dsterf.c

提供矩阵类的函数库

#include "blaswrap.h"
/*  -- translated by f2c (version 19990503).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Common Block Declarations */

struct {
    doublereal ops, itcnt;
} latime_;

#define latime_1 latime_

/* Table of constant values */

static integer c__0 = 0;
static integer c__1 = 1;
static doublereal c_b32 = 1.;

/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e, 
	integer *info)
{
    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2, d__3;

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

    /* Local variables */
    static doublereal oldc;
    static integer lend, jtot;
    extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal 
	    *, doublereal *, doublereal *);
    static doublereal c__;
    static integer i__, l, m;
    static doublereal p, gamma, r__, s, alpha, sigma, anorm;
    static integer l1;
    extern doublereal dlapy2_(doublereal *, doublereal *);
    static doublereal bb;
    extern doublereal dlamch_(char *);
    static integer iscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *);
    static doublereal oldgam, safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static doublereal safmax;
    extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
    extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, 
	    integer *);
    static integer lendsv;
    static doublereal ssfmin;
    static integer nmaxit;
    static doublereal ssfmax, rt1, rt2, eps, rte;
    static integer lsv;
    static doublereal eps2;


/*  -- LAPACK routine (instrumented to count operations, version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   

       Common block to return operation count and iteration count   
       ITCNT is initialized to 0, OPS is only incremented   

    Purpose   
    =======   

    DSTERF computes all eigenvalues of a symmetric tridiagonal matrix   
    using the Pal-Walker-Kahan variant of the QL or QR algorithm.   

    Arguments   
    =========   

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

    D       (input/output) DOUBLE PRECISION array, dimension (N)   
            On entry, the n 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.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  the algorithm failed to find all of the eigenvalues in   
                  a total of 30*N iterations; if INFO = i, then i   
                  elements of E have not converged to zero.   

    =====================================================================   


       Test the input parameters.   

       Parameter adjustments */
    --e;
    --d__;

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

    latime_1.itcnt = 0.;
    if (*n < 0) {
	*info = -1;
	i__1 = -(*info);
	xerbla_("DSTERF", &i__1);
	return 0;
    }
    if (*n <= 1) {
	return 0;
    }

/*     Determine the unit roundoff for this environment. */

    latime_1.ops += 6;
    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 of the tridiagonal matrix. */

    nmaxit = *n * 30;
    sigma = 0.;
    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;

L10:
    if (l1 > *n) {
	goto L170;
    }
    if (l1 > 1) {
	e[l1 - 1] = 0.;
    }
    i__1 = *n - 1;
    for (m = l1; m <= i__1; ++m) {
	latime_1.ops += 4;
	if ((d__3 = e[m], abs(d__3)) <= 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 */

    latime_1.ops += lend - l + 1 << 1;
    i__1 = lend - l + 1;
    anorm = dlanst_("I", &i__1, &d__[l], &e[l]);
    iscale = 0;
    if (anorm > ssfmax) {
	iscale = 1;
	latime_1.ops = latime_1.ops + (lend - l << 1) + 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;
	latime_1.ops = latime_1.ops + (lend - l << 1) + 1;
	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);
    }

    latime_1.ops += lend - l << 1;
    i__1 = lend - 1;
    for (i__ = l; i__ <= i__1; ++i__) {
/* Computing 2nd power */
	d__1 = e[i__];
	e[i__] = d__1 * d__1;
/* L40: */
    }

/*     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. */

L50:
	if (l != lend) {
	    i__1 = lend - 1;
	    for (m = l; m <= i__1; ++m) {
		latime_1.ops += 3;
		if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m 
			+ 1], abs(d__1))) {
		    goto L70;
		}
/* L60: */
	    }
	}
	m = lend;

L70:
	if (m < lend) {
	    e[m] = 0.;
	}
	p = d__[l];
	if (m == l) {
	    goto L90;
	}

/*        If remaining matrix is 2 by 2, use DLAE2 to compute its   
          eigenvalues. */

	if (m == l + 1) {
	    latime_1.ops += 16;
	    rte = sqrt(e[l]);
	    dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2);
	    d__[l] = rt1;
	    d__[l + 1] = rt2;
	    e[l] = 0.;
	    l += 2;
	    if (l <= lend) {
		goto L50;
	    }
	    goto L150;
	}

	if (jtot == nmaxit) {
	    goto L150;
	}
	++jtot;

