mirror of https://github.com/opencv/opencv.git
Open Source Computer Vision Library
https://opencv.org/
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
530 lines
14 KiB
530 lines
14 KiB
/* slaed2.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 real c_b3 = -1.f; |
|
static integer c__1 = 1; |
|
|
|
/* Subroutine */ int slaed2_(integer *k, integer *n, integer *n1, real *d__, |
|
real *q, integer *ldq, integer *indxq, real *rho, real *z__, real * |
|
dlamda, real *w, real *q2, integer *indx, integer *indxc, integer * |
|
indxp, integer *coltyp, integer *info) |
|
{ |
|
/* System generated locals */ |
|
integer q_dim1, q_offset, i__1, i__2; |
|
real r__1, r__2, r__3, r__4; |
|
|
|
/* Builtin functions */ |
|
double sqrt(doublereal); |
|
|
|
/* Local variables */ |
|
real c__; |
|
integer i__, j; |
|
real s, t; |
|
integer k2, n2, ct, nj, pj, js, iq1, iq2, n1p1; |
|
real eps, tau, tol; |
|
integer psm[4], imax, jmax, ctot[4]; |
|
extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, |
|
integer *, real *, real *), sscal_(integer *, real *, real *, |
|
integer *), scopy_(integer *, real *, integer *, real *, integer * |
|
); |
|
extern doublereal slapy2_(real *, real *), slamch_(char *); |
|
extern /* Subroutine */ int xerbla_(char *, integer *); |
|
extern integer isamax_(integer *, real *, integer *); |
|
extern /* Subroutine */ int slamrg_(integer *, integer *, real *, integer |
|
*, integer *, integer *), slacpy_(char *, integer *, integer *, |
|
real *, integer *, real *, integer *); |
|
|
|
|
|
/* -- LAPACK routine (version 3.2) -- */ |
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
|
/* November 2006 */ |
|
|
|
/* .. Scalar Arguments .. */ |
|
/* .. */ |
|
/* .. Array Arguments .. */ |
|
/* .. */ |
|
|
|
/* Purpose */ |
|
/* ======= */ |
|
|
|
/* SLAED2 merges the two sets of eigenvalues together into a single */ |
|
/* sorted set. Then it tries to deflate the size of the problem. */ |
|
/* There are two ways in which deflation can occur: when two or more */ |
|
/* eigenvalues are close together or if there is a tiny entry in the */ |
|
/* Z vector. For each such occurrence the order of the related secular */ |
|
/* equation problem is reduced by one. */ |
|
|
|
/* Arguments */ |
|
/* ========= */ |
|
|
|
/* K (output) INTEGER */ |
|
/* The number of non-deflated eigenvalues, and the order of the */ |
|
/* related secular equation. 0 <= K <=N. */ |
|
|
|
/* N (input) INTEGER */ |
|
/* The dimension of the symmetric tridiagonal matrix. N >= 0. */ |
|
|
|
/* N1 (input) INTEGER */ |
|
/* The location of the last eigenvalue in the leading sub-matrix. */ |
|
/* min(1,N) <= N1 <= N/2. */ |
|
|
|
/* D (input/output) REAL array, dimension (N) */ |
|
/* On entry, D contains the eigenvalues of the two submatrices to */ |
|
/* be combined. */ |
|
/* On exit, D contains the trailing (N-K) updated eigenvalues */ |
|
/* (those which were deflated) sorted into increasing order. */ |
