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convert linalg library from Fortran to C++

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Axel Kohlmeyer
2022-12-28 13:18:38 -05:00
parent 7cceabe5bd
commit c5a87f75d6
410 changed files with 80736 additions and 30 deletions
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lib/linalg/dlaed3.cpp Normal file
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/* fortran/dlaed3.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__1 = 1;
static doublereal c_b22 = 1.;
static doublereal c_b23 = 0.;
/* > \brief \b DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Us
ed when the original matrix is tridiagonal. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DLAED3 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed3.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed3.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed3.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, */
/* CTOT, W, S, INFO ) */
/* .. Scalar Arguments .. */
/* INTEGER INFO, K, LDQ, N, N1 */
/* DOUBLE PRECISION RHO */
/* .. */
/* .. Array Arguments .. */
/* INTEGER CTOT( * ), INDX( * ) */
/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), */
/* $ S( * ), W( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLAED3 finds the roots of the secular equation, as defined by the */
/* > values in D, W, and RHO, between 1 and K. It makes the */
/* > appropriate calls to DLAED4 and then updates the eigenvectors by */
/* > multiplying the matrix of eigenvectors of the pair of eigensystems */
/* > being combined by the matrix of eigenvectors of the K-by-K system */
/* > which is solved here. */
/* > */
/* > This code makes very mild assumptions about floating point */
/* > arithmetic. It will work on machines with a guard digit in */
/* > add/subtract, or on those binary machines without guard digits */
/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
/* > It could conceivably fail on hexadecimal or decimal machines */
/* > without guard digits, but we know of none. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] K */
/* > \verbatim */
/* > K is INTEGER */
/* > The number of terms in the rational function to be solved by */
/* > DLAED4. K >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of rows and columns in the Q matrix. */
/* > N >= K (deflation may result in N>K). */
/* > \endverbatim */
/* > */
/* > \param[in] N1 */
/* > \verbatim */
/* > N1 is INTEGER */
/* > The location of the last eigenvalue in the leading submatrix. */
/* > min(1,N) <= N1 <= N/2. */
/* > \endverbatim */
/* > */
/* > \param[out] D */
/* > \verbatim */
/* > D is DOUBLE PRECISION array, dimension (N) */
/* > D(I) contains the updated eigenvalues for */
/* > 1 <= I <= K. */
/* > \endverbatim */
/* > */
/* > \param[out] Q */
/* > \verbatim */
/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
/* > Initially the first K columns are used as workspace. */
/* > On output the columns 1 to K contain */
/* > the updated eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* > LDQ is INTEGER */
/* > The leading dimension of the array Q. LDQ >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] RHO */
/* > \verbatim */
/* > RHO is DOUBLE PRECISION */
/* > The value of the parameter in the rank one update equation. */
/* > RHO >= 0 required. */
/* > \endverbatim */
/* > */
/* > \param[in,out] DLAMDA */
/* > \verbatim */
/* > DLAMDA is DOUBLE PRECISION array, dimension (K) */
/* > The first K elements of this array contain the old roots */
/* > of the deflated updating problem. These are the poles */
/* > of the secular equation. May be changed on output by */
/* > having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */
/* > Cray-2, or Cray C-90, as described above. */
/* > \endverbatim */
/* > */
/* > \param[in] Q2 */
/* > \verbatim */
/* > Q2 is DOUBLE PRECISION array, dimension (LDQ2*N) */
/* > The first K columns of this matrix contain the non-deflated */
/* > eigenvectors for the split problem. */
/* > \endverbatim */
/* > */
/* > \param[in] INDX */
/* > \verbatim */
/* > INDX is INTEGER array, dimension (N) */
/* > The permutation used to arrange the columns of the deflated */
/* > Q matrix into three groups (see DLAED2). */
/* > The rows of the eigenvectors found by DLAED4 must be likewise */
/* > permuted before the matrix multiply can take place. */
/* > \endverbatim */
/* > */
/* > \param[in] CTOT */
/* > \verbatim */
/* > CTOT is INTEGER array, dimension (4) */
/* > A count of the total number of the various types of columns */
/* > in Q, as described in INDX. The fourth column type is any */
/* > column which has been deflated. */
/* > \endverbatim */
/* > */
/* > \param[in,out] W */
/* > \verbatim */
/* > W is DOUBLE PRECISION array, dimension (K) */
/* > The first K elements of this array contain the components */
