opencv/3rdparty/lapack/dgebd2.c

#include "clapack.h"

/* Table of constant values */

static integer c__1 = 1;

/* Subroutine */ int dgebd2_(integer *m, integer *n, doublereal *a, integer *
	lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal *
	taup, doublereal *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;

    /* Local variables */
    integer i__;
    extern /* Subroutine */ int dlarf_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *), 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 */
/*  ======= */

/*  DGEBD2 reduces a real general m by n matrix A to upper or lower */
/*  bidiagonal form B by an orthogonal transformation: Q' * A * P = B. */

/*  If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */

/*  Arguments */
/*  ========= */

/*  M       (input) INTEGER */
/*          The number of rows in the matrix A.  M >= 0. */

/*  N       (input) INTEGER */
/*          The number of columns in the matrix A.  N >= 0. */

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/*          On entry, the m by n general matrix to be reduced. */
/*          On exit, */
/*          if m >= n, the diagonal and the first superdiagonal are */
/*            overwritten with the upper bidiagonal matrix B; the */
/*            elements below the diagonal, with the array TAUQ, represent */
/*            the orthogonal matrix Q as a product of elementary */
/*            reflectors, and the elements above the first superdiagonal, */
/*            with the array TAUP, represent the orthogonal matrix P as */
/*            a product of elementary reflectors; */
/*          if m < n, the diagonal and the first subdiagonal are */
/*            overwritten with the lower bidiagonal matrix B; the */
/*            elements below the first subdiagonal, with the array TAUQ, */
/*            represent the orthogonal matrix Q as a product of */
/*            elementary reflectors, and the elements above the diagonal, */
/*            with the array TAUP, represent the orthogonal matrix P as */
/*            a product of elementary reflectors. */
/*          See Further Details. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,M). */

/*  D       (output) DOUBLE PRECISION array, dimension (min(M,N)) */
/*          The diagonal elements of the bidiagonal matrix B: */
/*          D(i) = A(i,i). */

/*  E       (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */
/*          The off-diagonal elements of the bidiagonal matrix B: */
/*          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */
/*          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */

/*  TAUQ    (output) DOUBLE PRECISION array dimension (min(M,N)) */
/*          The scalar factors of the elementary reflectors which */
/*          represent the orthogonal matrix Q. See Further Details. */

/*  TAUP    (output) DOUBLE PRECISION array, dimension (min(M,N)) */
/*          The scalar factors of the elementary reflectors which */
/*          represent the orthogonal matrix P. See Further Details. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (max(M,N)) */

/*  INFO    (output) INTEGER */
/*          = 0: successful exit. */
/*          < 0: if INFO = -i, the i-th argument had an illegal value. */

/*  Further Details */
/*  =============== */

/*  The matrices Q and P are represented as products of elementary */
/*  reflectors: */

/*  If m >= n, */

/*     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1) */

/*  Each H(i) and G(i) has the form: */

/*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u' */

/*  where tauq and taup are real scalars, and v and u are real vectors; */
/*  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */
/*  u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */
/*  tauq is stored in TAUQ(i) and taup in TAUP(i). */

/*  If m < n, */

/*     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m) */

/*  Each H(i) and G(i) has the form: */

/*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u' */

/*  where tauq and taup are real scalars, and v and u are real vectors; */
/*  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */
/*  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */
/*  tauq is stored in TAUQ(i) and taup in TAUP(i). */

/*  The contents of A on exit are illustrated by the following examples: */

/*  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n): */

/*    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 ) */
/*    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 ) */
/*    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 ) */
/*    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 ) */
/*    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 ) */
/*    (  v1  v2  v3  v4  v5 ) */

/*  where d and e denote diagonal and off-diagonal elements of B, vi */
/*  denotes an element of the vector defining H(i), and ui an element of */
/*  the vector defining G(i). */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --d__;
    --e;
    --tauq;
    --taup;
    --work;

    /* Function Body */
    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*m)) {
	*info = -4;
    }
    if (*info < 0) {
	i__1 = -(*info);
	xerbla_("DGEBD2", &i__1);
	return 0;
    }

    if (*m >= *n) {

/*        Reduce to upper bidiagonal form */

	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {

/*           Generate elementary reflector H(i) to annihilate A(i+1:m,i) */

	    i__2 = *m - i__ + 1;
/* Computing MIN */
	    i__3 = i__ + 1;
	    dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ * 
		    a_dim1], &c__1, &tauq[i__]);
	    d__[i__] = a[i__ + i__ * a_dim1];
	    a[i__ + i__ * a_dim1] = 1.;

/*           Apply H(i) to A(i:m,i+1:n) from the left */

	    if (i__ < *n) {
		i__2 = *m - i__ + 1;
		i__3 = *n - i__;
		dlarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
			tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]
);
	    }
	    a[i__ + i__ * a_dim1] = d__[i__];

	    if (i__ < *n) {

/*              Generate elementary reflector G(i) to annihilate */
/*              A(i,i+2:n) */

		i__2 = *n - i__;
/* Computing MIN */
		i__3 = i__ + 2;
		dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min(
			i__3, *n)* a_dim1], lda, &taup[i__]);
		e[i__] = a[i__ + (i__ + 1) * a_dim1];
		a[i__ + (i__ + 1) * a_dim1] = 1.;

/*              Apply G(i) to A(i+1:m,i+1:n) from the right */

		i__2 = *m - i__;
		i__3 = *n - i__;
		dlarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], 
			lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], 
			lda, &work[1]);
		a[i__ + (i__ + 1) * a_dim1] = e[i__];
	    } else {
		taup[i__] = 0.;
	    }
/* L10: */
	}
    } else {

/*        Reduce to lower bidiagonal form */

	i__1 = *m;
	for (i__ = 1; i__ <= i__1; ++i__) {

/*           Generate elementary reflector G(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];
	    a[i__ + i__ * a_dim1] = 1.;

/*           Apply G(i) to A(i+1:m,i:n) from the right */

	    if (i__ < *m) {
		i__2 = *m - i__;
		i__3 = *n - i__ + 1;
		dlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &
			taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
	    }
	    a[i__ + i__ * a_dim1] = d__[i__];

	    if (i__ < *m) {

/*              Generate elementary reflector H(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.;

/*              Apply H(i) to A(i+1:m,i+1:n) from the left */

		i__2 = *m - i__;
		i__3 = *n - i__;
		dlarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &
			c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], 
			lda, &work[1]);
		a[i__ + 1 + i__ * a_dim1] = e[i__];
	    } else {
		tauq[i__] = 0.;
	    }
/* L20: */
	}
    }
    return 0;

/*     End of DGEBD2 */

} /* dgebd2_ */