sggsvd.c

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/*                      dimension (max(3*N,M,P)+N) */

/*  IWORK   (workspace/output) INTEGER array, dimension (N) */
/*          On exit, IWORK stores the sorting information. More */
/*          precisely, the following loop will sort ALPHA */
/*             for I = K+1, min(M,K+L) */
/*                 swap ALPHA(I) and ALPHA(IWORK(I)) */
/*             endfor */
/*          such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(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 STGSJA. */

/*  Internal Parameters */
/*  =================== */

/*  TOLA    REAL */
/*  TOLB    REAL */
/*          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. */

/*  Further Details */
/*  =============== */

/*  2-96 Based on modifications by */
/*     Ming Gu and Huan Ren, Computer Science Division, University of */
/*     California at Berkeley, USA */

/*  ===================================================================== */

/*     .. Local Scalars .. */
/*<       LOGICAL            WANTQ, WANTU, WANTV >*/
/*<       INTEGER            I, IBND, ISUB, J, NCYCLE >*/
/*<       REAL               ANORM, BNORM, SMAX, TEMP, TOLA, TOLB, ULP, UNFL >*/
/*     .. */
/*     .. External Functions .. */
/*<       LOGICAL            LSAME >*/
/*<       REAL               SLAMCH, SLANGE >*/
/*<       EXTERNAL           LSAME, SLAMCH, SLANGE >*/
/*     .. */
/*     .. External Subroutines .. */
/*<       EXTERNAL           SCOPY, SGGSVP, STGSJA, XERBLA >*/
/*     .. */
/*     .. Intrinsic Functions .. */
/*<       INTRINSIC          MAX, MIN >*/
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters */

/*<       WANTU = LSAME( JOBU, 'U' ) >*/
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --alpha;
    --beta;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    --work;
    --iwork;

    /* Function Body */
    wantu = lsame_(jobu, "U", (ftnlen)1, (ftnlen)1);
/*<       WANTV = LSAME( JOBV, 'V' ) >*/
    wantv = lsame_(jobv, "V", (ftnlen)1, (ftnlen)1);
/*<       WANTQ = LSAME( JOBQ, 'Q' ) >*/
    wantq = lsame_(jobq, "Q", (ftnlen)1, (ftnlen)1);

/*<       INFO = 0 >*/
    *info = 0;
/*<       IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN >*/
    if (! (wantu || lsame_(jobu, "N", (ftnlen)1, (ftnlen)1))) {
/*<          INFO = -1 >*/
        *info = -1;
/*<       ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN >*/
    } else if (! (wantv || lsame_(jobv, "N", (ftnlen)1, (ftnlen)1))) {
/*<          INFO = -2 >*/
        *info = -2;
/*<       ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN >*/
    } else if (! (wantq || lsame_(jobq, "N", (ftnlen)1, (ftnlen)1))) {
/*<          INFO = -3 >*/
        *info = -3;
/*<       ELSE IF( M.LT.0 ) THEN >*/
    } else if (*m < 0) {
/*<          INFO = -4 >*/
        *info = -4;
/*<       ELSE IF( N.LT.0 ) THEN >*/
    } else if (*n < 0) {
/*<          INFO = -5 >*/
        *info = -5;
/*<       ELSE IF( P.LT.0 ) THEN >*/
    } else if (*p < 0) {
/*<          INFO = -6 >*/
        *info = -6;
/*<       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
    } else if (*lda < max(1,*m)) {
/*<          INFO = -10 >*/
        *info = -10;
/*<       ELSE IF( LDB.LT.MAX( 1, P ) ) THEN >*/
    } else if (*ldb < max(1,*p)) {
/*<          INFO = -12 >*/
        *info = -12;
/*<       ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN >*/
    } else if (*ldu < 1 || (wantu && *ldu < *m)) {
/*<          INFO = -16 >*/
        *info = -16;
/*<       ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN >*/
    } else if (*ldv < 1 || (wantv && *ldv < *p)) {
/*<          INFO = -18 >*/
        *info = -18;
/*<       ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN >*/
    } else if (*ldq < 1 || (wantq && *ldq < *n)) {
/*<          INFO = -20 >*/
        *info = -20;
/*<       END IF >*/
    }
/*<       IF( INFO.NE.0 ) THEN >*/
    if (*info != 0) {
/*<          CALL XERBLA( 'SGGSVD', -INFO ) >*/
        i__1 = -(*info);
        xerbla_("SGGSVD", &i__1, (ftnlen)6);
/*<          RETURN >*/
        return 0;
/*<       END IF >*/
    }

