--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static doublereal c_b5 = -1.;
+static doublereal c_b6 = 1.;
+static integer c__1 = 1;
+static doublereal c_b16 = 0.;
+
+/* Subroutine */ int dlatrd_(char *uplo, integer *n, integer *nb, doublereal *
+ a, integer *lda, doublereal *e, doublereal *tau, doublereal *w,
+ integer *ldw)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
+
+ /* Local variables */
+ integer i__, iw;
+ extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
+ integer *);
+ doublereal alpha;
+ extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
+ integer *);
+ extern logical lsame_(char *, char *);
+ extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
+ doublereal *, doublereal *, integer *, doublereal *, integer *,
+ doublereal *, doublereal *, integer *), daxpy_(integer *,
+ doublereal *, doublereal *, integer *, doublereal *, integer *),
+ dsymv_(char *, integer *, doublereal *, doublereal *, integer *,
+ doublereal *, integer *, doublereal *, doublereal *, integer *), dlarfg_(integer *, doublereal *, doublereal *, integer *,
+ doublereal *);
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLATRD reduces NB rows and columns of a real symmetric matrix A to */
+/* symmetric tridiagonal form by an orthogonal similarity */
+/* transformation Q' * A * Q, and returns the matrices V and W which are */
+/* needed to apply the transformation to the unreduced part of A. */
+
+/* If UPLO = 'U', DLATRD reduces the last NB rows and columns of a */
+/* matrix, of which the upper triangle is supplied; */
+/* if UPLO = 'L', DLATRD reduces the first NB rows and columns of a */
+/* matrix, of which the lower triangle is supplied. */
+
+/* This is an auxiliary routine called by DSYTRD. */
+
+/* Arguments */
+/* ========= */
+
+/* UPLO (input) CHARACTER*1 */
+/* Specifies whether the upper or lower triangular part of the */
+/* symmetric matrix A is stored: */
+/* = 'U': Upper triangular */
+/* = 'L': Lower triangular */
+
+/* N (input) INTEGER */
+/* The order of the matrix A. */
+
+/* NB (input) INTEGER */
+/* The number of rows and columns to be reduced. */
+
+/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
+/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */
+/* n-by-n upper triangular part of A contains the upper */
+/* triangular part of the matrix A, and the strictly lower */
+/* triangular part of A is not referenced. If UPLO = 'L', the */
+/* leading n-by-n lower triangular part of A contains the lower */
+/* triangular part of the matrix A, and the strictly upper */
+/* triangular part of A is not referenced. */
+/* On exit: */
+/* if UPLO = 'U', the last NB columns have been reduced to */
+/* tridiagonal form, with the diagonal elements overwriting */
+/* the diagonal elements of A; the elements above the diagonal */
+/* with the array TAU, represent the orthogonal matrix Q as a */
+/* product of elementary reflectors; */
+/* if UPLO = 'L', the first NB columns have been reduced to */
+/* tridiagonal form, with the diagonal elements overwriting */
+/* the diagonal elements of A; the elements below the diagonal */
+/* with the array TAU, represent the orthogonal matrix Q as a */
+/* product of elementary reflectors. */
+/* See Further Details. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= (1,N). */
+
+/* E (output) DOUBLE PRECISION array, dimension (N-1) */
+/* If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */
+/* elements of the last NB columns of the reduced matrix; */
+/* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */
+/* the first NB columns of the reduced matrix. */
+
+/* TAU (output) DOUBLE PRECISION array, dimension (N-1) */
+/* The scalar factors of the elementary reflectors, stored in */
+/* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */
+/* See Further Details. */
+
+/* W (output) DOUBLE PRECISION array, dimension (LDW,NB) */
+/* The n-by-nb matrix W required to update the unreduced part */
+/* of A. */
+
+/* LDW (input) INTEGER */
+/* The leading dimension of the array W. LDW >= max(1,N). */
+
+/* Further Details */
+/* =============== */
+
+/* If UPLO = 'U', the matrix Q is represented as a product of elementary */
+/* reflectors */
+
+/* Q = H(n) H(n-1) . . . H(n-nb+1). */
+
+/* Each H(i) has the form */
+
+/* H(i) = I - tau * v * v' */
+
+/* where tau is a real scalar, and v is a real vector with */
+/* v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */
+/* and tau in TAU(i-1). */
+
+/* If UPLO = 'L', the matrix Q is represented as a product of elementary */
+/* reflectors */
+
+/* Q = H(1) H(2) . . . H(nb). */
+
+/* Each H(i) has the form */
+
+/* H(i) = I - tau * v * v' */
+
+/* where tau is a real scalar, and v is a real vector with */
+/* v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
+/* and tau in TAU(i). */
+
+/* The elements of the vectors v together form the n-by-nb matrix V */
+/* which is needed, with W, to apply the transformation to the unreduced */
+/* part of the matrix, using a symmetric rank-2k update of the form: */
+/* A := A - V*W' - W*V'. */
+
