--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+
+/* Subroutine */ int slaed1_(integer *n, real *d__, real *q, integer *ldq,
+ integer *indxq, real *rho, integer *cutpnt, real *work, integer *
+ iwork, integer *info)
+{
+ /* System generated locals */
+ integer q_dim1, q_offset, i__1, i__2;
+
+ /* Local variables */
+ integer i__, k, n1, n2, is, iw, iz, iq2, cpp1, indx, indxc, indxp;
+ extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
+ integer *), slaed2_(integer *, integer *, integer *, real *, real
+ *, integer *, integer *, real *, real *, real *, real *, real *,
+ integer *, integer *, integer *, integer *, integer *), slaed3_(
+ integer *, integer *, integer *, real *, real *, integer *, real *
+, real *, real *, integer *, integer *, real *, real *, integer *)
+ ;
+ integer idlmda;
+ extern /* Subroutine */ int xerbla_(char *, integer *), slamrg_(
+ integer *, integer *, real *, integer *, integer *, integer *);
+ integer coltyp;
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAED1 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 eigenvectors of a tridiagonal matrix. SLAED7 handles */
+/* the case in which eigenvalues only or eigenvalues and eigenvectors */
+/* of a full symmetric matrix (which was reduced to tridiagonal form) */
+/* 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 SLAED2. */
+
+/* The second stage consists of calculating the updated */
+/* eigenvalues. This is done by finding the roots of the secular */
+/* equation via the routine SLAED4 (as called by SLAED3). */
+/* 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 */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The dimension of the symmetric tridiagonal matrix. N >= 0. */
+
+/* D (input/output) REAL array, dimension (N) */
+/* On entry, the eigenvalues of the rank-1-perturbed matrix. */
+/* On exit, the eigenvalues of the repaired matrix. */
+
+/* Q (input/output) REAL 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 (input/output) INTEGER array, dimension (N) */
+/* On entry, the permutation which separately sorts the two */
+/* subproblems in D into ascending order. */
+/* On exit, the permutation which will reintegrate the */
+/* subproblems back into sorted order, */
+/* i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. */
+
+/* RHO (input) REAL */
+/* The subdiagonal entry used to create the rank-1 modification. */
+
+/* CUTPNT (input) INTEGER */
+/* The location of the last eigenvalue in the leading sub-matrix. */
+/* min(1,N) <= CUTPNT <= N/2. */
+
+/* WORK (workspace) REAL array, dimension (4*N + N**2) */
+
+/* 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 */
+/* Modified by Francoise Tisseur, University of Tennessee. */
+
+/* ===================================================================== */
+
+/* .. 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;
+ --work;
+ --iwork;
+
+ /* Function Body */
+ *info = 0;
+
+ if (*n < 0) {
+ *info = -1;
+ } else if (*ldq < max(1,*n)) {
+ *info = -4;
+ } else /* if(complicated condition) */ {
+/* Computing MIN */
+ i__1 = 1, i__2 = *n / 2;
+ if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) {
+ *info = -7;
+ }
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("SLAED1", &i__1);
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+/* The following values are integer pointers which indicate */
+/* the portion of the workspace */
+/* used by a particular array in SLAED2 and SLAED3. */
+
+ iz = 1;
+ idlmda = iz + *n;
+ iw = idlmda + *n;
+ iq2 = iw + *n;
+
+ 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. */
+
+ scopy_(cutpnt, &q[*cutpnt + q_dim1], ldq, &work[iz], &c__1);
+ cpp1 = *cutpnt + 1;
+ i__1 = *n - *cutpnt;
+ scopy_(&i__1, &q[cpp1 + cpp1 * q_dim1], ldq, &work[iz + *cutpnt], &c__1);
+
+/* Deflate eigenvalues. */
+
+ slaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[
+ iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[
+ indxc], &iwork[indxp], &iwork[coltyp], info);
+
+ if (*info != 0) {
+ goto L20;
+ }
+
+/* Solve Secular Equation. */
+
+ if (k != 0) {
+ is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp +
+ 1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2;
+ slaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda],
+ &work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[
+ is], info);
+ if (*info != 0) {
+ goto L20;
+ }
+
+/* Prepare the INDXQ sorting permutation. */
+
+ n1 = k;
+ n2 = *n - k;
+ slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ indxq[i__] = i__;
+/* L10: */
+ }
+ }
+
+L20:
+ return 0;
+
+/* End of SLAED1 */
+
+} /* slaed1_ */
projects / opencv / blobdiff