dtgevc.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_true = TRUE_;
static integer c__2 = 2;
static doublereal c_b35 = 1.;
static integer c__1 = 1;
static doublereal c_b37 = 0.;
static logical c_false = FALSE_;

/* Subroutine */ int dtgevc_(char *side, char *howmny, logical *select, 
	integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
	doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, integer 
	*mm, integer *m, doublereal *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, 
	    vr_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2, d__3, d__4, d__5, d__6;

    /* Local variables */
    static integer ibeg, ieig, iend;
    static doublereal dmin__, temp, suma[4]	/* was [2][2] */, sumb[4]	
	    /* was [2][2] */, xmax, opst;
    extern /* Subroutine */ int dlag2_(doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
	     doublereal *, doublereal *);
    static doublereal cim2a, cim2b, cre2a, cre2b, temp2, bdiag[2];
    static integer i__, j;
    static doublereal acoef, scale;
    static logical ilall;
    static integer iside;
    static doublereal sbeta;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *);
    static logical il2by2;
    static integer iinfo, in2by2;
    static doublereal small;
    static logical compl;
    static doublereal anorm, bnorm;
    static logical compr;
    extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *, doublereal *,
	     doublereal *, doublereal *, integer *, doublereal *, doublereal *
	    , doublereal *, integer *, doublereal *, doublereal *, integer *);
    static doublereal temp2i;
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    static doublereal temp2r;
    static integer ja;
    static logical ilabad, ilbbad;
    static integer jc, je, na;
    static doublereal acoefa, bcoefa, cimaga, cimagb;
    static logical ilback;
    static integer im;
    static doublereal bcoefi, ascale, bscale, creala;
    static integer jr;
    static doublereal crealb;
    extern doublereal dlamch_(char *);
    static doublereal bcoefr;
    static integer jw, nw;
    static doublereal salfar, safmin;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *);
    static doublereal xscale, bignum;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static logical ilcomp;
    static doublereal opssca;
    static logical ilcplx;
    static integer ihwmny;
    static doublereal big;
    static logical lsa, lsb;
    static doublereal ulp, sum[4]	/* was [2][2] */;


#define suma_ref(a_1,a_2) suma[(a_2)*2 + a_1 - 3]
#define sumb_ref(a_1,a_2) sumb[(a_2)*2 + a_1 - 3]
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_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]
#define sum_ref(a_1,a_2) sum[(a_2)*2 + a_1 - 3]


/*  -- 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   


       ---------------------- Begin Timing Code -------------------------   
       Common block to return operation count and iteration count   
       ITCNT is initialized to 0, OPS is only incremented   
       OPST is used to accumulate small contributions to OPS   
       to avoid roundoff error   
       ----------------------- End Timing Code --------------------------   


    Purpose   
    =======   

    DTGEVC computes some or all of the right and/or left generalized   
    eigenvectors of a pair of real upper triangular matrices (A,B).   

    The right generalized eigenvector x and the left generalized   
    eigenvector y of (A,B) corresponding to a generalized eigenvalue   
    w are defined by:   

            (A - wB) * x = 0  and  y**H * (A - wB) = 0   

    where y**H denotes the conjugate tranpose of y.   

    If an eigenvalue w is determined by zero diagonal elements of both A   
    and B, a unit vector is returned as the corresponding eigenvector.   

    If all eigenvectors are requested, the routine may either return   
    the matrices X and/or Y of right or left eigenvectors of (A,B), or   
    the products Z*X and/or Q*Y, where Z and Q are input orthogonal   
    matrices.  If (A,B) was obtained from the generalized real-Schur   
    factorization of an original pair of matrices   
       (A0,B0) = (Q*A*Z**H,Q*B*Z**H),   
    then Z*X and Q*Y are the matrices of right or left eigenvectors of   
    A.   

    A must be block upper triangular, with 1-by-1 and 2-by-2 diagonal   
    blocks.  Corresponding to each 2-by-2 diagonal block is a complex   
    conjugate pair of eigenvalues and eigenvectors; only one   
    eigenvector of the pair is computed, namely the one corresponding   
    to the eigenvalue with positive imaginary part.   

    Arguments   
    =========   

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

    HOWMNY  (input) CHARACTER*1   
            = 'A': compute all right and/or left eigenvectors;   
            = 'B': compute all right and/or left eigenvectors, and   
                   backtransform them using the input matrices supplied   
                   in VR and/or VL;   
            = 'S': compute selected right and/or left eigenvectors,   
                   specified by the logical array SELECT.   

    SELECT  (input) LOGICAL array, dimension (N)   
            If HOWMNY='S', SELECT specifies the eigenvectors to be   
            computed.   
            If HOWMNY='A' or 'B', SELECT is not referenced.   
            To select the real eigenvector corresponding to the real   
            eigenvalue w(j), SELECT(j) must be set to .TRUE.  To select   
            the complex eigenvector corresponding to a complex conjugate   
            pair w(j) and w(j+1), either SELECT(j) or SELECT(j+1) must   
            be set to .TRUE..   

    N       (input) INTEGER   
            The order of the matrices A and B.  N >= 0.   

    A       (input) DOUBLE PRECISION array, dimension (LDA,N)   
            The upper quasi-triangular matrix A.   

    LDA     (input) INTEGER   
            The leading dimension of array A.  LDA >= max(1,N).   

    B       (input) DOUBLE PRECISION array, dimension (LDB,N)   
            The upper triangular matrix B.  If A has a 2-by-2 diagonal   
            block, then the corresponding 2-by-2 block of B must be   
            diagonal with positive elements.   