|
|
|
/* Q (input/output) REAL array, dimension (LDQ, N) */ |
|
/* On entry, Q contains the eigenvectors of two submatrices in */ |
|
/* the two square blocks with corners at (1,1), (N1,N1) */ |
|
/* and (N1+1, N1+1), (N,N). */ |
|
/* On exit, Q contains the trailing (N-K) updated eigenvectors */ |
|
/* (those which were deflated) in its last N-K columns. */ |
|
|
|
/* LDQ (input) INTEGER */ |
|
/* The leading dimension of the array Q. LDQ >= max(1,N). */ |
|
|
|
/* INDXQ (input/output) INTEGER array, dimension (N) */ |
|
/* The permutation which separately sorts the two sub-problems */ |
|
/* in D into ascending order. Note that elements in the second */ |
|
/* half of this permutation must first have N1 added to their */ |
|
/* values. Destroyed on exit. */ |
|
|
|
/* RHO (input/output) REAL */ |
|
/* On entry, the off-diagonal element associated with the rank-1 */ |
|
/* cut which originally split the two submatrices which are now */ |
|
/* being recombined. */ |
|
/* On exit, RHO has been modified to the value required by */ |
|
/* SLAED3. */ |
|
|
|
/* Z (input) REAL array, dimension (N) */ |
|
/* On entry, Z contains the updating vector (the last */ |
|
/* row of the first sub-eigenvector matrix and the first row of */ |
|
/* the second sub-eigenvector matrix). */ |
|
/* On exit, the contents of Z have been destroyed by the updating */ |
|
/* process. */ |
|
|
|
/* DLAMDA (output) REAL array, dimension (N) */ |
|
/* A copy of the first K eigenvalues which will be used by */ |
|
/* SLAED3 to form the secular equation. */ |
|
|
|
/* W (output) REAL array, dimension (N) */ |
|
/* The first k values of the final deflation-altered z-vector */ |
|
/* which will be passed to SLAED3. */ |
|
|
|
/* Q2 (output) REAL array, dimension (N1**2+(N-N1)**2) */ |
|
/* A copy of the first K eigenvectors which will be used by */ |
|
/* SLAED3 in a matrix multiply (SGEMM) to solve for the new */ |
|
/* eigenvectors. */ |
|
|
|
/* INDX (workspace) INTEGER array, dimension (N) */ |
|
/* The permutation used to sort the contents of DLAMDA into */ |
|
/* ascending order. */ |
|
|
|
/* INDXC (output) INTEGER array, dimension (N) */ |
|
/* The permutation used to arrange the columns of the deflated */ |
|
/* Q matrix into three groups: the first group contains non-zero */ |
|
/* elements only at and above N1, the second contains */ |
|
/* non-zero elements only below N1, and the third is dense. */ |
|
|
|
/* INDXP (workspace) INTEGER array, dimension (N) */ |
|
/* The permutation used to place deflated values of D at the end */ |
|
/* of the array. INDXP(1:K) points to the nondeflated D-values */ |
|
/* and INDXP(K+1:N) points to the deflated eigenvalues. */ |
|
|
|
/* COLTYP (workspace/output) INTEGER array, dimension (N) */ |
|
/* During execution, a label which will indicate which of the */ |
|
/* following types a column in the Q2 matrix is: */ |
|
