X-Git-Url: https://vcs.maemo.org/git/?a=blobdiff_plain;f=3rdparty%2Flapack%2Fdsytd2.c;fp=3rdparty%2Flapack%2Fdsytd2.c;h=30095123cc4ad1f1b9aefbcf7872c0208982cd03;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hp=0000000000000000000000000000000000000000;hpb=454138ff8a20f6edb9b65a910101403d8b520643;p=opencv

diff --git a/3rdparty/lapack/dsytd2.c b/3rdparty/lapack/dsytd2.c
new file mode 100644
index 0000000..3009512
--- /dev/null
+++ b/3rdparty/lapack/dsytd2.c
@@ -0,0 +1,293 @@
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static doublereal c_b8 = 0.;
+static doublereal c_b14 = -1.;
+
+/* Subroutine */ int dsytd2_(char *uplo, integer *n, doublereal *a, integer *
+	lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+
+    /* Local variables */
+    integer i__;
+    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
+	    integer *);
+    doublereal taui;
+    extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, 
+	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
+	    integer *);
+    doublereal alpha;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
+	    integer *, doublereal *, integer *);
+    logical upper;
+    extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *, 
+	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
+	    doublereal *, integer *), dlarfg_(integer *, doublereal *, 
+	     doublereal *, integer *, doublereal *), 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 */
+/*  ======= */
+
+/*  DSYTD2 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) 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 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) DOUBLE PRECISION array, dimension (N) */
+/*          The diagonal elements of the tridiagonal matrix T: */
+/*          D(i) = A(i,i). */
+
+/*  E       (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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_("DSYTD2", &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) */
+
+	    dlarfg_(&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.) {
+
+/*              Apply H(i) from both sides to A(1:i,1:i) */
+
+		a[i__ + (i__ + 1) * a_dim1] = 1.;
+
+/*              Compute  x := tau * A * v  storing x in TAU(1:i) */
+
+		dsymv_(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 * -.5 * ddot_(&i__, &tau[1], &c__1, &a[(i__ + 1) 
+			* a_dim1 + 1], &c__1);
+		daxpy_(&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' */
+
+		dsyr2_(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;
+	    dlarfg_(&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.) {
+
+/*              Apply H(i) from both sides to A(i+1:n,i+1:n) */
+
+		a[i__ + 1 + i__ * a_dim1] = 1.;
+
+/*              Compute  x := tau * A * v  storing y in TAU(i:n-1) */
+
+		i__2 = *n - i__;
+		dsymv_(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 * -.5 * ddot_(&i__2, &tau[i__], &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, &tau[
+			i__], &c__1);
+
+/*              Apply the transformation as a rank-2 update: */
+/*                 A := A - v * w' - w * v' */
+
+		i__2 = *n - i__;
+		dsyr2_(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 DSYTD2 */
+
+} /* dsytd2_ */