dggsvd.c

来自「InsightToolkit-1.4.0(有大量的优化算法程序)」· C语言 代码 · 共 278 行 · 第 1/2 页

/*          See Purpose for details.                                      */
/*                                                                        */
/*  LDA     (input) INTEGER                                               */
/*          The leading dimension of the array A. LDA >= max(1,M).        */
/*                                                                        */
/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)      */
/*          On entry, the P-by-N matrix B.                                */
/*          On exit, B contains the triangular matrix R if M-K-L < 0.     */
/*          See Purpose for details.                                      */
/*                                                                        */
/*  LDB     (input) INTEGER                                               */
/*          The leading dimension of the array B. LDA >= max(1,P).        */
/*                                                                        */
/*  ALPHA   (output) DOUBLE PRECISION array, dimension (N)                */
/*  BETA    (output) DOUBLE PRECISION array, dimension (N)                */
/*          On exit, ALPHA and BETA contain the generalized singular      */
/*          value pairs of A and B;                                       */
/*            ALPHA(1:K) = 1,                                             */
/*            BETA(1:K)  = 0,                                             */
/*          and if M-K-L >= 0,                                            */
/*            ALPHA(K+1:K+L) = C,                                         */
/*            BETA(K+1:K+L)  = S,                                         */
/*          or if M-K-L < 0,                                              */
/*            ALPHA(K+1:M)=C, ALPHA(M+1:K+L)=0                            */
/*            BETA(K+1:M) =S, BETA(M+1:K+L) =1                            */
/*          and                                                           */
/*            ALPHA(K+L+1:N) = 0                                          */
/*            BETA(K+L+1:N)  = 0                                          */
/*                                                                        */
/*  U       (output) DOUBLE PRECISION array, dimension (LDU,M)            */
/*          If JOBU = 'U', U contains the M-by-M orthogonal matrix U.     */
/*          If JOBU = 'N', U is not referenced.                           */
/*                                                                        */
/*  LDU     (input) INTEGER                                               */
/*          The leading dimension of the array U. LDU >= max(1,M) if      */
/*          JOBU = 'U'; LDU >= 1 otherwise.                               */
/*                                                                        */
/*  V       (output) DOUBLE PRECISION array, dimension (LDV,P)            */
/*          If JOBV = 'V', V contains the P-by-P orthogonal matrix V.     */
/*          If JOBV = 'N', V is not referenced.                           */
/*                                                                        */
/*  LDV     (input) INTEGER                                               */
/*          The leading dimension of the array V. LDV >= max(1,P) if      */
/*          JOBV = 'V'; LDV >= 1 otherwise.                               */
/*                                                                        */
/*  Q       (output) DOUBLE PRECISION array, dimension (LDQ,N)            */
/*          If JOBQ = 'Q', Q contains the N-by-N orthogonal matrix Q.     */
/*          If JOBQ = 'N', Q is not referenced.                           */
/*                                                                        */
/*  LDQ     (input) INTEGER                                               */
/*          The leading dimension of the array Q. LDQ >= max(1,N) if      */
/*          JOBQ = 'Q'; LDQ >= 1 otherwise.                               */
/*                                                                        */
/*  WORK    (workspace) DOUBLE PRECISION array,                           */
/*                      dimension (max(3*N,M,P)+N)                        */
/*                                                                        */
/*  IWORK   (workspace) INTEGER array, dimension (N)                      */
/*                                                                        */
/*  INFO    (output)INTEGER                                               */
/*          = 0:  successful exit                                         */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value.   */
/*          > 0:  if INFO = 1, the Jacobi-type procedure failed to        */
/*                converge.  For further details, see subroutine DTGSJA.  */
/*                                                                        */
/*  Internal Parameters                                                   */
/*  ===================                                                   */
/*                                                                        */
/*  TOLA    DOUBLE PRECISION                                              */
/*  TOLB    DOUBLE PRECISION                                              */
/*          TOLA and TOLB are the thresholds to determine the effective   */
/*          rank of (A',B')'. Generally, they are set to                  */
/*                   TOLA = MAX(M,N)*norm(A)*MACHEPS,                     */
/*                   TOLB = MAX(P,N)*norm(B)*MACHEPS.                     */
/*          The size of TOLA and TOLB may affect the size of backward     */
/*          errors of the decomposition.                                  */
/*                                                                        */
/*  ===================================================================== */

/*     Test the input parameters */

    wantu = lsame_(jobu, "U");
    wantv = lsame_(jobv, "V");
    wantq = lsame_(jobq, "Q");

    *info = 0;
    if (! (wantu || lsame_(jobu, "N"))) {
        *info = -1;
    } else if (! (wantv || lsame_(jobv, "N"))) {
        *info = -2;
    } else if (! (wantq || lsame_(jobq, "N"))) {
        *info = -3;
    } else if (*m < 0) {
        *info = -4;
    } else if (*n < 0) {
        *info = -5;
    } else if (*p < 0) {
        *info = -6;
    } else if (*lda < max(1,*m)) {
        *info = -10;
    } else if (*ldb < max(1,*p)) {
        *info = -12;
    } else if (*ldu < 1 || (wantu && *ldu < *m)) {
        *info = -16;
    } else if (*ldv < 1 || (wantv && *ldv < *p)) {
        *info = -18;
    } else if (*ldq < 1 || (wantq && *ldq < *n)) {
        *info = -20;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DGGSVD", &i__1);
        return;
    }

/*     Compute the Frobenius norm of matrices A and B */

    anorm = dlange_("1", m, n, a, lda, work);
    bnorm = dlange_("1", p, n, b, ldb, work);

/*     Get machine precision and set up threshold for determining */
/*     the effective numerical rank of the matrices A and B. */

    ulp = dlamch_("Precision");
    unfl = dlamch_("Safe Minimum");
    tola = max(*m,*n) * max(anorm,unfl) * ulp;
    tolb = max(*p,*n) * max(bnorm,unfl) * ulp;

/*     Preprocessing */

    dggsvp_(jobu, jobv, jobq, m, p, n, a, lda, b, ldb, &tola, &tolb, k, l,
            u, ldu, v, ldv, q, ldq, iwork, work, &work[*n], info);

/*     Compute the GSVD of two upper "triangular" matrices */

    dtgsja_(jobu, jobv, jobq, m, p, n, k, l, a, lda, b, ldb, &tola, &tolb,
            alpha, beta, u, ldu, v, ldv, q, ldq, work, &ncycle, info);

} /* dggsvd_ */