+/* The contents of A on exit are illustrated by the following examples */
+/* with n = 5 and nb = 2: */
+
+/* if UPLO = 'U': if UPLO = 'L': */
+
+/* ( a a a v4 v5 ) ( d ) */
+/* ( a a v4 v5 ) ( 1 d ) */
+/* ( a 1 v5 ) ( v1 1 a ) */
+/* ( d 1 ) ( v1 v2 a a ) */
+/* ( d ) ( v1 v2 a a a ) */
+
+/* where d denotes a diagonal element of the reduced matrix, a denotes */
+/* an element of the original matrix that is unchanged, and vi denotes */
+/* an element of the vector defining H(i). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --e;
+ --tau;
+ w_dim1 = *ldw;
+ w_offset = 1 + w_dim1;
+ w -= w_offset;
+
+ /* Function Body */
+ if (*n <= 0) {
+ return 0;
+ }
+
+ if (lsame_(uplo, "U")) {
+
+/* Reduce last NB columns of upper triangle */
+
+ i__1 = *n - *nb + 1;
+ for (i__ = *n; i__ >= i__1; --i__) {
+ iw = i__ - *n + *nb;
+ if (i__ < *n) {
+
+/* Update A(1:i,i) */
+
+ i__2 = *n - i__;
+ dgemv_("No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) *
+ a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &
+ c_b6, &a[i__ * a_dim1 + 1], &c__1);
+ i__2 = *n - i__;
+ dgemv_("No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) *
+ w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &
+ c_b6, &a[i__ * a_dim1 + 1], &c__1);
+ }
+ if (i__ > 1) {
+
+/* Generate elementary reflector H(i) to annihilate */
+/* A(1:i-2,i) */
+
+ i__2 = i__ - 1;
+ dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 +
+ 1], &c__1, &tau[i__ - 1]);
+ e[i__ - 1] = a[i__ - 1 + i__ * a_dim1];
+ a[i__ - 1 + i__ * a_dim1] = 1.;
+
+/* Compute W(1:i-1,i) */
+
+ i__2 = i__ - 1;
+ dsymv_("Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ *
+ a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], &
+ c__1);
+ if (i__ < *n) {
+ i__2 = i__ - 1;
+ i__3 = *n - i__;
+ dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) *
+ w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, &
+ c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);
+ i__2 = i__ - 1;
+ i__3 = *n - i__;
+ dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *
+ a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &
+ c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);
+ i__2 = i__ - 1;
+ i__3 = *n - i__;
+ dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) *
+ a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, &
+ c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);
+ i__2 = i__ - 1;
+ i__3 = *n - i__;
+ dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) *
+ w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &
+ c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);
+ }
+ i__2 = i__ - 1;
+ dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);
+ i__2 = i__ - 1;
+ alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1],
+ &c__1, &a[i__ * a_dim1 + 1], &c__1);
+ i__2 = i__ - 1;
+ daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw *
+ w_dim1 + 1], &c__1);
+ }
+
+/* L10: */
+ }
+ } else {
+
+/* Reduce first NB columns of lower triangle */
+
+ i__1 = *nb;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+
+/* Update A(i:n,i) */
+
+ i__2 = *n - i__ + 1;
+ i__3 = i__ - 1;
+ dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda,
+ &w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], &
+ c__1);
+ i__2 = *n - i__ + 1;
+ i__3 = i__ - 1;
+ dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw,
+ &a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], &
+ c__1);
+ if (i__ < *n) {
+
+/* Generate elementary reflector H(i) to annihilate */
+/* A(i+2:n,i) */
+
+ i__2 = *n - i__;
+/* Computing MIN */
+ i__3 = i__ + 2;
+ dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n)+
+ i__ * a_dim1], &c__1, &tau[i__]);
+ e[i__] = a[i__ + 1 + i__ * a_dim1];
+ a[i__ + 1 + i__ * a_dim1] = 1.;
+
+/* Compute W(i+1:n,i) */
+
+ i__2 = *n - i__;
+ dsymv_("Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1]
+, lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
+ i__ + 1 + i__ * w_dim1], &c__1);
+ i__2 = *n - i__;
+ i__3 = i__ - 1;
+ dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1],
+ ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
+ i__ * w_dim1 + 1], &c__1);
+ i__2 = *n - i__;
+ i__3 = i__ - 1;
+ dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 +
+ a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
+ i__ + 1 + i__ * w_dim1], &c__1);
+ i__2 = *n - i__;
+ i__3 = i__ - 1;
+ dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1],
+ lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[
+ i__ * w_dim1 + 1], &c__1);
+ i__2 = *n - i__;
+ i__3 = i__ - 1;
+ dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 +
+ w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[
+ i__ + 1 + i__ * w_dim1], &c__1);
+ i__2 = *n - i__;
+ dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);
+ i__2 = *n - i__;
+ alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ *
+ w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
+ i__2 = *n - i__;
+ daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[
+ i__ + 1 + i__ * w_dim1], &c__1);
+ }
+
+/* L20: */
+ }
+ }
+
+ return 0;
+
+/* End of DLATRD */
+
+} /* dlatrd_ */
projects / opencv / blobdiff