484 lines
16 KiB
C++
484 lines
16 KiB
C++
/* fortran/dlaed7.f -- translated by f2c (version 20200916).
|
|
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
|
|
*/
|
|
|
|
#ifdef __cplusplus
|
|
extern "C" {
|
|
#endif
|
|
#include "lmp_f2c.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;
|
|
|
|
/* > \brief \b DLAED7 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification
|
|
by a rank-one symmetric matrix. Used when the original matrix is dense. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLAED7 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed7.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed7.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed7.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, */
|
|
/* LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, */
|
|
/* PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, */
|
|
/* INFO ) */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, */
|
|
/* $ QSIZ, TLVLS */
|
|
/* DOUBLE PRECISION RHO */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), */
|
|
/* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) */
|
|
/* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), */
|
|
/* $ QSTORE( * ), WORK( * ) */
|
|
/* .. */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > 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**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) */
|
|
/* > */
|
|
/* > where Z = Q**Tu, 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 occurrence 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. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] ICOMPQ */
|
|
/* > \verbatim */
|
|
/* > ICOMPQ is 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] QSIZ */
|
|
/* > \verbatim */
|
|
/* > QSIZ is INTEGER */
|
|
/* > The dimension of the orthogonal matrix used to reduce */
|
|
/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TLVLS */
|
|
/* > \verbatim */
|
|
/* > TLVLS is INTEGER */
|
|
/* > The total number of merging levels in the overall divide and */
|
|
/* > conquer tree. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CURLVL */
|
|
/* > \verbatim */
|
|
/* > CURLVL is INTEGER */
|
|
/* > The current level in the overall merge routine, */
|
|
/* > 0 <= CURLVL <= TLVLS. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CURPBM */
|
|
/* > \verbatim */
|
|
/* > CURPBM is INTEGER */
|
|
/* > The current problem in the current level in the overall */
|
|
/* > merge routine (counting from upper left to lower right). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On entry, the eigenvalues of the rank-1-perturbed matrix. */
|
|
/* > On exit, the eigenvalues of the repaired matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. LDQ >= max(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INDXQ */
|
|
/* > \verbatim */
|
|
/* > INDXQ is 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RHO */
|
|
/* > \verbatim */
|
|
/* > RHO is DOUBLE PRECISION */
|
|
/* > The subdiagonal element used to create the rank-1 */
|
|
/* > modification. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CUTPNT */
|
|
/* > \verbatim */
|
|
/* > CUTPNT is INTEGER */
|
|
/* > Contains the location of the last eigenvalue in the leading */
|
|
/* > sub-matrix. min(1,N) <= CUTPNT <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] QSTORE */
|
|
/* > \verbatim */
|
|
/* > QSTORE is 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] QPTR */
|
|
/* > \verbatim */
|
|
/* > QPTR is 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] PRMPTR */
|
|
/* > \verbatim */
|
|
/* > PRMPTR is 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] PERM */
|
|
/* > \verbatim */
|
|
/* > PERM is INTEGER array, dimension (N lg N) */
|
|
/* > Contains the permutations (from deflation and sorting) to be */
|
|
/* > applied to each eigenblock. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GIVPTR */
|
|
/* > \verbatim */
|
|
/* > GIVPTR is 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GIVCOL */
|
|
/* > \verbatim */
|
|
/* > GIVCOL is INTEGER array, dimension (2, N lg N) */
|
|
/* > Each pair of numbers indicates a pair of columns to take place */
|
|
/* > in a Givens rotation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GIVNUM */
|
|
/* > \verbatim */
|
|
/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */
|
|
/* > Each number indicates the S value to be used in the */
|
|
/* > corresponding Givens rotation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (4*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is 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 */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \ingroup auxOTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Jeff Rutter, Computer Science Division, University of California */
|
|
/* > at Berkeley, USA */
|
|
|
|
/* ===================================================================== */
|
|
/* 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 *, ftnlen, ftnlen);
|
|
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 *,
|
|
ftnlen);
|
|
integer coltyp;
|
|
|
|
|
|
/* -- LAPACK computational routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* .. 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 = -3;
|
|
} 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_((char *)"DLAED7", &i__1, (ftnlen)6);
|
|
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_((char *)"N", (char *)"N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[
|
|
qptr[curr]], &k, &c_b11, &q[q_offset], ldq, (ftnlen)1, (
|
|
ftnlen)1);
|
|
}
|
|
/* 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_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|