dhsein.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 logical c_false = FALSE_;
static logical c_true = TRUE_;

/* Subroutine */ int dhsein_(char *side, char *eigsrc, char *initv, logical *
	select, integer *n, doublereal *h__, integer *ldh, doublereal *wr, 
	doublereal *wi, doublereal *vl, integer *ldvl, doublereal *vr, 
	integer *ldvr, integer *mm, integer *m, doublereal *work, integer *
	ifaill, integer *ifailr, integer *info)
{
    /* System generated locals */
    integer h_dim1, h_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, 
	    i__2;
    doublereal d__1, d__2;

    /* Local variables */
    static logical pair;
    static doublereal unfl, opst;
    static integer i__, k;
    extern logical lsame_(char *, char *);
    static integer iinfo;
    static logical leftv, bothv;
    static doublereal hnorm;
    static integer kl;
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int dlaein_(logical *, logical *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, doublereal *,
	     doublereal *, doublereal *, integer *, doublereal *, doublereal *
	    , doublereal *, doublereal *, integer *);
    static integer kr;
    extern doublereal dlanhs_(char *, integer *, doublereal *, integer *, 
	    doublereal *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static doublereal bignum;
    static logical noinit;
    static integer ldwork;
    static logical rightv, fromqr;
    static doublereal smlnum;
    static integer kln, ksi;
    static doublereal wki;
    static integer ksr;
    static doublereal ulp, wkr, eps3;


#define h___ref(a_1,a_2) h__[(a_2)*h_dim1 + a_1]
#define vl_ref(a_1,a_2) vl[(a_2)*vl_dim1 + a_1]
#define vr_ref(a_1,a_2) vr[(a_2)*vr_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   
       September 30, 1994   

       Common block to return operation count.   

    Purpose   
    =======   

    DHSEIN uses inverse iteration to find specified right and/or left   
    eigenvectors of a real upper Hessenberg matrix H.   

    The right eigenvector x and the left eigenvector y of the matrix H   
    corresponding to an eigenvalue w are defined by:   

                 H * x = w * x,     y**h * H = w * y**h   

    where y**h denotes the conjugate transpose of the vector y.   

    Arguments   
    =========   

    SIDE    (input) CHARACTER*1   
            = 'R': compute right eigenvectors only;   
            = 'L': compute left eigenvectors only;   
            = 'B': compute both right and left eigenvectors.   

    EIGSRC  (input) CHARACTER*1   
            Specifies the source of eigenvalues supplied in (WR,WI):   
            = 'Q': the eigenvalues were found using DHSEQR; thus, if   
                   H has zero subdiagonal elements, and so is   
                   block-triangular, then the j-th eigenvalue can be   
                   assumed to be an eigenvalue of the block containing   
                   the j-th row/column.  This property allows DHSEIN to   
                   perform inverse iteration on just one diagonal block.   
            = 'N': no assumptions are made on the correspondence   
                   between eigenvalues and diagonal blocks.  In this   
                   case, DHSEIN must always perform inverse iteration   
                   using the whole matrix H.   

    INITV   (input) CHARACTER*1   
            = 'N': no initial vectors are supplied;   
            = 'U': user-supplied initial vectors are stored in the arrays   
                   VL and/or VR.   

    SELECT  (input/output) LOGICAL array, dimension(N)   
            Specifies the eigenvectors to be computed. To select the   
            real eigenvector corresponding to a real eigenvalue WR(j),   
            SELECT(j) must be set to .TRUE.. To select the complex   
            eigenvector corresponding to a complex eigenvalue   
            (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)),   
            either SELECT(j) or SELECT(j+1) or both must be set to   
            .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is   
            .FALSE..   

    N       (input) INTEGER   
            The order of the matrix H.  N >= 0.   

    H       (input) DOUBLE PRECISION array, dimension (LDH,N)   
            The upper Hessenberg matrix H.   

