WORK (workspace) DOUBLE PRECISION 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_("DLAED7", &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 DLAED8 and DLAED9. */
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;
dlaeda_(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. */
dlaed8_(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) {
dlaed9_(&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) {
dgemm_("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;
dlamrg_(&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 DLAED7 */
} /* dlaed7_ */
|