    LDB     (input) INTEGER   
            The leading dimension of array B.  LDB >= max(1,N).   

    VL      (input/output) DOUBLE PRECISION array, dimension (LDVL,MM)   
            On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must   
            contain an N-by-N matrix Q (usually the orthogonal matrix Q   
            of left Schur vectors returned by DHGEQZ).   
            On exit, if SIDE = 'L' or 'B', VL contains:   
            if HOWMNY = 'A', the matrix Y of left eigenvectors of (A,B);   
            if HOWMNY = 'B', the matrix Q*Y;   
            if HOWMNY = 'S', the left eigenvectors of (A,B) specified by   
                        SELECT, stored consecutively in the columns of   
                        VL, in the same order as their eigenvalues.   
            If SIDE = 'R', VL is not referenced.   

            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.   

    LDVL    (input) INTEGER   
            The leading dimension of 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 SIDE = 'R' or 'B' and HOWMNY = 'B', VR must   
            contain an N-by-N matrix Q (usually the orthogonal matrix Z   
            of right Schur vectors returned by DHGEQZ).   
            On exit, if SIDE = 'R' or 'B', VR contains:   
            if HOWMNY = 'A', the matrix X of right eigenvectors of (A,B);   
            if HOWMNY = 'B', the matrix Z*X;   
            if HOWMNY = 'S', the right eigenvectors of (A,B) specified by   
                        SELECT, stored consecutively in the columns of   
                        VR, in the same order as their eigenvalues.   
            If SIDE = 'L', VR is not referenced.   

            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.   

    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 actually   
            used to store the eigenvectors.  If HOWMNY = 'A' or 'B', M   
            is set to N.  Each selected real eigenvector occupies one   
            column and each selected complex eigenvector occupies two   
            columns.   

    WORK    (workspace) DOUBLE PRECISION array, dimension (6*N)   

    INFO    (output) INTEGER   
            = 0:  successful exit.   
            < 0:  if INFO = -i, the i-th argument had an illegal value.   
            > 0:  the 2-by-2 block (INFO:INFO+1) does not have a complex   
                  eigenvalue.   

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

    Allocation of workspace:   
    ---------- -- ---------   

       WORK( j ) = 1-norm of j-th column of A, above the diagonal   
       WORK( N+j ) = 1-norm of j-th column of B, above the diagonal   
       WORK( 2*N+1:3*N ) = real part of eigenvector   
       WORK( 3*N+1:4*N ) = imaginary part of eigenvector   
       WORK( 4*N+1:5*N ) = real part of back-transformed eigenvector   
       WORK( 5*N+1:6*N ) = imaginary part of back-transformed eigenvector   

    Rowwise vs. columnwise solution methods:   
    ------- --  ---------- -------- -------   

    Finding a generalized eigenvector consists basically of solving the   
    singular triangular system   

     (A - w B) x = 0     (for right) or:   (A - w B)**H y = 0  (for left)   

    Consider finding the i-th right eigenvector (assume all eigenvalues   
    are real). The equation to be solved is:   
         n                   i   
    0 = sum  C(j,k) v(k)  = sum  C(j,k) v(k)     for j = i,. . .,1   
        k=j                 k=j   

    where  C = (A - w B)  (The components v(i+1:n) are 0.)   

    The "rowwise" method is:   

    (1)  v(i) := 1   
    for j = i-1,. . .,1:   
                            i   
        (2) compute  s = - sum C(j,k) v(k)   and   
                          k=j+1   

        (3) v(j) := s / C(j,j)   

    Step 2 is sometimes called the "dot product" step, since it is an   
    inner product between the j-th row and the portion of the eigenvector   
    that has been computed so far.   

    The "columnwise" method consists basically in doing the sums   
    for all the rows in parallel.  As each v(j) is computed, the   
    contribution of v(j) times the j-th column of C is added to the   
    partial sums.  Since FORTRAN arrays are stored columnwise, this has   
    the advantage that at each step, the elements of C that are accessed   
    are adjacent to one another, whereas with the rowwise method, the   
    elements accessed at a step are spaced LDA (and LDB) words apart.   

    When finding left eigenvectors, the matrix in question is the   
    transpose of the one in storage, so the rowwise method then   
    actually accesses columns of A and B at each step, and so is the   
    preferred method.   

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


       Decode and Test the input parameters   

       Parameter adjustments */
    --select;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    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;

    /* Function Body */
    if (lsame_(howmny, "A")) {
	ihwmny = 1;
	ilall = TRUE_;
	ilback = FALSE_;
    } else if (lsame_(howmny, "S")) {
	ihwmny = 2;
	ilall = FALSE_;
	ilback = FALSE_;
    } else if (lsame_(howmny, "B") || lsame_(howmny, 
	    "T")) {
	ihwmny = 3;
	ilall = TRUE_;
	ilback = TRUE_;
    } else {
	ihwmny = -1;
	ilall = TRUE_;
    }

    if (lsame_(side, "R")) {
	iside = 1;
	compl = FALSE_;
	compr = TRUE_;
    } else if (lsame_(side, "L")) {
	iside = 2;
	compl = TRUE_;
	compr = FALSE_;
    } else if (lsame_(side, "B")) {
	iside = 3;
	compl = TRUE_;
	compr = TRUE_;
    } else {
	iside = -1;
    }

    *info = 0;
    if (iside < 0) {
	*info = -1;
    } else if (ihwmny < 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DTGEVC", &i__1);
	return 0;
    }

/*     Count the number of eigenvectors to be computed */

    if (! ilall) {
	im = 0;
	ilcplx = FALSE_;
	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {