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opencv/3rdparty/lapack/dlaed8.c

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#include "clapack.h"
/* Table of constant values */
static doublereal c_b3 = -1.;
static integer c__1 = 1;
/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer
*qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq,
doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda,
doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer
*givptr, integer *givcol, doublereal *givnum, integer *indxp, integer
*indx, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, q2_dim1, q2_offset, i__1;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal c__;
integer i__, j;
doublereal s, t;
integer k2, n1, n2, jp, n1p1;
doublereal eps, tau, tol;
integer jlam, imax, jmax;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *), dscal_(
integer *, doublereal *, doublereal *, integer *), dcopy_(integer
*, doublereal *, integer *, doublereal *, integer *);
extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
integer *, integer *, integer *), dlacpy_(char *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAED8 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 element in the */
/* Z vector. For each such occurrence the order of the related secular */
/* equation problem is reduced by one. */
/* 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. */
/* K (output) INTEGER */
/* The number of non-deflated eigenvalues, and the order of the */
/* related secular equation. */
/* 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. */
/* D (input/output) DOUBLE PRECISION array, dimension (N) */
/* On entry, the eigenvalues of the two submatrices to be */
/* combined. On exit, the trailing (N-K) updated eigenvalues */
/* (those which were deflated) sorted into increasing order. */
/* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) */
/* If ICOMPQ = 0, Q is not referenced. Otherwise, */
/* on entry, Q contains the eigenvectors of the partially solved */
/* system which has been previously updated in matrix */
/* multiplies with other partially solved eigensystems. */
/* 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) 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 CUTPNT added to */
/* their values in order to be accurate. */
/* RHO (input/output) DOUBLE PRECISION */
/* 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 */
/* DLAED3. */
/* CUTPNT (input) INTEGER */
/* The location of the last eigenvalue in the leading */
/* sub-matrix. min(1,N) <= CUTPNT <= N. */
/* Z (input) DOUBLE PRECISION 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 are destroyed by the updating */
/* process. */
/* DLAMDA (output) DOUBLE PRECISION array, dimension (N) */
/* A copy of the first K eigenvalues which will be used by */
/* DLAED3 to form the secular equation. */
/* Q2 (output) DOUBLE PRECISION array, dimension (LDQ2,N) */
/* If ICOMPQ = 0, Q2 is not referenced. Otherwise, */
/* a copy of the first K eigenvectors which will be used by */
/* DLAED7 in a matrix multiply (DGEMM) to update the new */
/* eigenvectors. */
/* LDQ2 (input) INTEGER */
/* The leading dimension of the array Q2. LDQ2 >= max(1,N). */
/* W (output) DOUBLE PRECISION array, dimension (N) */
/* The first k values of the final deflation-altered z-vector and */
/* will be passed to DLAED3. */
/* PERM (output) INTEGER array, dimension (N) */
/* The permutations (from deflation and sorting) to be applied */
/* to each eigenblock. */
/* GIVPTR (output) INTEGER */
/* The number of Givens rotations which took place in this */
/* subproblem. */
/* GIVCOL (output) INTEGER array, dimension (2, N) */
/* Each pair of numbers indicates a pair of columns to take place */
/* in a Givens rotation. */
/* GIVNUM (output) DOUBLE PRECISION array, dimension (2, N) */
/* Each number indicates the S value to be used in the */
/* corresponding Givens rotation. */
/* 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. */
/* INDX (workspace) INTEGER array, dimension (N) */
/* The permutation used to sort the contents of D into ascending */
/* order. */
/* 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 */
/* ===================================================================== */
/* .. 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;
--indxq;
--z__;
--dlamda;
q2_dim1 = *ldq2;
q2_offset = 1 + q2_dim1;
q2 -= q2_offset;
--w;
--perm;
givcol -= 3;
givnum -= 3;
--indxp;
--indx;
/* Function Body */
*info = 0;
