"atomic bomb" commit. Reorganized OpenCV directory structure
This commit is contained in:
Vadim Pisarevsky
421
3rdparty/lapack/dlabrd.c
vendored
Normal file
421
3rdparty/lapack/dlabrd.c
vendored
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@@ -0,0 +1,421 @@
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#include "clapack.h"
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/* Table of constant values */
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static doublereal c_b4 = -1.;
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static doublereal c_b5 = 1.;
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static integer c__1 = 1;
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static doublereal c_b16 = 0.;
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/* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal *
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a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq,
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doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer
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*ldy)
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{
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/* System generated locals */
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integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2,
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i__3;
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/* Local variables */
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integer i__;
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
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integer *), dgemv_(char *, integer *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *), dlarfg_(integer *, doublereal *,
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doublereal *, integer *, doublereal *);
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/* -- LAPACK auxiliary routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DLABRD reduces the first NB rows and columns of a real general */
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/* m by n matrix A to upper or lower bidiagonal form by an orthogonal */
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/* transformation Q' * A * P, and returns the matrices X and Y which */
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/* are needed to apply the transformation to the unreduced part of A. */
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/* If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */
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/* bidiagonal form. */
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/* This is an auxiliary routine called by DGEBRD */
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/* Arguments */
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/* ========= */
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/* M (input) INTEGER */
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/* The number of rows in the matrix A. */
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/* N (input) INTEGER */
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/* The number of columns in the matrix A. */
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/* NB (input) INTEGER */
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/* The number of leading rows and columns of A to be reduced. */
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
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/* On entry, the m by n general matrix to be reduced. */
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/* On exit, the first NB rows and columns of the matrix are */
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/* overwritten; the rest of the array is unchanged. */
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/* If m >= n, elements on and below the diagonal in the first NB */
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/* columns, with the array TAUQ, represent the orthogonal */
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/* matrix Q as a product of elementary reflectors; and */
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/* elements above the diagonal in the first NB rows, with the */
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/* array TAUP, represent the orthogonal matrix P as a product */
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/* of elementary reflectors. */
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/* If m < n, elements below the diagonal in the first NB */
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/* columns, with the array TAUQ, represent the orthogonal */
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/* matrix Q as a product of elementary reflectors, and */
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/* elements on and above the diagonal in the first NB rows, */
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/* with the array TAUP, represent the orthogonal matrix P as */
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/* a product of elementary reflectors. */
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/* See Further Details. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,M). */
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/* D (output) DOUBLE PRECISION array, dimension (NB) */
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/* The diagonal elements of the first NB rows and columns of */
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/* the reduced matrix. D(i) = A(i,i). */
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/* E (output) DOUBLE PRECISION array, dimension (NB) */
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/* The off-diagonal elements of the first NB rows and columns of */
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/* the reduced matrix. */
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/* TAUQ (output) DOUBLE PRECISION array dimension (NB) */
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/* The scalar factors of the elementary reflectors which */
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/* represent the orthogonal matrix Q. See Further Details. */
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/* TAUP (output) DOUBLE PRECISION array, dimension (NB) */
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/* The scalar factors of the elementary reflectors which */
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/* represent the orthogonal matrix P. See Further Details. */
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/* X (output) DOUBLE PRECISION array, dimension (LDX,NB) */
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/* The m-by-nb matrix X required to update the unreduced part */
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/* of A. */
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/* LDX (input) INTEGER */
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/* The leading dimension of the array X. LDX >= M. */
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/* Y (output) DOUBLE PRECISION array, dimension (LDY,NB) */
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/* The n-by-nb matrix Y required to update the unreduced part */
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/* of A. */
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/* LDY (input) INTEGER */
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/* The leading dimension of the array Y. LDY >= N. */
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/* Further Details */
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/* =============== */
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/* The matrices Q and P are represented as products of elementary */
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/* reflectors: */
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/* Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) */
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/* Each H(i) and G(i) has the form: */
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/* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */
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/* where tauq and taup are real scalars, and v and u are real vectors. */
