slaed3.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 integer c__1 = 1;
static real c_b22 = 1.f;
static real c_b23 = 0.f;

/* Subroutine */ int slaed3_(integer *k, integer *n, integer *n1, real *d__, 
	real *q, integer *ldq, real *rho, real *dlamda, real *q2, integer *
	indx, integer *ctot, real *w, real *s, integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, i__1, i__2;
    real r__1;

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

    /* Local variables */
    static real temp;
    extern doublereal snrm2_(integer *, real *, integer *);
    static integer i__, j;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *), scopy_(integer *, real *, 
	    integer *, real *, integer *);
    static integer n2;
    extern /* Subroutine */ int slaed4_(integer *, integer *, real *, real *, 
	    real *, real *, real *, integer *);
    extern doublereal slamc3_(real *, real *);
    static integer n12, ii, n23;
    extern /* Subroutine */ int xerbla_(char *, integer *), slacpy_(
	    char *, integer *, integer *, real *, integer *, real *, integer *
	    ), slaset_(char *, integer *, integer *, real *, real *, 
	    real *, integer *);
    static integer iq2;


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


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

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

    Purpose   
    =======   

    SLAED3 finds the roots of the secular equation, as defined by the   
    values in D, W, and RHO, between 1 and K.  It makes the   
    appropriate calls to SLAED4 and then updates the eigenvectors by   
    multiplying the matrix of eigenvectors of the pair of eigensystems   
    being combined by the matrix of eigenvectors of the K-by-K system   
    which is solved here.   

    This code makes very mild assumptions about floating point   
    arithmetic. It will work on machines with a guard digit in   
    add/subtract, or on those binary machines without guard digits   
    which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.   
    It could conceivably fail on hexadecimal or decimal machines   
    without guard digits, but we know of none.   

    Arguments   
    =========   

    K       (input) INTEGER   
            The number of terms in the rational function to be solved by   
            SLAED4.  K >= 0.   

    N       (input) INTEGER   
            The number of rows and columns in the Q matrix.   
            N >= K (deflation may result in N>K).   

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

    D       (output) REAL array, dimension (N)   
            D(I) contains the updated eigenvalues for   
            1 <= I <= K.   

    Q       (output) REAL array, dimension (LDQ,N)   
            Initially the first K columns are used as workspace.   
            On output the columns 1 to K contain   
            the updated eigenvectors.   

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

    RHO     (input) REAL   
            The value of the parameter in the rank one update equation.   
            RHO >= 0 required.   

    DLAMDA  (input/output) REAL array, dimension (K)   
            The first K elements of this array contain the old roots   
            of the deflated updating problem.  These are the poles   
            of the secular equation. May be changed on output by   
            having lowest order bit set to zero on Cray X-MP, Cray Y-MP,   
            Cray-2, or Cray C-90, as described above.   

    Q2      (input) REAL array, dimension (LDQ2, N)   
            The first K columns of this matrix contain the non-deflated   
            eigenvectors for the split problem.   

    INDX    (input) INTEGER array, dimension (N)   
            The permutation used to arrange the columns of the deflated   
            Q matrix into three groups (see SLAED2).   
            The rows of the eigenvectors found by SLAED4 must be likewise   
            permuted before the matrix multiply can take place.   

    CTOT    (input) INTEGER array, dimension (4)   
            A count of the total number of the various types of columns   
            in Q, as described in INDX.  The fourth column type is any   
            column which has been deflated.   

    W       (input/output) REAL array, dimension (K)   
            The first K elements of this array contain the components   
            of the deflation-adjusted updating vector. Destroyed on   
            output.   

    S       (workspace) REAL array, dimension (N1 + 1)*K   
            Will contain the eigenvectors of the repaired matrix which   
            will be multiplied by the previously accumulated eigenvectors   
            to update the system.   

    LDS     (input) INTEGER   
            The leading dimension of S.  LDS >= max(1,K).   

