csteqr.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 {
    real ops, itcnt;
} latime_;

#define latime_1 latime_

/* Table of constant values */

static complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__0 = 0;
static integer c__1 = 1;
static integer c__2 = 2;
static real c_b41 = 1.f;

/* Subroutine */ int csteqr_(char *compz, integer *n, real *d__, real *e, 
	complex *z__, integer *ldz, real *work, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2;
    real r__1, r__2;

    /* Builtin functions */
    double sqrt(doublereal), r_sign(real *, real *);

    /* Local variables */
    static integer lend, jtot;
    extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *)
	    ;
    static real b, c__, f, g;
    static integer i__, j, k, l, m;
    static real p, r__, s;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int clasr_(char *, char *, char *, integer *, 
	    integer *, real *, real *, complex *, integer *);
    static real anorm;
    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
	    complex *, integer *);
    static integer l1, lendm1, lendp1;
    extern /* Subroutine */ int slaev2_(real *, real *, real *, real *, real *
	    , real *, real *);
    extern doublereal slapy2_(real *, real *);
    static integer ii, mm, iscale;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int claset_(char *, integer *, integer *, complex 
	    *, complex *, complex *, integer *);
    static real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real safmax;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    static integer lendsv;
    extern /* Subroutine */ int slartg_(real *, real *, real *, real *, real *
	    );
    static real ssfmin;
    static integer nmaxit, icompz;
    static real ssfmax;
    extern doublereal slanst_(char *, integer *, real *, real *);
    extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);
    static integer lm1, mm1, nm1;
    static real rt1, rt2, eps;
    static integer lsv;
    static real tst, eps2;


#define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1
#define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)]


/*  -- 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   
       September 30, 1994   

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

    Purpose   
    =======   

    CSTEQR 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 complex Hermitian matrix can also   
    be found if CHETRD or CHPTRD or CHBTRD 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   
                    Hermitian matrix.  On entry, Z must contain the   
                    unitary 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) REAL 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) REAL array, dimension (N-1)   
            On entry, the (n-1) subdiagonal elements of the tridiagonal   
            matrix.   
            On exit, E has been destroyed.   

    Z       (input/output) COMPLEX array, dimension (LDZ, N)   
            On entry, if  COMPZ = 'V', then Z contains the unitary   
            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 Hermitian 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) REAL 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 unitarily similar to the original   
                  matrix.   

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


       Test the input parameters.   

       Parameter adjustments */
    --d__;
    --e;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    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_("CSTEQR", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

    if (*n == 1) {
	if (icompz == 2) {
	    i__1 = z___subscr(1, 1);
	    z__[i__1].r = 1.f, z__[i__1].i = 0.f;
	}
	return 0;
    }

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

    latime_1.ops += 6;
    eps = slamch_("E");
/* Computing 2nd power */
    r__1 = eps;
    eps2 = r__1 * r__1;
    safmin = slamch_("S");
    safmax = 1.f / safmin;
    ssfmax = sqrt(safmax) / 3.f;
    ssfmin = sqrt(safmin) / eps2;

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

    if (icompz == 2) {
	claset_("Full", n, n, &c_b1, &c_b2, &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.f;
    }
    if (l1 <= nm1) {
	i__1 = nm1;
	for (m = l1; m <= i__1; ++m) {
	    tst = (r__1 = e[m], dabs(r__1));
	    if (tst == 0.f) {
		goto L30;
	    }
	    latime_1.ops += 4;
	    if (tst <= sqrt((r__1 = d__[m], dabs(r__1))) * sqrt((r__2 = d__[m 
		    + 1], dabs(r__2))) * eps) {
		e[m] = 0.f;
		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 = slanst_("I", &i__1, &d__[l], &e[l]);
    iscale = 0;
    if (anorm == 0.f) {
	goto L10;
    }
    if (anorm > ssfmax) {
	iscale = 1;
	latime_1.ops = latime_1.ops + (lend - l << 1) + 1;
	i__1 = lend - l + 1;
	slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, 
		info);
	i__1 = lend - l;
	slascl_("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;
	slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, 
		info);
	i__1 = lend - l;
	slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, 
		info);
    }

/*     Choose between QL and QR iteration */

    if ((r__1 = d__[lend], dabs(r__1)) < (r__2 = d__[l], dabs(r__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 */
		r__2 = (r__1 = e[m], dabs(r__1));
		tst = r__2 * r__2;
		latime_1.ops += 4;
		if (tst <= eps2 * (r__1 = d__[m], dabs(r__1)) * (r__2 = d__[m 
			+ 1], dabs(r__2)) + safmin) {
		    goto L60;
		}
/* L50: */
	    }
	}