X-Git-Url: http://vcs.maemo.org/git/?a=blobdiff_plain;f=3rdparty%2Flapack%2Fdlatrd.c;fp=3rdparty%2Flapack%2Fdlatrd.c;h=845b9ace8aadf7010a8ec48f442075d70d9766a5;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hp=0000000000000000000000000000000000000000;hpb=454138ff8a20f6edb9b65a910101403d8b520643;p=opencv

diff --git a/3rdparty/lapack/dlatrd.c b/3rdparty/lapack/dlatrd.c
new file mode 100644
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--- /dev/null
+++ b/3rdparty/lapack/dlatrd.c
@@ -0,0 +1,342 @@
+#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_ */