dlasq1.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 {
    doublereal ops, itcnt;
} latime_;

#define latime_1 latime_

/* Table of constant values */

static integer c__1 = 1;
static integer c__2 = 2;
static integer c__0 = 0;

/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e, 
	doublereal *work, integer *info)
{
    /* System generated locals */
    integer i__1, i__2;
    doublereal d__1, d__2, d__3;

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

    /* Local variables */
    extern /* Subroutine */ int dlas2_(doublereal *, doublereal *, doublereal 
	    *, doublereal *, doublereal *);
    static integer i__;
    static doublereal scale;
    static integer iinfo;
    static doublereal sigmn;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static doublereal sigmx;
    extern /* Subroutine */ int dlasq2_(integer *, doublereal *, integer *);
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *);
    static doublereal safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *), dlasrt_(
	    char *, integer *, doublereal *, integer *);
    static doublereal eps;


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


    Purpose   
    =======   

    DLASQ1 computes the singular values of a real N-by-N bidiagonal   
    matrix with diagonal D and off-diagonal E. The singular values   
    are computed to high relative accuracy, in the absence of   
    denormalization, underflow and overflow. The algorithm was first   
    presented in   

    "Accurate singular values and differential qd algorithms" by K. V.   
    Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,   
    1994,   

    and the present implementation is described in "An implementation of   
    the dqds Algorithm (Positive Case)", LAPACK Working Note.   

    Arguments   
    =========   

    N     (input) INTEGER   
          The number of rows and columns in the matrix. N >= 0.   

    D     (input/output) DOUBLE PRECISION array, dimension (N)   
          On entry, D contains the diagonal elements of the   
          bidiagonal matrix whose SVD is desired. On normal exit,   
          D contains the singular values in decreasing order.   

    E     (input/output) DOUBLE PRECISION array, dimension (N)   
          On entry, elements E(1:N-1) contain the off-diagonal elements   
          of the bidiagonal matrix whose SVD is desired.   
          On exit, E is overwritten.   

    WORK  (workspace) DOUBLE PRECISION array, dimension (4*N)   

    INFO  (output) INTEGER   
          = 0: successful exit   
          < 0: if INFO = -i, the i-th argument had an illegal value   
          > 0: the algorithm failed   
               = 1, a split was marked by a positive value in E   
               = 2, current block of Z not diagonalized after 30*N   
                    iterations (in inner while loop)   
               = 3, termination criterion of outer while loop not met   
                    (program created more than N unreduced blocks)   

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


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

    /* Function Body */
    *info = 0;
    if (*n < 0) {
	*info = -2;
	i__1 = -(*info);
	xerbla_("DLASQ1", &i__1);
	return 0;
    } else if (*n == 0) {
	return 0;
    } else if (*n == 1) {
	d__[1] = abs(d__[1]);
	return 0;
    } else if (*n == 2) {
	dlas2_(&d__[1], &e[1], &d__[2], &sigmn, &sigmx);
	d__[1] = sigmx;
	d__[2] = sigmn;
	return 0;
    }

/*     Estimate the largest singular value. */

    sigmx = 0.;
    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
	d__[i__] = (d__1 = d__[i__], abs(d__1));
/* Computing MAX */
	d__2 = sigmx, d__3 = (d__1 = e[i__], abs(d__1));
	sigmx = max(d__2,d__3);
/* L10: */
    }
    d__[*n] = (d__1 = d__[*n], abs(d__1));

/*     Early return if SIGMX is zero (matrix is already diagonal). */

    if (sigmx == 0.) {
	dlasrt_("D", n, &d__[1], &iinfo);
	return 0;
    }

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
	d__1 = sigmx, d__2 = d__[i__];
	sigmx = max(d__1,d__2);
/* L20: */
    }

/*     Copy D and E into WORK (in the Z format) and scale (squaring the   
       input data makes scaling by a power of the radix pointless). */

    latime_1.ops += (doublereal) ((*n << 1) + 1);
    eps = dlamch_("Precision");
    safmin = dlamch_("Safe minimum");
    scale = sqrt(eps / safmin);
    dcopy_(n, &d__[1], &c__1, &work[1], &c__2);
    i__1 = *n - 1;
    dcopy_(&i__1, &e[1], &c__1, &work[2], &c__2);
    i__1 = (*n << 1) - 1;
    i__2 = (*n << 1) - 1;
    dlascl_("G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2, 
	    &iinfo);

/*     Compute the q's and e's. */

    latime_1.ops += (doublereal) ((*n << 1) - 1);
    i__1 = (*n << 1) - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing 2nd power */
	d__1 = work[i__];
	work[i__] = d__1 * d__1;
/* L30: */
    }
    work[*n * 2] = 0.;

    dlasq2_(n, &work[1], info);

    if (*info == 0) {
	latime_1.ops += (doublereal) (*n << 1);
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    d__[i__] = sqrt(work[i__]);
/* L40: */
	}
	dlascl_("G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, &
		iinfo);
    }

    return 0;

/*     End of DLASQ1 */

} /* dlasq1_ */