/* 1 : non-zero in the upper half only; */ |
|
/* 2 : dense; */ |
|
/* 3 : non-zero in the lower half only; */ |
|
/* 4 : deflated. */ |
|
/* On exit, COLTYP(i) is the number of columns of type i, */ |
|
/* for i=1 to 4 only. */ |
|
|
|
/* INFO (output) INTEGER */ |
|
/* = 0: successful exit. */ |
|
/* < 0: if INFO = -i, the i-th argument had an illegal value. */ |
|
|
|
/* Further Details */ |
|
/* =============== */ |
|
|
|
/* Based on contributions by */ |
|
/* Jeff Rutter, Computer Science Division, University of California */ |
|
/* at Berkeley, USA */ |
|
/* Modified by Francoise Tisseur, University of Tennessee. */ |
|
|
|
/* ===================================================================== */ |
|
|
|
/* .. Parameters .. */ |
|
/* .. */ |
|
/* .. Local Arrays .. */ |
|
/* .. */ |
|
/* .. 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; |
|
--indxq; |
|
--z__; |
|
--dlamda; |
|
--w; |
|
--q2; |
|
--indx; |
|
--indxc; |
|
--indxp; |
|
--coltyp; |
|
|
|
/* Function Body */ |
|
*info = 0; |
|
|
|
if (*n < 0) { |
|
*info = -2; |
|
} else if (*ldq < max(1,*n)) { |
|
*info = -6; |
|
} else /* if(complicated condition) */ { |
|
/* Computing MIN */ |
|
i__1 = 1, i__2 = *n / 2; |
|
if (min(i__1,i__2) > *n1 || *n / 2 < *n1) { |
|
*info = -3; |
|
} |
|
} |
|
if (*info != 0) { |
|
i__1 = -(*info); |
|
xerbla_("SLAED2", &i__1); |
|
return 0; |
|
} |
|
|
|
/* Quick return if possible */ |
|
|
|
if (*n == 0) { |
|
return 0; |
|
} |
|
|
|
n2 = *n - *n1; |
|
n1p1 = *n1 + 1; |
|
|
|
if (*rho < 0.f) { |
|
sscal_(&n2, &c_b3, &z__[n1p1], &c__1); |
|
} |
|
|
|
/* Normalize z so that norm(z) = 1. Since z is the concatenation of */ |
|
/* two normalized vectors, norm2(z) = sqrt(2). */ |
|
|
|
t = 1.f / sqrt(2.f); |
|
sscal_(n, &t, &z__[1], &c__1); |
|
|
|
/* RHO = ABS( norm(z)**2 * RHO ) */ |
|
|
|
*rho = (r__1 = *rho * 2.f, dabs(r__1)); |
|
|
|
/* Sort the eigenvalues into increasing order */ |
|
|
|
i__1 = *n; |
|
for (i__ = n1p1; i__ <= i__1; ++i__) { |
|
indxq[i__] += *n1; |
|
/* L10: */ |
|
} |
|
|
|
/* re-integrate the deflated parts from the last pass */ |
|
|
|
i__1 = *n; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
dlamda[i__] = d__[indxq[i__]]; |
|
/* L20: */ |
|
} |
|
slamrg_(n1, &n2, &dlamda[1], &c__1, &c__1, &indxc[1]); |
|
i__1 = *n; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
indx[i__] = indxq[indxc[i__]]; |
|
/* L30: */ |
|
} |
|
|
|
/* Calculate the allowable deflation tolerance */ |
|
|
|
imax = isamax_(n, &z__[1], &c__1); |
|
jmax = isamax_(n, &d__[1], &c__1); |
|
eps = slamch_("Epsilon"); |
|
/* Computing MAX */ |
|
r__3 = (r__1 = d__[jmax], dabs(r__1)), r__4 = (r__2 = z__[imax], dabs( |
|
r__2)); |
|
tol = eps * 8.f * dmax(r__3,r__4); |
|
|
|
/* If the rank-1 modifier is small enough, no more needs to be done */ |
|
/* except to reorganize Q so that its columns correspond with the */ |
|
/* elements in D. */ |
|
|
|
if (*rho * (r__1 = z__[imax], dabs(r__1)) <= tol) { |