    INFO    (output) INTEGER   
            = 0:  successful exit.   
            < 0:  if INFO = -i, the i-th argument had an illegal value.   
            > 0:  if INFO = 1, an eigenvalue did not converge   

    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;
    --dlamda;
    --q2;
    --indx;
    --ctot;
    --w;
    --s;

    /* Function Body */
    *info = 0;

    if (*k < 0) {
	*info = -1;
    } else if (*n < *k) {
	*info = -2;
    } else if (*ldq < max(1,*n)) {
	*info = -6;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SLAED3", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can   
       be computed with high relative accuracy (barring over/underflow).   
       This is a problem on machines without a guard digit in   
       add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).   
       The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I),   
       which on any of these machines zeros out the bottommost   
       bit of DLAMDA(I) if it is 1; this makes the subsequent   
       subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation   
       occurs. On binary machines with a guard digit (almost all   
       machines) it does not change DLAMDA(I) at all. On hexadecimal   
       and decimal machines with a guard digit, it slightly   
       changes the bottommost bits of DLAMDA(I). It does not account   
       for hexadecimal or decimal machines without guard digits   
       (we know of none). We use a subroutine call to compute   
       2*DLAMBDA(I) to prevent optimizing compilers from eliminating   
       this code. */

    latime_1.ops += *n << 1;
    i__1 = *k;
    for (i__ = 1; i__ <= i__1; ++i__) {
	dlamda[i__] = slamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
/* L10: */
    }

    i__1 = *k;
    for (j = 1; j <= i__1; ++j) {
	slaed4_(k, &j, &dlamda[1], &w[1], &q_ref(1, j), rho, &d__[j], info);

/*        If the zero finder fails, the computation is terminated. */

	if (*info != 0) {
	    goto L120;
	}
/* L20: */
    }

    if (*k == 1) {
	goto L110;
    }
    if (*k == 2) {
	i__1 = *k;
	for (j = 1; j <= i__1; ++j) {
	    w[1] = q_ref(1, j);
	    w[2] = q_ref(2, j);
	    ii = indx[1];
	    q_ref(1, j) = w[ii];
	    ii = indx[2];
	    q_ref(2, j) = w[ii];
/* L30: */
	}
	goto L110;
    }

/*     Compute updated W. */

    scopy_(k, &w[1], &c__1, &s[1], &c__1);

/*     Initialize W(I) = Q(I,I) */

    i__1 = *ldq + 1;
    scopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
    latime_1.ops += *k * 3 * (*k - 1);
    i__1 = *k;
    for (j = 1; j <= i__1; ++j) {
	i__2 = j - 1;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    w[i__] *= q_ref(i__, j) / (dlamda[i__] - dlamda[j]);
/* L40: */
	}
	i__2 = *k;
	for (i__ = j + 1; i__ <= i__2; ++i__) {
	    w[i__] *= q_ref(i__, j) / (dlamda[i__] - dlamda[j]);
/* L50: */
	}
/* L60: */
    }
    latime_1.ops += *k;
    i__1 = *k;
    for (i__ = 1; i__ <= i__1; ++i__) {
	r__1 = sqrt(-w[i__]);
	w[i__] = r_sign(&r__1, &s[i__]);
/* L70: */
    }

/*     Compute eigenvectors of the modified rank-1 modification. */

    latime_1.ops += (*k << 2) * *k;
    i__1 = *k;
    for (j = 1; j <= i__1; ++j) {
	i__2 = *k;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    s[i__] = w[i__] / q_ref(i__, j);
/* L80: */
	}
	temp = snrm2_(k, &s[1], &c__1);
	i__2 = *k;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    ii = indx[i__];
	    q_ref(i__, j) = s[ii] / temp;
/* L90: */
	}
/* L100: */
    }

/*     Compute the updated eigenvectors. */

L110:

    n2 = *n - *n1;
    n12 = ctot[1] + ctot[2];
    n23 = ctot[2] + ctot[3];

    slacpy_("A", &n23, k, &q_ref(ctot[1] + 1, 1), ldq, &s[1], &n23)
	    ;
    iq2 = *n1 * n12 + 1;
    if (n23 != 0) {
	latime_1.ops += (real) n2 * 2 * *k * n23;
	sgemm_("N", "N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, &
		c_b23, &q_ref(*n1 + 1, 1), ldq);
    } else {
	slaset_("A", &n2, k, &c_b23, &c_b23, &q_ref(*n1 + 1, 1), ldq);
    }

    slacpy_("A", &n12, k, &q[q_offset], ldq, &s[1], &n12);
    if (n12 != 0) {
	latime_1.ops += (real) (*n1) * 2 * *k * n12;
	sgemm_("N", "N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23,
		 &q[q_offset], ldq);
    } else {
	slaset_("A", n1, k, &c_b23, &c_b23, &q_ref(1, 1), ldq);
    }


L120:
    return 0;

/*     End of SLAED3 */

} /* slaed3_ */

#undef q_ref