slaed2.c

著名的LAPACK矩阵计算软件包, 是比较新的版本, 一般用到矩阵分解的朋友也许会用到

#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 real c_b3 = -1.f;
static integer c__1 = 1;

/* Subroutine */ int slaed2_(integer *k, integer *n, integer *n1, real *d__, 
	real *q, integer *ldq, integer *indxq, real *rho, real *z__, real *
	dlamda, real *w, real *q2, integer *indx, integer *indxc, integer *
	indxp, integer *coltyp, integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, i__1, i__2;
    real r__1, r__2, r__3, r__4;

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

    /* Local variables */
    static integer imax, jmax, ctot[4];
    extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, 
	    integer *, real *, real *);
    static real c__;
    static integer i__, j;
    static real s, t;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    static integer k2;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *);
    static integer n2;
    extern doublereal slapy2_(real *, real *);
    static integer ct, nj, pj, js;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer isamax_(integer *, real *, integer *);
    extern /* Subroutine */ int slamrg_(integer *, integer *, real *, integer 
	    *, integer *, integer *), slacpy_(char *, integer *, integer *, 
	    real *, integer *, real *, integer *);
    static integer iq1, iq2, n1p1;
    static real eps, tau, tol;
    static integer psm[4];


#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]


/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       October 31, 1999   

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

    Purpose   
    =======   

    SLAED2 merges the two sets of eigenvalues together into a single   
    sorted set.  Then it tries to deflate the size of the problem.   
    There are two ways in which deflation can occur:  when two or more   
    eigenvalues are close together or if there is a tiny entry in the   
    Z vector.  For each such occurrence the order of the related secular   
    equation problem is reduced by one.   

    Arguments   
    =========   

    K      (output) INTEGER   
           The number of non-deflated eigenvalues, and the order of the   
           related secular equation. 0 <= K <=N.   

    N      (input) INTEGER   
           The dimension of the symmetric tridiagonal matrix.  N >= 0.   

    N1     (input) INTEGER   
           The location of the last eigenvalue in the leading sub-matrix.   
           min(1,N) <= N1 <= N/2.   

    D      (input/output) REAL array, dimension (N)   
           On entry, D contains the eigenvalues of the two submatrices to   
           be combined.   
           On exit, D contains the trailing (N-K) updated eigenvalues   
           (those which were deflated) sorted into increasing order.   

    Q      (input/output) REAL array, dimension (LDQ, N)   
           On entry, Q contains the eigenvectors of two submatrices in   
           the two square blocks with corners at (1,1), (N1,N1)   
           and (N1+1, N1+1), (N,N).   
           On exit, Q contains the trailing (N-K) updated eigenvectors   
           (those which were deflated) in its last N-K columns.   

    LDQ    (input) INTEGER   
           The leading dimension of the array Q.  LDQ >= max(1,N).   

    INDXQ  (input/output) INTEGER array, dimension (N)   
           The permutation which separately sorts the two sub-problems   
           in D into ascending order.  Note that elements in the second   
           half of this permutation must first have N1 added to their   
           values. Destroyed on exit.   

    RHO    (input/output) REAL   
           On entry, the off-diagonal element associated with the rank-1   
           cut which originally split the two submatrices which are now   
           being recombined.   
           On exit, RHO has been modified to the value required by   
           SLAED3.   

    Z      (input) REAL array, dimension (N)   
           On entry, Z contains the updating vector (the last   
           row of the first sub-eigenvector matrix and the first row of   
           the second sub-eigenvector matrix).   
           On exit, the contents of Z have been destroyed by the updating   
           process.   

    DLAMDA (output) REAL array, dimension (N)   
           A copy of the first K eigenvalues which will be used by   
           SLAED3 to form the secular equation.   

    W      (output) REAL array, dimension (N)   
           The first k values of the final deflation-altered z-vector   
           which will be passed to SLAED3.   

    Q2     (output) REAL array, dimension (N1**2+(N-N1)**2)   
           A copy of the first K eigenvectors which will be used by   
           SLAED3 in a matrix multiply (SGEMM) to solve for the new   
           eigenvectors.   

    INDX   (workspace) INTEGER array, dimension (N)   
           The permutation used to sort the contents of DLAMDA into   
           ascending order.   

    INDXC  (output) INTEGER array, dimension (N)   
           The permutation used to arrange the columns of the deflated   
           Q matrix into three groups:  the first group contains non-zero   
           elements only at and above N1, the second contains   
           non-zero elements only below N1, and the third is dense.   

    INDXP  (workspace) INTEGER array, dimension (N)   
           The permutation used to place deflated values of D at the end   
           of the array.  INDXP(1:K) points to the nondeflated D-values   
           and INDXP(K+1:N) points to the deflated eigenvalues.   

    COLTYP (workspace/output) INTEGER array, dimension (N)   
           During execution, a label which will indicate which of the   
           following types a column in the Q2 matrix is:   
           1 : non-zero in the upper half only;   
           2 : dense;   
           3 : non-zero in the lower half only;   
           4 : deflated.   
           On exit, COLTYP(i) is the number of columns of type i,   
           for i=1 to 4 only.   

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

    Further Details   
    ===============   

    Based on contributions by   
       Jeff Rutter, Computer Science Division, University of California   
       at Berkeley, USA   
    Modified by Francoise Tisseur, University of Tennessee.   

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


       Test the input parameters.   

       Parameter adjustments */
    --d__;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --indxq;
    --z__;
    --dlamda;
    --w;
    --q2;
    --indx;
    --indxc;
    --indxp;
    --coltyp;

    /* Function Body */
    *info = 0;

    if (*n < 0) {
	*info = -2;
    } else if (*ldq < max(1,*n)) {
	*info = -6;
    } else /* if(complicated condition) */ {
/* Computing MIN */
	i__1 = 1, i__2 = *n / 2;
	if (min(i__1,i__2) > *n1 || *n / 2 < *n1) {
	    *info = -3;
	}
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SLAED2", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

    n2 = *n - *n1;
    n1p1 = *n1 + 1;

    if (*rho < 0.f) {
	latime_1.ops += n2;
	sscal_(&n2, &c_b3, &z__[n1p1], &c__1);
    }

/*     Normalize z so that norm(z) = 1.  Since z is the concatenation of   
       two normalized vectors, norm2(z) = sqrt(2). */

    latime_1.ops = latime_1.ops + *n + 3;
    t = 1.f / sqrt(2.f);
    sscal_(n, &t, &z__[1], &c__1);

/*     RHO = ABS( norm(z)**2 * RHO ) */

    *rho = (r__1 = *rho * 2.f, dabs(r__1));

/*     Sort the eigenvalues into increasing order */

    i__1 = *n;
    for (i__ = n1p1; i__ <= i__1; ++i__) {
	indxq[i__] += *n1;
/* L10: */
    }

/*     re-integrate the deflated parts from the last pass */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	dlamda[i__] = d__[indxq[i__]];
/* L20: */
    }
    slamrg_(n1, &n2, &dlamda[1], &c__1, &c__1, &indxc[1]);
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	indx[i__] = indxq[indxc[i__]];
/* L30: */
    }

/*     Calculate the allowable deflation tolerance */

    imax = isamax_(n, &z__[1], &c__1);
    jmax = isamax_(n, &d__[1], &c__1);