|
*k = 0; |
|
iq2 = 1; |
|
i__1 = *n; |
|
for (j = 1; j <= i__1; ++j) { |
|
i__ = indx[j]; |
|
scopy_(n, &q[i__ * q_dim1 + 1], &c__1, &q2[iq2], &c__1); |
|
dlamda[j] = d__[i__]; |
|
iq2 += *n; |
|
/* L40: */ |
|
} |
|
slacpy_("A", n, n, &q2[1], n, &q[q_offset], ldq); |
|
scopy_(n, &dlamda[1], &c__1, &d__[1], &c__1); |
|
goto L190; |
|
} |
|
|
|
/* If there are multiple eigenvalues then the problem deflates. Here */ |
|
/* the number of equal eigenvalues are found. As each equal */ |
|
/* eigenvalue is found, an elementary reflector is computed to rotate */ |
|
/* the corresponding eigensubspace so that the corresponding */ |
|
/* components of Z are zero in this new basis. */ |
|
|
|
i__1 = *n1; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
coltyp[i__] = 1; |
|
/* L50: */ |
|
} |
|
i__1 = *n; |
|
for (i__ = n1p1; i__ <= i__1; ++i__) { |
|
coltyp[i__] = 3; |
|
/* L60: */ |
|
} |
|
|
|
|
|
*k = 0; |
|
k2 = *n + 1; |
|
i__1 = *n; |
|
for (j = 1; j <= i__1; ++j) { |
|
nj = indx[j]; |
|
if (*rho * (r__1 = z__[nj], dabs(r__1)) <= tol) { |
|
|
|
/* Deflate due to small z component. */ |
|
|
|
--k2; |
|
coltyp[nj] = 4; |
|
indxp[k2] = nj; |
|
if (j == *n) { |
|
goto L100; |
|
} |
|
} else { |
|
pj = nj; |
|
goto L80; |
|
} |
|
/* L70: */ |
|
} |
|
L80: |
|
++j; |
|
nj = indx[j]; |
|
if (j > *n) { |
|
goto L100; |
|
} |
|
if (*rho * (r__1 = z__[nj], dabs(r__1)) <= tol) { |
|
|
|
/* Deflate due to small z component. */ |
|
|
|
--k2; |
|
coltyp[nj] = 4; |
|
indxp[k2] = nj; |
|
} else { |
|
|
|
/* Check if eigenvalues are close enough to allow deflation. */ |
|
|
|
s = z__[pj]; |
|
c__ = z__[nj]; |
|
|
|
/* Find sqrt(a**2+b**2) without overflow or */ |
|
/* destructive underflow. */ |
|
|
|
tau = slapy2_(&c__, &s); |
|
t = d__[nj] - d__[pj]; |
|
c__ /= tau; |
|
s = -s / tau; |
|
if ((r__1 = t * c__ * s, dabs(r__1)) <= tol) { |
|
|
|
/* Deflation is possible. */ |
|
|
|
z__[nj] = tau; |
|
z__[pj] = 0.f; |
|
if (coltyp[nj] != coltyp[pj]) { |
|
coltyp[nj] = 2; |
|
} |
|
coltyp[pj] = 4; |
|
srot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, & |
|
c__, &s); |
|
/* Computing 2nd power */ |
|
r__1 = c__; |
|
/* Computing 2nd power */ |
|
r__2 = s; |
|
t = d__[pj] * (r__1 * r__1) + d__[nj] * (r__2 * r__2); |
|
/* Computing 2nd power */ |
|
r__1 = s; |
|
/* Computing 2nd power */ |
|
r__2 = c__; |
|
d__[nj] = d__[pj] * (r__1 * r__1) + d__[nj] * (r__2 * r__2); |
|
d__[pj] = t; |
|
--k2; |
|
i__ = 1; |
|
L90: |
|
if (k2 + i__ <= *n) { |
|
if (d__[pj] < d__[indxp[k2 + i__]]) { |
|
indxp[k2 + i__ - 1] = indxp[k2 + i__]; |
|
indxp[k2 + i__] = pj; |
|
++i__; |
|
goto L90; |
|
} else { |
|
indxp[k2 + i__ - 1] = pj; |
|
} |
|
} else { |
|
indxp[k2 + i__ - 1] = pj; |
|
} |
|
pj = nj; |
|
} else { |
|
++(*k); |
|
dlamda[*k] = d__[pj]; |
|
w[*k] = z__[pj]; |
|
indxp[*k] = pj; |
|
pj = nj; |
|
} |
|
} |
|
goto L80; |
|
L100: |
|
|
|
/* Record the last eigenvalue. */ |
|
|
|
++(*k); |
