cstedc.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__2 = 2;
static integer c__9 = 9;
static integer c__0 = 0;
static real c_b18 = 0.f;
static real c_b19 = 1.f;
static integer c__1 = 1;

/* Subroutine */ int cstedc_(char *compz, integer *n, real *d__, real *e, 
	complex *z__, integer *ldz, complex *work, integer *lwork, real *
	rwork, integer *lrwork, integer *iwork, integer *liwork, integer *
	info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2, i__3, i__4;
    real r__1, r__2;

    /* Builtin functions */
    double log(doublereal);
    integer pow_ii(integer *, integer *);
    double sqrt(doublereal);

    /* Local variables */
    static real tiny;
    static integer i__, j, k, m;
    static real p;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
	    complex *, integer *);
    static integer lwmin;
    extern /* Subroutine */ int claed0_(integer *, integer *, real *, real *, 
	    complex *, integer *, complex *, integer *, real *, integer *, 
	    integer *);
    static integer start, ii, ll;
    extern /* Subroutine */ int clacrm_(integer *, integer *, complex *, 
	    integer *, real *, integer *, complex *, integer *, real *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), xerbla_(char *, 
	    integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), sstedc_(char *, integer *, real *, real *, real *, 
	    integer *, real *, integer *, integer *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
	    real *, integer *);
    static integer liwmin, icompz;
    extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, 
	    complex *, integer *, real *, integer *);
    static real orgnrm;
    extern doublereal slanst_(char *, integer *, real *, real *);
    extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
    static integer lrwmin;
    static logical lquery;
    static integer smlsiz;
    extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *, 
	    real *, integer *, real *, integer *);
    static integer end, lgn;
    static real eps;


#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   
       June 30, 1999   

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

    Purpose   
    =======   

    CSTEDC computes all eigenvalues and, optionally, eigenvectors of a   
    symmetric tridiagonal matrix using the divide and conquer 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.   

    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.  See SLAED3 for details.   

    Arguments   
    =========   

    COMPZ   (input) CHARACTER*1   
            = 'N':  Compute eigenvalues only.   
            = 'I':  Compute eigenvectors of tridiagonal matrix also.   
            = 'V':  Compute eigenvectors of original Hermitian matrix   
                    also.  On entry, Z contains the unitary matrix used   
                    to reduce the original matrix to tridiagonal form.   

    N       (input) INTEGER   
            The dimension of the symmetric tridiagonal 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 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.   
            If eigenvectors are desired, then LDZ >= max(1,N).   

    WORK    (workspace/output) COMPLEX array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK.   
            If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.   
            If COMPZ = 'V' and N > 1, LWORK must be at least N*N.   

            If LWORK = -1, then a workspace query is assumed; the routine   
            only calculates the optimal size of the WORK array, returns   
            this value as the first entry of the WORK array, and no error   
            message related to LWORK is issued by XERBLA.   

    RWORK   (workspace/output) REAL array,   
                                           dimension (LRWORK)   
            On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.   

    LRWORK  (input) INTEGER   
            The dimension of the array RWORK.   
            If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.   
            If COMPZ = 'V' and N > 1, LRWORK must be at least   
                           1 + 3*N + 2*N*lg N + 3*N**2 ,   
                           where lg( N ) = smallest integer k such   
                           that 2**k >= N.   
            If COMPZ = 'I' and N > 1, LRWORK must be at least   
                           1 + 4*N + 2*N**2 .   

            If LRWORK = -1, then a workspace query is assumed; the   
            routine only calculates the optimal size of the RWORK array,   
            returns this value as the first entry of the RWORK array, and   
            no error message related to LRWORK is issued by XERBLA.   

    IWORK   (workspace/output) INTEGER array, dimension (LIWORK)   
            On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.   

    LIWORK  (input) INTEGER   
            The dimension of the array IWORK.   
            If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.   
            If COMPZ = 'V' or N > 1,  LIWORK must be at least   
                                      6 + 6*N + 5*N*lg N.   
            If COMPZ = 'I' or N > 1,  LIWORK must be at least   
                                      3 + 5*N .   

            If LIWORK = -1, then a workspace query is assumed; the   
            routine only calculates the optimal size of the IWORK array,   
            returns this value as the first entry of the IWORK array, and   
            no error message related to LIWORK is issued by XERBLA.   

    INFO    (output) INTEGER   
            = 0:  successful exit.   
            < 0:  if INFO = -i, the i-th argument had an illegal value.   
            > 0:  The algorithm failed to compute an eigenvalue while   
                  working on the submatrix lying in rows and columns   
                  INFO/(N+1) through mod(INFO,N+1).   

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

    Based on contributions by   
       Jeff Rutter, Computer Science Division, University of California   
       at Berkeley, USA   

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


       Test the input parameters.   

       Parameter adjustments */
    --d__;
    --e;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --work;
    --rwork;
    --iwork;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;

    if (lsame_(compz, "N")) {
	icompz = 0;
    } else if (lsame_(compz, "V")) {
	icompz = 1;
    } else if (lsame_(compz, "I")) {
	icompz = 2;
    } else {
	icompz = -1;
    }
    if (*n <= 1 || icompz <= 0) {
	lwmin = 1;
	liwmin = 1;
	lrwmin = 1;
    } else {
	lgn = (integer) (log((real) (*n)) / log(2.f));
	if (pow_ii(&c__2, &lgn) < *n) {
	    ++lgn;
	}
	if (pow_ii(&c__2, &lgn) < *n) {
	    ++lgn;
	}
	if (icompz == 1) {
	    lwmin = *n * *n;