slaed1.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 integer c__1 = 1;
static integer c_n1 = -1;

/* Subroutine */ int slaed1_(integer *n, real *d__, real *q, integer *ldq, 
	integer *indxq, real *rho, integer *cutpnt, real *work, integer *
	iwork, integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, i__1, i__2;

    /* Local variables */
    static integer indx, i__, k, indxc, indxp;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *);
    static integer n1, n2;
    extern /* Subroutine */ int slaed2_(integer *, integer *, integer *, real 
	    *, real *, integer *, integer *, real *, real *, real *, real *, 
	    real *, integer *, integer *, integer *, integer *, integer *), 
	    slaed3_(integer *, integer *, integer *, real *, real *, integer *
	    , real *, real *, real *, integer *, integer *, real *, real *, 
	    integer *);
    static integer idlmda, is, iw, iz;
    extern /* Subroutine */ int xerbla_(char *, integer *), slamrg_(
	    integer *, integer *, real *, integer *, integer *, integer *);
    static integer coltyp, iq2, cpp1;


#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, 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 unchanged, OPS is only incremented   

    Purpose   
    =======   

    SLAED1 computes the updated eigensystem of a diagonal   
    matrix after modification by a rank-one symmetric matrix.  This   
    routine is used only for the eigenproblem which requires all   
    eigenvalues and eigenvectors of a tridiagonal matrix.  SLAED7 handles   
    the case in which eigenvalues only or eigenvalues and eigenvectors   
    of a full symmetric matrix (which was reduced to tridiagonal form)   
    are desired.   

      T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)   

       where Z = Q'u, u is a vector of length N with ones in the   
       CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.   

       The eigenvectors of the original matrix are stored in Q, and the   
       eigenvalues are in D.  The algorithm consists of three stages:   

          The first stage consists of deflating the size of the problem   
          when there are multiple eigenvalues or if there is a zero in   
          the Z vector.  For each such occurence the dimension of the   
          secular equation problem is reduced by one.  This stage is   
          performed by the routine SLAED2.   

          The second stage consists of calculating the updated   
          eigenvalues. This is done by finding the roots of the secular   
          equation via the routine SLAED4 (as called by SLAED3).   
          This routine also calculates the eigenvectors of the current   
          problem.   

          The final stage consists of computing the updated eigenvectors   
          directly using the updated eigenvalues.  The eigenvectors for   
          the current problem are multiplied with the eigenvectors from   
          the overall problem.   

    Arguments   
    =========   

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

    D      (input/output) REAL array, dimension (N)   
           On entry, the eigenvalues of the rank-1-perturbed matrix.   
           On exit, the eigenvalues of the repaired matrix.   

    Q      (input/output) REAL array, dimension (LDQ,N)   
           On entry, the eigenvectors of the rank-1-perturbed matrix.   
           On exit, the eigenvectors of the repaired tridiagonal matrix.   

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

    INDXQ  (input/output) INTEGER array, dimension (N)   
           On entry, the permutation which separately sorts the two   
           subproblems in D into ascending order.   
           On exit, the permutation which will reintegrate the   
           subproblems back into sorted order,   
           i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.   

    RHO    (input) REAL   
           The subdiagonal entry used to create the rank-1 modification.   

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

    WORK   (workspace) REAL array, dimension (4*N + N**2)   

    IWORK  (workspace) INTEGER array, dimension (4*N)   

    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;
    --indxq;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*n < 0) {
	*info = -1;
    } else if (*ldq < max(1,*n)) {
	*info = -4;
    } else /* if(complicated condition) */ {
/* Computing MIN */
	i__1 = 1, i__2 = *n / 2;
	if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) {
	    *info = -7;
	}
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SLAED1", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     The following values are integer pointers which indicate   
       the portion of the workspace   
       used by a particular array in SLAED2 and SLAED3. */

    iz = 1;
    idlmda = iz + *n;
    iw = idlmda + *n;
    iq2 = iw + *n;

    indx = 1;
    indxc = indx + *n;
    coltyp = indxc + *n;
    indxp = coltyp + *n;


/*     Form the z-vector which consists of the last row of Q_1 and the   
       first row of Q_2. */

    scopy_(cutpnt, &q_ref(*cutpnt, 1), ldq, &work[iz], &c__1);
    cpp1 = *cutpnt + 1;
    i__1 = *n - *cutpnt;
    scopy_(&i__1, &q_ref(cpp1, cpp1), ldq, &work[iz + *cutpnt], &c__1);

/*     Deflate eigenvalues. */

    slaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[
	    iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[
	    indxc], &iwork[indxp], &iwork[coltyp], info);

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

/*     Solve Secular Equation. */

    if (k != 0) {
	is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp + 
		1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2;
	slaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda],
		 &work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[
		is], info);
	if (*info != 0) {
	    goto L20;
	}

/*     Prepare the INDXQ sorting permutation. */

	n1 = k;
	n2 = *n - k;
	slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
    } else {
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    indxq[i__] = i__;
/* L10: */
	}
    }

L20:
    return 0;

/*     End of SLAED1 */

} /* slaed1_ */

#undef q_ref