if (*icompq < 0 || *icompq > 1) {
*info = -1;
} else if (*n < 0) {
*info = -3;
} else if (*icompq == 1 && *qsiz < *n) {
*info = -4;
} else if (*ldq < max(1,*n)) {
*info = -7;
} else if (*cutpnt < min(1,*n) || *cutpnt > *n) {
*info = -10;
} else if (*ldq2 < max(1,*n)) {
*info = -14;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DLAED8", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
n1 = *cutpnt;
n2 = *n - n1;
n1p1 = n1 + 1;
if (*rho < 0.) {
dscal_(&n2, &c_b3, &z__[n1p1], &c__1);
}
/* Normalize z so that norm(z) = 1 */
t = 1. / sqrt(2.);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
indx[j] = j;
/* L10: */
}
dscal_(n, &t, &z__[1], &c__1);
*rho = (d__1 = *rho * 2., abs(d__1));
/* Sort the eigenvalues into increasing order */
i__1 = *n;
for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) {
indxq[i__] += *cutpnt;
/* L20: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dlamda[i__] = d__[indxq[i__]];
w[i__] = z__[indxq[i__]];
/* L30: */
}
i__ = 1;
j = *cutpnt + 1;
dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]);
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = dlamda[indx[i__]];
z__[i__] = w[indx[i__]];
/* L40: */
}
/* Calculate the allowable deflation tolerence */
imax = idamax_(n, &z__[1], &c__1);
jmax = idamax_(n, &d__[1], &c__1);
eps = dlamch_("Epsilon");
tol = eps * 8. * (d__1 = d__[jmax], abs(d__1));
/* 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 * (d__1 = z__[imax], abs(d__1)) <= tol) {
*k = 0;
if (*icompq == 0) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
perm[j] = indxq[indx[j]];
/* L50: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
perm[j] = indxq[indx[j]];
dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1
+ 1], &c__1);
/* L60: */
}
dlacpy_("A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq);
}
return 0;
}
/* 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. */
*k = 0;
*givptr = 0;
k2 = *n + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {
/* Deflate due to small z component. */
--k2;
indxp[k2] = j;
if (j == *n) {
goto L110;
}
} else {
jlam = j;
goto L80;
}
/* L70: */
}
L80:
++j;
if (j > *n) {
goto L100;
}
if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {
/* Deflate due to small z component. */
--k2;
indxp[k2] = j;
} else {
/* Check if eigenvalues are close enough to allow deflation. */
s = z__[jlam];
c__ = z__[j];
/* Find sqrt(a**2+b**2) without overflow or */
/* destructive underflow. */
tau = dlapy2_(&c__, &s);
t = d__[j] - d__[jlam];
c__ /= tau;
s = -s / tau;
if ((d__1 = t * c__ * s, abs(d__1)) <= tol) {
/* Deflation is possible. */
z__[j] = tau;
z__[jlam] = 0.;
/* Record the appropriate Givens rotation */
++(*givptr);
givcol[(*givptr << 1) + 1] = indxq[indx[jlam]];
givcol[(*givptr << 1) + 2] = indxq[indx[j]];
givnum[(*givptr << 1) + 1] = c__;
givnum[(*givptr << 1) + 2] = s;
if (*icompq == 1) {
drot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[
indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s);
}
t = d__[jlam] * c__ * c__ + d__[j] * s * s;
d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__;
d__[jlam] = t;
--k2;
i__ = 1;
L90:
if (k2 + i__ <= *n) {
if (d__[jlam] < d__[indxp[k2 + i__]]) {
indxp[k2 + i__ - 1] = indxp[k2 + i__];
indxp[k2 + i__] = jlam;
++i__;
goto L90;
} else {
indxp[k2 + i__ - 1] = jlam;
}
} else {
indxp[k2 + i__ - 1] = jlam;
}
jlam = j;
} else {
++(*k);
w[*k] = z__[jlam];
dlamda[*k] = d__[jlam];
indxp[*k] = jlam;
jlam = j;
}
}
goto L80;
L100:
/* Record the last eigenvalue. */
++(*k);
w[*k] = z__[jlam];
dlamda[*k] = d__[jlam];
indxp[*k] = jlam;
L110:
/* 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. */
if (*icompq == 0) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jp = indxp[j];
dlamda[j] = d__[jp];
perm[j] = indxq[indx[jp]];
/* L120: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jp = indxp[j];
dlamda[j] = d__[jp];
perm[j] = indxq[indx[jp]];
dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1]
, &c__1);
/* L130: */
}
}
/* The deflated eigenvalues and their corresponding vectors go back */
/* into the last N - K slots of D and Q respectively. */
if (*k < *n) {
if (*icompq == 0) {
i__1 = *n - *k;
dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
} else {
i__1 = *n - *k;
dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
i__1 = *n - *k;
dlacpy_("A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*
k + 1) * q_dim1 + 1], ldq);
}
}
return 0;
/* End of DLAED8 */
} /* dlaed8_ */
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