opencv/3rdparty/lapack/dsteqr.c

#include "clapack.h"

/* Table of constant values */

static doublereal c_b9 = 0.;
static doublereal c_b10 = 1.;
static integer c__0 = 0;
static integer c__1 = 1;
static integer c__2 = 2;

/* Subroutine */ int dsteqr_(char *compz, integer *n, doublereal *d__, 
	doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 
	integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Builtin functions */
    double sqrt(doublereal), d_sign(doublereal *, doublereal *);

    /* Local variables */
    doublereal b, c__, f, g;
    integer i__, j, k, l, m;
    doublereal p, r__, s;
    integer l1, ii, mm, lm1, mm1, nm1;
    doublereal rt1, rt2, eps;
    integer lsv;
    doublereal tst, eps2;
    integer lend, jtot;
    extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal 
	    *, doublereal *, doublereal *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, 
	    integer *, doublereal *, doublereal *, doublereal *, integer *);
    doublereal anorm;
    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
	    doublereal *, integer *), dlaev2_(doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *);
    integer lendm1, lendp1;
    extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
    integer iscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *), dlaset_(char *, integer *, integer 
	    *, doublereal *, doublereal *, doublereal *, integer *);
    doublereal safmin;
    extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *);
    doublereal safmax;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
    extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, 
	    integer *);
    integer lendsv;
    doublereal ssfmin;
    integer nmaxit, icompz;
    doublereal ssfmax;


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DSTEQR computes all eigenvalues and, optionally, eigenvectors of a */
/*  symmetric tridiagonal matrix using the implicit QL or QR method. */
/*  The eigenvectors of a full or band symmetric matrix can also be found */
/*  if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to */
/*  tridiagonal form. */

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

/*  COMPZ   (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only. */
/*          = 'V':  Compute eigenvalues and eigenvectors of the original */
/*                  symmetric matrix.  On entry, Z must contain the */
/*                  orthogonal matrix used to reduce the original matrix */
/*                  to tridiagonal form. */
/*          = 'I':  Compute eigenvalues and eigenvectors of the */
/*                  tridiagonal matrix.  Z is initialized to the identity */
/*                  matrix. */

/*  N       (input) INTEGER */
/*          The order of the matrix.  N >= 0. */

/*  D       (input/output) DOUBLE PRECISION array, dimension (N) */
/*          On entry, the diagonal elements of the tridiagonal matrix. */
/*          On exit, if INFO = 0, the eigenvalues in ascending order. */

/*  E       (input/output) DOUBLE PRECISION array, dimension (N-1) */
/*          On entry, the (n-1) subdiagonal elements of the tridiagonal */
/*          matrix. */
/*          On exit, E has been destroyed. */

/*  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ, N) */
/*          On entry, if  COMPZ = 'V', then Z contains the orthogonal */
/*          matrix used in the reduction to tridiagonal form. */
/*          On exit, if INFO = 0, then if  COMPZ = 'V', Z contains the */
/*          orthonormal eigenvectors of the original symmetric matrix, */
/*          and if COMPZ = 'I', Z contains the orthonormal eigenvectors */
/*          of the symmetric tridiagonal matrix. */
/*          If COMPZ = 'N', then Z is not referenced. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z.  LDZ >= 1, and if */
/*          eigenvectors are desired, then  LDZ >= max(1,N). */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2)) */
/*          If COMPZ = 'N', then WORK is not referenced. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  the algorithm has failed to find all the eigenvalues in */
/*                a total of 30*N iterations; if INFO = i, then i */
/*                elements of E have not converged to zero; on exit, D */
/*                and E contain the elements of a symmetric tridiagonal */
/*                matrix which is orthogonally similar to the original */
/*                matrix. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    --e;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;

    /* Function Body */
    *info = 0;

    if (lsame_(compz, "N")) {
	icompz = 0;
    } else if (lsame_(compz, "V")) {
	icompz = 1;
    } else if (lsame_(compz, "I")) {
	icompz = 2;
    } else {
	icompz = -1;
    }
    if (icompz < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) {
	*info = -6;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DSTEQR", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

    if (*n == 1) {
	if (icompz == 2) {
	    z__[z_dim1 + 1] = 1.;
	}
	return 0;
    }

/*     Determine the unit roundoff and over/underflow thresholds. */

    eps = dlamch_("E");
/* Computing 2nd power */
    d__1 = eps;
    eps2 = d__1 * d__1;
    safmin = dlamch_("S");
    safmax = 1. / safmin;
    ssfmax = sqrt(safmax) / 3.;
    ssfmin = sqrt(safmin) / eps2;