/*        Form shift. */

	latime_1.ops += 14;
	rte = sqrt(e[l]);
	sigma = (d__[l + 1] - p) / (rte * 2.);
	r__ = dlapy2_(&sigma, &c_b32);
	sigma = p - rte / (sigma + d_sign(&r__, &sigma));

	c__ = 1.;
	s = 0.;
	gamma = d__[m] - sigma;
	p = gamma * gamma;

/*        Inner loop */

	latime_1.ops += (m - l) * 12;
	i__1 = l;
	for (i__ = m - 1; i__ >= i__1; --i__) {
	    bb = e[i__];
	    r__ = p + bb;
	    if (i__ != m - 1) {
		e[i__ + 1] = s * r__;
	    }
	    oldc = c__;
	    c__ = p / r__;
	    s = bb / r__;
	    oldgam = gamma;
	    alpha = d__[i__];
	    gamma = c__ * (alpha - sigma) - s * oldgam;
	    d__[i__ + 1] = oldgam + (alpha - gamma);
	    if (c__ != 0.) {
		p = gamma * gamma / c__;
	    } else {
		p = oldc * bb;
	    }
/* L80: */
	}

	latime_1.ops += 2;
	e[l] = s * p;
	d__[l] = sigma + gamma;
	goto L50;

/*        Eigenvalue found. */

L90:
	d__[l] = p;

	++l;
	if (l <= lend) {
	    goto L50;
	}
	goto L150;

    } else {

/*        QR Iteration   

          Look for small superdiagonal element. */

L100:
	i__1 = lend + 1;
	for (m = l; m >= i__1; --m) {
	    latime_1.ops += 3;
	    if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m 
		    - 1], abs(d__1))) {
		goto L120;
	    }
/* L110: */
	}
	m = lend;

L120:
	if (m > lend) {
	    e[m - 1] = 0.;
	}
	p = d__[l];
	if (m == l) {
	    goto L140;
	}

/*        If remaining matrix is 2 by 2, use DLAE2 to compute its   
          eigenvalues. */

	if (m == l - 1) {
	    latime_1.ops += 16;
	    rte = sqrt(e[l - 1]);
	    dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2);
	    d__[l] = rt1;
	    d__[l - 1] = rt2;
	    e[l - 1] = 0.;
	    l += -2;
	    if (l >= lend) {
		goto L100;
	    }
	    goto L150;
	}

	if (jtot == nmaxit) {
	    goto L150;
	}
	++jtot;

/*        Form shift. */

	latime_1.ops += 14;
	rte = sqrt(e[l - 1]);
	sigma = (d__[l - 1] - p) / (rte * 2.);
	r__ = dlapy2_(&sigma, &c_b32);
	sigma = p - rte / (sigma + d_sign(&r__, &sigma));

	c__ = 1.;
	s = 0.;
	gamma = d__[m] - sigma;
	p = gamma * gamma;

/*        Inner loop */

	latime_1.ops += (l - m) * 12;
	i__1 = l - 1;
	for (i__ = m; i__ <= i__1; ++i__) {
	    bb = e[i__];
	    r__ = p + bb;
	    if (i__ != m) {
		e[i__ - 1] = s * r__;
	    }
	    oldc = c__;
	    c__ = p / r__;
	    s = bb / r__;
	    oldgam = gamma;
	    alpha = d__[i__ + 1];
	    gamma = c__ * (alpha - sigma) - s * oldgam;
	    d__[i__] = oldgam + (alpha - gamma);
	    if (c__ != 0.) {
		p = gamma * gamma / c__;
	    } else {
		p = oldc * bb;
	    }
/* L130: */
	}

	latime_1.ops += 2;
	e[l - 1] = s * p;
	d__[l] = sigma + gamma;
	goto L100;

/*        Eigenvalue found. */

L140:
	d__[l] = p;

	--l;
	if (l >= lend) {
	    goto L100;
	}
	goto L150;

    }

/*     Undo scaling if necessary */

L150:
    if (iscale == 1) {
	latime_1.ops = latime_1.ops + lendsv - lsv + 1;
	i__1 = lendsv - lsv + 1;
	dlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], 
		n, info);
    }
    if (iscale == 2) {
	latime_1.ops = latime_1.ops + lendsv - lsv + 1;
	i__1 = lendsv - lsv + 1;
	dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[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);
	}
/* L160: */
    }
    goto L180;

/*     Sort eigenvalues in increasing order. */

L170:
    dlasrt_("I", n, &d__[1], info);

L180:
    return 0;

/*     End of DSTERF */

} /* dsterf_ */