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/* If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */
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/* A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */
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/* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
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/* If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */
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/* A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */
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/* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
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/* The elements of the vectors v and u together form the m-by-nb matrix */
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/* V and the nb-by-n matrix U' which are needed, with X and Y, to apply */
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/* the transformation to the unreduced part of the matrix, using a block */
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/* update of the form: A := A - V*Y' - X*U'. */
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/* The contents of A on exit are illustrated by the following examples */
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/* with nb = 2: */
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/* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */
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/* ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) */
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/* ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) */
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/* ( v1 v2 a a a ) ( v1 1 a a a a ) */
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/* ( v1 v2 a a a ) ( v1 v2 a a a a ) */
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/* ( v1 v2 a a a ) ( v1 v2 a a a a ) */
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/* ( v1 v2 a a a ) */
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/* where a denotes an element of the original matrix which is unchanged, */
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/* vi denotes an element of the vector defining H(i), and ui an element */
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/* of the vector defining G(i). */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Quick return if possible */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--d__;
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--e;
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--tauq;
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--taup;
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x_dim1 = *ldx;
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x_offset = 1 + x_dim1;
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x -= x_offset;
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y_dim1 = *ldy;
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y_offset = 1 + y_dim1;
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y -= y_offset;
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/* Function Body */
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if (*m <= 0 || *n <= 0) {
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return 0;
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}
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if (*m >= *n) {
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/* Reduce to upper bidiagonal form */
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i__1 = *nb;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Update A(i:m,i) */
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i__2 = *m - i__ + 1;
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i__3 = i__ - 1;
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dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda,
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&y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], &
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c__1);
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i__2 = *m - i__ + 1;
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i__3 = i__ - 1;
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dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx,
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&a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ *
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a_dim1], &c__1);
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/* Generate reflection Q(i) to annihilate A(i+1:m,i) */
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i__2 = *m - i__ + 1;
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/* Computing MIN */
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i__3 = i__ + 1;
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dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ *
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a_dim1], &c__1, &tauq[i__]);
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d__[i__] = a[i__ + i__ * a_dim1];
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if (i__ < *n) {
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a[i__ + i__ * a_dim1] = 1.;
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/* Compute Y(i+1:n,i) */
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i__2 = *m - i__ + 1;
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i__3 = *n - i__;
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dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) *
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a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &
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y[i__ + 1 + i__ * y_dim1], &c__1);
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i__2 = *m - i__ + 1;
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i__3 = i__ - 1;
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dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1],
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lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ *
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y_dim1 + 1], &c__1);
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i__2 = *n - i__;
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i__3 = i__ - 1;
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dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 +
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y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
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i__ + 1 + i__ * y_dim1], &c__1);
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i__2 = *m - i__ + 1;
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i__3 = i__ - 1;
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dgemv_("Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1],
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ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ *
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y_dim1 + 1], &c__1);
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i__2 = i__ - 1;
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i__3 = *n - i__;
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dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) *
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a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5,
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&y[i__ + 1 + i__ * y_dim1], &c__1);
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i__2 = *n - i__;
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dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
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/* Update A(i,i+1:n) */
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i__2 = *n - i__;
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dgemv_("No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 +
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y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + (
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i__ + 1) * a_dim1], lda);
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i__2 = i__ - 1;
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i__3 = *n - i__;