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

/*<       ANORM = SLANGE( '1', M, N, A, LDA, WORK ) >*/
    anorm = slange_("1", m, n, &a[a_offset], lda, &work[1], (ftnlen)1);
/*<       BNORM = SLANGE( '1', P, N, B, LDB, WORK ) >*/
    bnorm = slange_("1", p, n, &b[b_offset], ldb, &work[1], (ftnlen)1);

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

/*<       ULP = SLAMCH( 'Precision' ) >*/
    ulp = slamch_("Precision", (ftnlen)9);
/*<       UNFL = SLAMCH( 'Safe Minimum' ) >*/
    unfl = slamch_("Safe Minimum", (ftnlen)12);
/*<       TOLA = MAX( M, N )*MAX( ANORM, UNFL )*ULP >*/
    tola = max(*m,*n) * dmax(anorm,unfl) * ulp;
/*<       TOLB = MAX( P, N )*MAX( BNORM, UNFL )*ULP >*/
    tolb = max(*p,*n) * dmax(bnorm,unfl) * ulp;

/*     Preprocessing */

/*<    >*/
    sggsvp_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset], ldb, &
            tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv, &q[
            q_offset], ldq, &iwork[1], &work[1], &work[*n + 1], info, (ftnlen)
            1, (ftnlen)1, (ftnlen)1);

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

/*<    >*/
    stgsja_(jobu, jobv, jobq, m, p, n, k, l, &a[a_offset], lda, &b[b_offset], 
            ldb, &tola, &tolb, &alpha[1], &beta[1], &u[u_offset], ldu, &v[
            v_offset], ldv, &q[q_offset], ldq, &work[1], &ncycle, info, (
            ftnlen)1, (ftnlen)1, (ftnlen)1);

/*     Sort the singular values and store the pivot indices in IWORK */
/*     Copy ALPHA to WORK, then sort ALPHA in WORK */

/*<       CALL SCOPY( N, ALPHA, 1, WORK, 1 ) >*/
    scopy_(n, &alpha[1], &c__1, &work[1], &c__1);
/*<       IBND = MIN( L, M-K ) >*/
/* Computing MIN */
    i__1 = *l, i__2 = *m - *k;
    ibnd = min(i__1,i__2);
/*<       DO 20 I = 1, IBND >*/
    i__1 = ibnd;
    for (i__ = 1; i__ <= i__1; ++i__) {

/*        Scan for largest ALPHA(K+I) */

/*<          ISUB = I >*/
        isub = i__;
/*<          SMAX = WORK( K+I ) >*/
        smax = work[*k + i__];
/*<          DO 10 J = I + 1, IBND >*/
        i__2 = ibnd;
        for (j = i__ + 1; j <= i__2; ++j) {
/*<             TEMP = WORK( K+J ) >*/
            temp = work[*k + j];
/*<             IF( TEMP.GT.SMAX ) THEN >*/
            if (temp > smax) {
/*<                ISUB = J >*/
                isub = j;
/*<                SMAX = TEMP >*/
                smax = temp;
/*<             END IF >*/
            }
/*<    10    CONTINUE >*/
/* L10: */
        }
/*<          IF( ISUB.NE.I ) THEN >*/
        if (isub != i__) {
/*<             WORK( K+ISUB ) = WORK( K+I ) >*/
            work[*k + isub] = work[*k + i__];
/*<             WORK( K+I ) = SMAX >*/
            work[*k + i__] = smax;
/*<             IWORK( K+I ) = K + ISUB >*/
            iwork[*k + i__] = *k + isub;
/*<          ELSE >*/
        } else {
/*<             IWORK( K+I ) = K + I >*/
            iwork[*k + i__] = *k + i__;
/*<          END IF >*/
        }
/*<    20 CONTINUE >*/
/* L20: */
    }

/*<       RETURN >*/
    return 0;

/*     End of SGGSVD */

/*<       END >*/
} /* sggsvd_ */

#ifdef __cplusplus
        }
#endif