--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static real c_b8 = 0.f;
+static real c_b14 = -1.f;
+
+/* Subroutine */ int ssytd2_(char *uplo, integer *n, real *a, integer *lda,
+ real *d__, real *e, real *tau, integer *info)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3;
+
+ /* Local variables */
+ integer i__;
+ real taui;
+ extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
+ extern /* Subroutine */ int ssyr2_(char *, integer *, real *, real *,
+ integer *, real *, integer *, real *, integer *);
+ real alpha;
+ extern logical lsame_(char *, char *);
+ logical upper;
+ extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
+ real *, integer *), ssymv_(char *, integer *, real *, real *,
+ integer *, real *, integer *, real *, real *, integer *),
+ xerbla_(char *, integer *), slarfg_(integer *, real *,
+ real *, integer *, real *);
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal */
+/* form T by an orthogonal similarity transformation: Q' * A * Q = T. */
+
+/* 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. N >= 0. */
+
+/* A (input/output) REAL 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 diagonal and first superdiagonal */
+/* of A are overwritten by the corresponding elements of the */
+/* tridiagonal matrix T, and the elements above the first */
+/* superdiagonal, with the array TAU, represent the orthogonal */
+/* matrix Q as a product of elementary reflectors; if UPLO */
+/* = 'L', the diagonal and first subdiagonal of A are over- */
+/* written by the corresponding elements of the tridiagonal */
+/* matrix T, and the elements below the first subdiagonal, 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 >= max(1,N). */
+
+/* D (output) REAL array, dimension (N) */
+/* The diagonal elements of the tridiagonal matrix T: */
+/* D(i) = A(i,i). */
+
+/* E (output) REAL array, dimension (N-1) */
+/* The off-diagonal elements of the tridiagonal matrix T: */
+/* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */
+
+/* TAU (output) REAL array, dimension (N-1) */
+/* The scalar factors of the elementary reflectors (see Further */
+/* Details). */
+
+/* INFO (output) INTEGER */
+/* = 0: successful exit */
+/* < 0: if INFO = -i, the i-th argument had an illegal value. */
+
+/* Further Details */
+/* =============== */
+
+/* If UPLO = 'U', the matrix Q is represented as a product of elementary */
+/* reflectors */
+
+/* Q = H(n-1) . . . H(2) H(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+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */
+/* A(1:i-1,i+1), and tau in TAU(i). */
+
+/* If UPLO = 'L', the matrix Q is represented as a product of elementary */
+/* reflectors */
+
+/* Q = H(1) H(2) . . . H(n-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(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */
+/* and tau in TAU(i). */
+
+/* The contents of A on exit are illustrated by the following examples */
+/* with n = 5: */
+
+/* if UPLO = 'U': if UPLO = 'L': */
+
+/* ( d e v2 v3 v4 ) ( d ) */
+/* ( d e v3 v4 ) ( e d ) */
+/* ( d e v4 ) ( v1 e d ) */
+/* ( d e ) ( v1 v2 e d ) */
+/* ( d ) ( v1 v2 v3 e d ) */
+
+/* where d and e denote diagonal and off-diagonal elements of T, and vi */
+/* denotes an element of the vector defining H(i). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Test the input parameters */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --d__;
+ --e;
+ --tau;
+
+ /* Function Body */
+ *info = 0;
+ upper = lsame_(uplo, "U");
+ if (! upper && ! lsame_(uplo, "L")) {
+ *info = -1;
+ } else if (*n < 0) {
+ *info = -2;
+ } else if (*lda < max(1,*n)) {
+ *info = -4;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("SSYTD2", &i__1);
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ if (*n <= 0) {
+ return 0;
+ }
+
+ if (upper) {
+
+/* Reduce the upper triangle of A */
+
+ for (i__ = *n - 1; i__ >= 1; --i__) {
+
+/* Generate elementary reflector H(i) = I - tau * v * v' */
+/* to annihilate A(1:i-1,i+1) */
+
+ slarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1
+ + 1], &c__1, &taui);
+ e[i__] = a[i__ + (i__ + 1) * a_dim1];
+
+ if (taui != 0.f) {
+
+/* Apply H(i) from both sides to A(1:i,1:i) */
+
+ a[i__ + (i__ + 1) * a_dim1] = 1.f;
+
+/* Compute x := tau * A * v storing x in TAU(1:i) */
+
+ ssymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) *
+ a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1);
+
+/* Compute w := x - 1/2 * tau * (x'*v) * v */
+
+ alpha = taui * -.5f * sdot_(&i__, &tau[1], &c__1, &a[(i__ + 1)
+ * a_dim1 + 1], &c__1);
+ saxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[
+ 1], &c__1);
+
+/* Apply the transformation as a rank-2 update: */
+/* A := A - v * w' - w * v' */
+
+ ssyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1,
+ &tau[1], &c__1, &a[a_offset], lda);
+
+ a[i__ + (i__ + 1) * a_dim1] = e[i__];
+ }
+ d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1];
+ tau[i__] = taui;
+/* L10: */
+ }
+ d__[1] = a[a_dim1 + 1];
+ } else {
+
+/* Reduce the lower triangle of A */
+
+ i__1 = *n - 1;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+
+/* Generate elementary reflector H(i) = I - tau * v * v' */
+/* to annihilate A(i+2:n,i) */
+
+ i__2 = *n - i__;
+/* Computing MIN */
+ i__3 = i__ + 2;
+ slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n)+ i__ *
+ a_dim1], &c__1, &taui);
+ e[i__] = a[i__ + 1 + i__ * a_dim1];
+
+ if (taui != 0.f) {
+
+/* Apply H(i) from both sides to A(i+1:n,i+1:n) */
+
+ a[i__ + 1 + i__ * a_dim1] = 1.f;
+
+/* Compute x := tau * A * v storing y in TAU(i:n-1) */
+
+ i__2 = *n - i__;
+ ssymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1],
+ lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[
+ i__], &c__1);
+
+/* Compute w := x - 1/2 * tau * (x'*v) * v */
+
+ i__2 = *n - i__;
+ alpha = taui * -.5f * sdot_(&i__2, &tau[i__], &c__1, &a[i__ +
+ 1 + i__ * a_dim1], &c__1);
+ i__2 = *n - i__;
+ saxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
+ i__], &c__1);
+
+/* Apply the transformation as a rank-2 update: */
+/* A := A - v * w' - w * v' */
+
+ i__2 = *n - i__;
+ ssyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1,
+ &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1],
+ lda);
+
+ a[i__ + 1 + i__ * a_dim1] = e[i__];
+ }
+ d__[i__] = a[i__ + i__ * a_dim1];
+ tau[i__] = taui;
+/* L20: */
+ }
+ d__[*n] = a[*n + *n * a_dim1];
+ }
+
+ return 0;
+
+/* End of SSYTD2 */
+
+} /* ssytd2_ */
projects / opencv / blobdiff