/* > of the deflation-adjusted updating vector. Destroyed on */
/* > output. */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* > S is DOUBLE PRECISION array, dimension (N1 + 1)*K */
/* > Will contain the eigenvectors of the repaired matrix which */
/* > will be multiplied by the previously accumulated eigenvectors */
/* > to update the system. */
/* > \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 \n */
/* > Modified by Francoise Tisseur, University of Tennessee */
/* > */
/* ===================================================================== */
/* Subroutine */ int dlaed3_(integer *k, integer *n, integer *n1, doublereal *
d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda,
doublereal *q2, integer *indx, integer *ctot, doublereal *w,
doublereal *s, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, i__1, i__2;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal), d_sign(doublereal *, doublereal *);
/* Local variables */
integer i__, j, n2, n12, ii, n23, iq2;
doublereal temp;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen),
dcopy_(integer *, doublereal *, integer *, doublereal *, integer
*), dlaed4_(integer *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *);
extern doublereal dlamc3_(doublereal *, doublereal *);
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, ftnlen),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, ftnlen), xerbla_(char *, integer *,
ftnlen);
/* -- 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 Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--dlamda;
--q2;
--indx;
--ctot;
--w;
--s;
/* Function Body */
*info = 0;
if (*k < 0) {
*info = -1;
} else if (*n < *k) {
*info = -2;
} else if (*ldq < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_((char *)"DLAED3", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*k == 0) {
return 0;
}
/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
/* be computed with high relative accuracy (barring over/underflow). */
/* This is a problem on machines without a guard digit in */
/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
/* which on any of these machines zeros out the bottommost */
/* bit of DLAMDA(I) if it is 1; this makes the subsequent */
/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
/* occurs. On binary machines with a guard digit (almost all */
/* machines) it does not change DLAMDA(I) at all. On hexadecimal */
/* and decimal machines with a guard digit, it slightly */
/* changes the bottommost bits of DLAMDA(I). It does not account */
/* for hexadecimal or decimal machines without guard digits */
/* (we know of none). We use a subroutine call to compute */
/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
/* this code. */
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
/* L10: */
}
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j],
info);
/* If the zero finder fails, the computation is terminated. */
if (*info != 0) {
goto L120;
}
/* L20: */
}
if (*k == 1) {
goto L110;
}
if (*k == 2) {
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
w[1] = q[j * q_dim1 + 1];
w[2] = q[j * q_dim1 + 2];
ii = indx[1];
q[j * q_dim1 + 1] = w[ii];
ii = indx[2];
q[j * q_dim1 + 2] = w[ii];
/* L30: */
}
goto L110;
}
/* Compute updated W. */
dcopy_(k, &w[1], &c__1, &s[1], &c__1);
/* Initialize W(I) = Q(I,I) */
i__1 = *ldq + 1;
dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
/* L40: */
}
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
/* L50: */
}
/* L60: */
}
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
d__1 = sqrt(-w[i__]);
w[i__] = d_sign(&d__1, &s[i__]);
/* L70: */
}
/* Compute eigenvectors of the modified rank-1 modification. */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = 1; i__ <= i__2; ++i__) {
s[i__] = w[i__] / q[i__ + j * q_dim1];
/* L80: */
}
temp = dnrm2_(k, &s[1], &c__1);
i__2 = *k;
for (i__ = 1; i__ <= i__2; ++i__) {
ii = indx[i__];
q[i__ + j * q_dim1] = s[ii] / temp;
/* L90: */
}
/* L100: */
}
/* Compute the updated eigenvectors. */
L110:
n2 = *n - *n1;
n12 = ctot[1] + ctot[2];
n23 = ctot[2] + ctot[3];
dlacpy_((char *)"A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23, (ftnlen)
1);
iq2 = *n1 * n12 + 1;
if (n23 != 0) {
dgemm_((char *)"N", (char *)"N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, &
c_b23, &q[*n1 + 1 + q_dim1], ldq, (ftnlen)1, (ftnlen)1);
} else {
dlaset_((char *)"A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq, (
ftnlen)1);
}
dlacpy_((char *)"A", &n12, k, &q[q_offset], ldq, &s[1], &n12, (ftnlen)1);
if (n12 != 0) {
dgemm_((char *)"N", (char *)"N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23,
&q[q_offset], ldq, (ftnlen)1, (ftnlen)1);
} else {
dlaset_((char *)"A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq, (ftnlen)1);
}
L120:
return 0;
/* End of DLAED3 */
} /* dlaed3_ */
#ifdef __cplusplus
}
#endif