/*     Compute the eigenvalues and eigenvectors of the tridiagonal */
/*     matrix. */

    if (icompz == 2) {
	dlaset_("Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz);
    }

    nmaxit = *n * 30;
    jtot = 0;

/*     Determine where the matrix splits and choose QL or QR iteration */
/*     for each block, according to whether top or bottom diagonal */
/*     element is smaller. */

    l1 = 1;
    nm1 = *n - 1;

L10:
    if (l1 > *n) {
	goto L160;
    }
    if (l1 > 1) {
	e[l1 - 1] = 0.;
    }
    if (l1 <= nm1) {
	i__1 = nm1;
	for (m = l1; m <= i__1; ++m) {
	    tst = (d__1 = e[m], abs(d__1));
	    if (tst == 0.) {
		goto L30;
	    }
	    if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m 
		    + 1], abs(d__2))) * eps) {
		e[m] = 0.;
		goto L30;
	    }
/* L20: */
	}
    }
    m = *n;

L30:
    l = l1;
    lsv = l;
    lend = m;
    lendsv = lend;
    l1 = m + 1;
    if (lend == l) {
	goto L10;
    }

/*     Scale submatrix in rows and columns L to LEND */

    i__1 = lend - l + 1;
    anorm = dlanst_("I", &i__1, &d__[l], &e[l]);
    iscale = 0;
    if (anorm == 0.) {
	goto L10;
    }
    if (anorm > ssfmax) {
	iscale = 1;
	i__1 = lend - l + 1;
	dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, 
		info);
	i__1 = lend - l;
	dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, 
		info);
    } else if (anorm < ssfmin) {
	iscale = 2;
	i__1 = lend - l + 1;
	dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, 
		info);
	i__1 = lend - l;
	dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, 
		info);
    }

/*     Choose between QL and QR iteration */

    if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
	lend = lsv;
	l = lendsv;
    }

    if (lend > l) {

/*        QL Iteration */

/*        Look for small subdiagonal element. */

L40:
	if (l != lend) {
	    lendm1 = lend - 1;
	    i__1 = lendm1;
	    for (m = l; m <= i__1; ++m) {
/* Computing 2nd power */
		d__2 = (d__1 = e[m], abs(d__1));
		tst = d__2 * d__2;
		if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m 
			+ 1], abs(d__2)) + safmin) {
		    goto L60;
		}
/* L50: */
	    }
	}

	m = lend;

L60:
	if (m < lend) {
	    e[m] = 0.;
	}
	p = d__[l];
	if (m == l) {
	    goto L80;
	}

/*        If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */
/*        to compute its eigensystem. */

	if (m == l + 1) {
	    if (icompz > 0) {
		dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
		work[l] = c__;
		work[*n - 1 + l] = s;
		dlasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
			z__[l * z_dim1 + 1], ldz);
	    } else {
		dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
	    }
	    d__[l] = rt1;
	    d__[l + 1] = rt2;
	    e[l] = 0.;
	    l += 2;
	    if (l <= lend) {
		goto L40;
	    }
	    goto L140;
	}

	if (jtot == nmaxit) {
	    goto L140;
	}
	++jtot;

/*        Form shift. */

	g = (d__[l + 1] - p) / (e[l] * 2.);
	r__ = dlapy2_(&g, &c_b10);
	g = d__[m] - p + e[l] / (g + d_sign(&r__, &g));

	s = 1.;
	c__ = 1.;
	p = 0.;

/*        Inner loop */

	mm1 = m - 1;
	i__1 = l;
	for (i__ = mm1; i__ >= i__1; --i__) {
	    f = s * e[i__];
	    b = c__ * e[i__];
	    dlartg_(&g, &f, &c__, &s, &r__);
	    if (i__ != m - 1) {
		e[i__ + 1] = r__;
	    }
	    g = d__[i__ + 1] - p;
	    r__ = (d__[i__] - g) * s + c__ * 2. * b;
	    p = s * r__;
	    d__[i__ + 1] = g + p;
	    g = c__ * r__ - b;

/*           If eigenvectors are desired, then save rotations. */

	    if (icompz > 0) {
		work[i__] = c__;
		work[*n - 1 + i__] = -s;
	    }

/* L70: */
	}

/*        If eigenvectors are desired, then apply saved rotations. */

	if (icompz > 0) {
	    mm = m - l + 1;
	    dlasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l 
		    * z_dim1 + 1], ldz);
	}

	d__[l] -= p;
	e[l] = g;
	goto L40;