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

    WR      (input/output) DOUBLE PRECISION array, dimension (N)   
    WI      (input) DOUBLE PRECISION array, dimension (N)   
            On entry, the real and imaginary parts of the eigenvalues of   
            H; a complex conjugate pair of eigenvalues must be stored in   
            consecutive elements of WR and WI.   
            On exit, WR may have been altered since close eigenvalues   
            are perturbed slightly in searching for independent   
            eigenvectors.   

    VL      (input/output) DOUBLE PRECISION array, dimension (LDVL,MM)   
            On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must   
            contain starting vectors for the inverse iteration for the   
            left eigenvectors; the starting vector for each eigenvector   
            must be in the same column(s) in which the eigenvector will   
            be stored.   
            On exit, if SIDE = 'L' or 'B', the left eigenvectors   
            specified by SELECT will be stored consecutively in the   
            columns of VL, in the same order as their eigenvalues. A   
            complex eigenvector corresponding to a complex eigenvalue is   
            stored in two consecutive columns, the first holding the real   
            part and the second the imaginary part.   
            If SIDE = 'R', VL is not referenced.   

    LDVL    (input) INTEGER   
            The leading dimension of the array VL.   
            LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.   

    VR      (input/output) DOUBLE PRECISION array, dimension (LDVR,MM)   
            On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must   
            contain starting vectors for the inverse iteration for the   
            right eigenvectors; the starting vector for each eigenvector   
            must be in the same column(s) in which the eigenvector will   
            be stored.   
            On exit, if SIDE = 'R' or 'B', the right eigenvectors   
            specified by SELECT will be stored consecutively in the   
            columns of VR, in the same order as their eigenvalues. A   
            complex eigenvector corresponding to a complex eigenvalue is   
            stored in two consecutive columns, the first holding the real   
            part and the second the imaginary part.   
            If SIDE = 'L', VR is not referenced.   

    LDVR    (input) INTEGER   
            The leading dimension of the array VR.   
            LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.   

    MM      (input) INTEGER   
            The number of columns in the arrays VL and/or VR. MM >= M.   

    M       (output) INTEGER   
            The number of columns in the arrays VL and/or VR required to   
            store the eigenvectors; each selected real eigenvector   
            occupies one column and each selected complex eigenvector   
            occupies two columns.   

    WORK    (workspace) DOUBLE PRECISION array, dimension ((N+2)*N)   

    IFAILL  (output) INTEGER array, dimension (MM)   
            If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left   
            eigenvector in the i-th column of VL (corresponding to the   
            eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the   
            eigenvector converged satisfactorily. If the i-th and (i+1)th   
            columns of VL hold a complex eigenvector, then IFAILL(i) and   
            IFAILL(i+1) are set to the same value.   
            If SIDE = 'R', IFAILL is not referenced.   

    IFAILR  (output) INTEGER array, dimension (MM)   
            If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right   
            eigenvector in the i-th column of VR (corresponding to the   
            eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the   
            eigenvector converged satisfactorily. If the i-th and (i+1)th   
            columns of VR hold a complex eigenvector, then IFAILR(i) and   
            IFAILR(i+1) are set to the same value.   
            If SIDE = 'L', IFAILR is not referenced.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  if INFO = i, i is the number of eigenvectors which   
                  failed to converge; see IFAILL and IFAILR for further   
                  details.   

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

    Each eigenvector is normalized so that the element of largest   
    magnitude has magnitude 1; here the magnitude of a complex number   
    (x,y) is taken to be |x|+|y|.   

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


       Decode and test the input parameters.   

       Parameter adjustments */
    --select;
    h_dim1 = *ldh;
    h_offset = 1 + h_dim1 * 1;
    h__ -= h_offset;
    --wr;
    --wi;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1 * 1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1 * 1;
    vr -= vr_offset;
    --work;
    --ifaill;
    --ifailr;

    /* Function Body */
    bothv = lsame_(side, "B");
    rightv = lsame_(side, "R") || bothv;
    leftv = lsame_(side, "L") || bothv;

    fromqr = lsame_(eigsrc, "Q");

    noinit = lsame_(initv, "N");

/*     Set M to the number of columns required to store the selected   
       eigenvectors, and standardize the array SELECT. */

    *m = 0;
    pair = FALSE_;