|
dlamda[*k] = d__[pj]; |
|
w[*k] = z__[pj]; |
|
indxp[*k] = pj; |
|
|
|
/* Count up the total number of the various types of columns, then */ |
|
/* form a permutation which positions the four column types into */ |
|
/* four uniform groups (although one or more of these groups may be */ |
|
/* empty). */ |
|
|
|
for (j = 1; j <= 4; ++j) { |
|
ctot[j - 1] = 0; |
|
/* L110: */ |
|
} |
|
i__1 = *n; |
|
for (j = 1; j <= i__1; ++j) { |
|
ct = coltyp[j]; |
|
++ctot[ct - 1]; |
|
/* L120: */ |
|
} |
|
|
|
/* PSM(*) = Position in SubMatrix (of types 1 through 4) */ |
|
|
|
psm[0] = 1; |
|
psm[1] = ctot[0] + 1; |
|
psm[2] = psm[1] + ctot[1]; |
|
psm[3] = psm[2] + ctot[2]; |
|
*k = *n - ctot[3]; |
|
|
|
/* Fill out the INDXC array so that the permutation which it induces */ |
|
/* will place all type-1 columns first, all type-2 columns next, */ |
|
/* then all type-3's, and finally all type-4's. */ |
|
|
|
i__1 = *n; |
|
for (j = 1; j <= i__1; ++j) { |
|
js = indxp[j]; |
|
ct = coltyp[js]; |
|
indx[psm[ct - 1]] = js; |
|
indxc[psm[ct - 1]] = j; |
|
++psm[ct - 1]; |
|
/* L130: */ |
|
} |
|
|
|
/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ |
|
/* and Q2 respectively. The eigenvalues/vectors which were not */ |
|
/* deflated go into the first K slots of DLAMDA and Q2 respectively, */ |
|
/* while those which were deflated go into the last N - K slots. */ |
|
|
|
i__ = 1; |
|
iq1 = 1; |
|
iq2 = (ctot[0] + ctot[1]) * *n1 + 1; |
|
i__1 = ctot[0]; |
|
for (j = 1; j <= i__1; ++j) { |
|
js = indx[i__]; |
|
scopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1); |
|
z__[i__] = d__[js]; |
|
++i__; |
|
iq1 += *n1; |
|
/* L140: */ |
|
} |
|
|
|
i__1 = ctot[1]; |
|
for (j = 1; j <= i__1; ++j) { |
|
js = indx[i__]; |
|
scopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1); |
|
scopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1); |
|
z__[i__] = d__[js]; |
|
++i__; |
|
iq1 += *n1; |
|
iq2 += n2; |
|
/* L150: */ |
|
} |
|
|
|
i__1 = ctot[2]; |
|
for (j = 1; j <= i__1; ++j) { |
|
js = indx[i__]; |
|
scopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1); |
|
z__[i__] = d__[js]; |
|
++i__; |
|
iq2 += n2; |
|
/* L160: */ |
|
} |
|
|
|
iq1 = iq2; |
|
i__1 = ctot[3]; |
|
for (j = 1; j <= i__1; ++j) { |
|
js = indx[i__]; |
|
scopy_(n, &q[js * q_dim1 + 1], &c__1, &q2[iq2], &c__1); |
|
iq2 += *n; |
|
z__[i__] = d__[js]; |
|
++i__; |
|
/* L170: */ |
|
} |
|
|
|
/* The deflated eigenvalues and their corresponding vectors go back */ |
|
/* into the last N - K slots of D and Q respectively. */ |
|
|
|
slacpy_("A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq); |
|
i__1 = *n - *k; |
|
scopy_(&i__1, &z__[*k + 1], &c__1, &d__[*k + 1], &c__1); |
|
|
|
/* Copy CTOT into COLTYP for referencing in SLAED3. */ |
|
|
|
for (j = 1; j <= 4; ++j) { |
|
coltyp[j] = ctot[j - 1]; |
|
/* L180: */ |
|
} |
|
|
|
L190: |
|
return 0; |
|
|
|
/* End of SLAED2 */ |
|
|
|
} /* slaed2_ */
|
|
|