/*        Eigenvalue found. */

L80:
	d__[l] = p;

	++l;
	if (l <= lend) {
	    goto L40;
	}
	goto L140;

    } else {

/*        QR Iteration */

/*        Look for small superdiagonal element. */

L90:
	if (l != lend) {
	    lendp1 = lend + 1;
	    i__1 = lendp1;
	    for (m = l; m >= i__1; --m) {
/* Computing 2nd power */
		d__2 = (d__1 = e[m - 1], abs(d__1));
		tst = d__2 * d__2;
		if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m 
			- 1], abs(d__2)) + safmin) {
		    goto L110;
		}
/* L100: */
	    }
	}

	m = lend;

L110:
	if (m > lend) {
	    e[m - 1] = 0.;
	}
	p = d__[l];
	if (m == l) {
	    goto L130;
	}

/*        If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */
/*        to compute its eigensystem. */

	if (m == l - 1) {
	    if (icompz > 0) {
		dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
			;
		work[m] = c__;
		work[*n - 1 + m] = s;
		dlasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
			z__[(l - 1) * z_dim1 + 1], ldz);
	    } else {
		dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
	    }
	    d__[l - 1] = rt1;
	    d__[l] = rt2;
	    e[l - 1] = 0.;
	    l += -2;
	    if (l >= lend) {
		goto L90;
	    }
	    goto L140;
	}

	if (jtot == nmaxit) {
	    goto L140;
	}
	++jtot;

/*        Form shift. */

	g = (d__[l - 1] - p) / (e[l - 1] * 2.);
	r__ = dlapy2_(&g, &c_b10);
	g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g));

	s = 1.;
	c__ = 1.;
	p = 0.;

/*        Inner loop */

	lm1 = l - 1;
	i__1 = lm1;
	for (i__ = m; i__ <= i__1; ++i__) {
	    f = s * e[i__];
	    b = c__ * e[i__];
	    dlartg_(&g, &f, &c__, &s, &r__);
	    if (i__ != m) {
		e[i__ - 1] = r__;
	    }
	    g = d__[i__] - p;
	    r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b;
	    p = s * r__;
	    d__[i__] = g + p;
	    g = c__ * r__ - b;

/*           If eigenvectors are desired, then save rotations. */

	    if (icompz > 0) {
		work[i__] = c__;
		work[*n - 1 + i__] = s;
	    }

/* L120: */
	}

/*        If eigenvectors are desired, then apply saved rotations. */

	if (icompz > 0) {
	    mm = l - m + 1;
	    dlasr_("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m 
		    * z_dim1 + 1], ldz);
	}

	d__[l] -= p;
	e[lm1] = g;
	goto L90;

/*        Eigenvalue found. */

L130:
	d__[l] = p;

	--l;
	if (l >= lend) {
	    goto L90;
	}
	goto L140;

    }

/*     Undo scaling if necessary */

L140:
    if (iscale == 1) {
	i__1 = lendsv - lsv + 1;
	dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], 
		n, info);
	i__1 = lendsv - lsv;
	dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, 
		info);
    } else if (iscale == 2) {
	i__1 = lendsv - lsv + 1;
	dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], 
		n, info);
	i__1 = lendsv - lsv;
	dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, 
		info);
    }

/*     Check for no convergence to an eigenvalue after a total */
/*     of N*MAXIT iterations. */

    if (jtot < nmaxit) {
	goto L10;
    }
    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if (e[i__] != 0.) {
	    ++(*info);
	}
/* L150: */
    }
    goto L190;

/*     Order eigenvalues and eigenvectors. */

L160:
    if (icompz == 0) {

/*        Use Quick Sort */

	dlasrt_("I", n, &d__[1], info);

    } else {

/*        Use Selection Sort to minimize swaps of eigenvectors */

	i__1 = *n;
	for (ii = 2; ii <= i__1; ++ii) {
	    i__ = ii - 1;
	    k = i__;
	    p = d__[i__];
	    i__2 = *n;
	    for (j = ii; j <= i__2; ++j) {
		if (d__[j] < p) {
		    k = j;
		    p = d__[j];
		}
/* L170: */
	    }
	    if (k != i__) {
		d__[k] = d__[i__];
		d__[i__] = p;
		dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], 
			 &c__1);
	    }
/* L180: */
	}
    }

L190:
    return 0;

/*     End of DSTEQR */

} /* dsteqr_ */