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dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) *
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a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[
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i__ + (i__ + 1) * a_dim1], lda);
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/* Generate reflection P(i) to annihilate A(i,i+2:n) */
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i__2 = *n - i__;
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/* Computing MIN */
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i__3 = i__ + 2;
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dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min(
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i__3, *n)* a_dim1], lda, &taup[i__]);
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e[i__] = a[i__ + (i__ + 1) * a_dim1];
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a[i__ + (i__ + 1) * a_dim1] = 1.;
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/* Compute X(i+1:m,i) */
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i__2 = *m - i__;
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i__3 = *n - i__;
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dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__
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+ 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1],
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lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1);
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i__2 = *n - i__;
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dgemv_("Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1],
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ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[
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i__ * x_dim1 + 1], &c__1);
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i__2 = *m - i__;
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dgemv_("No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 +
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a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
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i__ + 1 + i__ * x_dim1], &c__1);
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i__2 = i__ - 1;
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i__3 = *n - i__;
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dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *
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a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, &
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c_b16, &x[i__ * x_dim1 + 1], &c__1);
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i__2 = *m - i__;
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i__3 = i__ - 1;
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dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 +
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x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
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i__ + 1 + i__ * x_dim1], &c__1);
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i__2 = *m - i__;
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dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
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}
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/* L10: */
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}
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} else {
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/* Reduce to lower bidiagonal form */
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i__1 = *nb;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Update A(i,i:n) */
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i__2 = *n - i__ + 1;
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i__3 = i__ - 1;
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dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy,
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&a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1],
|
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lda);
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i__2 = i__ - 1;
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i__3 = *n - i__ + 1;
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||||
dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1],
|
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lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1],
|
||||
lda);
|
||||
|
||||
/* Generate reflection P(i) to annihilate A(i,i+1:n) */
|
||||
|
||||
i__2 = *n - i__ + 1;
|
||||
/* Computing MIN */
|
||||
i__3 = i__ + 1;
|
||||
dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)*
|
||||
a_dim1], lda, &taup[i__]);
|
||||
d__[i__] = a[i__ + i__ * a_dim1];
|
||||
if (i__ < *m) {
|
||||
a[i__ + i__ * a_dim1] = 1.;
|
||||
|
||||
/* Compute X(i+1:m,i) */
|
||||
|
||||
i__2 = *m - i__;
|
||||
i__3 = *n - i__ + 1;
|
||||
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ *
|
||||
a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &
|
||||
x[i__ + 1 + i__ * x_dim1], &c__1);
|
||||
i__2 = *n - i__ + 1;
|
||||
i__3 = i__ - 1;
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||||
dgemv_("Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1],
|
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ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ *
|
||||
x_dim1 + 1], &c__1);
|
||||
i__2 = *m - i__;
|
||||
i__3 = i__ - 1;
|
||||
dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 +
|
||||
a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
|
||||
i__ + 1 + i__ * x_dim1], &c__1);
|
||||
i__2 = i__ - 1;
|
||||
i__3 = *n - i__ + 1;
|
||||
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 +
|
||||
1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ *
|
||||
x_dim1 + 1], &c__1);
|
||||
i__2 = *m - i__;
|
||||
i__3 = i__ - 1;
|
||||
dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 +
|
||||
x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
|
||||
i__ + 1 + i__ * x_dim1], &c__1);
|
||||
i__2 = *m - i__;
|
||||
dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
|
||||
|
||||
/* Update A(i+1:m,i) */
|
||||
|
||||
i__2 = *m - i__;
|
||||
i__3 = i__ - 1;
|
||||
dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 +
|
||||
a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ +
|
||||
1 + i__ * a_dim1], &c__1);
|
||||
i__2 = *m - i__;
|
||||
dgemv_("No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 +
|
||||
x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[
|
||||
i__ + 1 + i__ * a_dim1], &c__1);
|
||||
|
||||
/* Generate reflection Q(i) to annihilate A(i+2:m,i) */
|
||||
|
||||
i__2 = *m - i__;
|
||||
/* Computing MIN */
|
||||
i__3 = i__ + 2;
|
||||
dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m)+
|
||||
i__ * a_dim1], &c__1, &tauq[i__]);
|
||||
e[i__] = a[i__ + 1 + i__ * a_dim1];
|
||||
a[i__ + 1 + i__ * a_dim1] = 1.;
|
||||
|
||||
/* Compute Y(i+1:n,i) */
|
||||
|
||||
i__2 = *m - i__;
|
||||
i__3 = *n - i__;
|
||||
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ +
|
||||
1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1,
|
||||
&c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1);
|
||||
i__2 = *m - i__;
|
||||
i__3 = i__ - 1;
|
||||
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1],
|
||||
lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
|
||||
i__ * y_dim1 + 1], &c__1);
|
||||
i__2 = *n - i__;
|
||||
i__3 = i__ - 1;
|
||||
dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 +
|
||||
y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
|
||||
i__ + 1 + i__ * y_dim1], &c__1);
|
||||
i__2 = *m - i__;
|
||||
dgemv_("Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1],
|
||||
ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
|
||||
i__ * y_dim1 + 1], &c__1);
|
||||
i__2 = *n - i__;
|
||||
dgemv_("Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1
|
||||
+ 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__
|
||||
+ 1 + i__ * y_dim1], &c__1);
|
||||
i__2 = *n - i__;
|
||||
dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
|
||||
}
|
||||
/* L20: */
|
||||
}
|
||||
}
|
||||
return 0;
|
||||
|
||||
/* End of DLABRD */
|
||||
|
||||
} /* dlabrd_ */
|
||||
Reference in New Issue
Block a user