zsvdc.c

InsightToolkit-1.4.0(有大量的优化算法程序)

L120:
        if (wantv)
        for (i = l+1; i < *p; ++i) {
            i__1 = i + l * *ldv; /* index [i,l] */
            v[i__1].r = e[i].r, v[i__1].i = e[i].i;
        }
    }

/*     set up the final bidiagonal matrix or order m. */

    m = min(*p-1, *n);
    if (nct < *p) {
        i__1 = nct * (*ldx+1); /* index [nct,nct] */
        s[nct].r = x[i__1].r, s[nct].i = x[i__1].i;
    }
    if (*n-1 < m) {
        s[m].r = 0., s[m].i = 0.;
    }
    if (nrt < m) {
        i__1 = nrt + m * *ldx; /* index [nrt,m] */
        e[nrt].r = x[i__1].r, e[nrt].i = x[i__1].i;
    }
    e[m].r = 0., e[m].i = 0.;

/*     if required, generate u. */

    if (wantu)
    for (j = nct; j < ncu; ++j) {
        for (i = 0; i < *n; ++i) {
            i__1 = i + j * *ldu; /* index [i,j] */
            u[i__1].r = 0., u[i__1].i = 0.;
        }
        i__1 = j + j * *ldu; /* index [j,j] */
        u[i__1].r = 1., u[i__1].i = 0.;
    }
    if (wantu)
    for (l = nct-1; l >= 0; --l) {
        if (s[l].r == 0. && s[l].i == 0.) {
            for (i = 0; i < *n; ++i) {
                i__1 = i + l * *ldu; /* index [i,l] */
                u[i__1].r = 0., u[i__1].i = 0.;
            }
            i__1 = l + l * *ldu; /* index [l,l] */
            u[i__1].r = 1., u[i__1].i = 0.;
            continue; /* next l */
        }
        i__1 = *n - l;
        i__2 = l + l * *ldu; /* index [l,l] */
        for (j = l+1; j < ncu; ++j) {
            zdotc_(&t, &i__1, &u[i__2], &c__1, &u[l+j* *ldu], &c__1);
            t.r = -t.r, t.i = -t.i;
            z_div(&t, &t, &u[i__2]);
            zaxpy_(&i__1, &t, &u[i__2], &c__1, &u[l+j* *ldu], &c__1);
        }
        zscal_(&i__1, &c_m1, &u[i__2], &c__1);
        u[i__2].r += 1.;
        for (i = 0; i < l; ++i) {
            i__1 = i + l * *ldu; /* index [i,l] */
            u[i__1].r = 0., u[i__1].i = 0.;
        }
    }

/*     if it is required, generate v. */

    if (wantv)
    for (l = *p-1; l >= 0; --l) {
        if (l < nrt && (e[l].r != 0. || e[l].i != 0.))
        for (j = l+1; j < *p; ++j) {
            i__1 = *p - l - 1;
            i__2 = l+1 + l * *ldv; /* index [l+1,l] */
            zdotc_(&t, &i__1, &v[i__2], &c__1, &v[l+1 +j* *ldv], &c__1);
            t.r = -t.r, t.i = -t.i;
            z_div(&t, &t, &v[i__2]);
            zaxpy_(&i__1, &t, &v[i__2], &c__1, &v[l+1 +j* *ldv], &c__1);
        }
        for (i = 0; i < *p; ++i) {
            i__1 = i + l * *ldv; /* index [i,l] */
            v[i__1].r = 0., v[i__1].i = 0.;
        }
        i__1 = l + l * *ldv; /* index [l,l] */
        v[i__1].r = 1., v[i__1].i = 0.;
    }

/*     transform s and e so that they are double precision. */

    for (i = 0; i <= m; ++i) {
        if (s[i].r != 0. || s[i].i != 0.) {
            t.r = z_abs(&s[i]), t.i = 0.;
            z_div(&r, &s[i], &t);
            s[i].r = t.r, s[i].i = t.i;
            if (i < m) {
                z_div(&e[i], &e[i], &r);
            }
            if (wantu) {
                zscal_(n, &r, &u[i* *ldu], &c__1);
            }
        }
        if (i == m) {
            break; /* last i */
        }
        if (e[i].r == 0. && e[i].i == 0.) {
            continue; /* next i */
        }
        t.r = z_abs(&e[i]), t.i = 0.;
        z_div(&r, &t, &e[i]);
        e[i].r = t.r, e[i].i = t.i;
        z__1.r = s[i+1].r * r.r - s[i+1].i * r.i,
        z__1.i = s[i+1].r * r.i + s[i+1].i * r.r;
        s[i+1].r = z__1.r, s[i+1].i = z__1.i;
        if (wantv) {
            zscal_(p, &r, &v[(i+1)* *ldv], &c__1);
        }
    }

/*     main iteration loop for the singular values. */

    mm = m;
    iter = 0;

/*        quit if all the singular values have been found. */

L400:
    if (m == -1) {
        return; /* exit from zsvdc */
    }

/*        if too many iterations have been performed, set */
/*        flag and return. */

    if (iter >= maxit) {
        *info = m+1;
        return; /* exit from zsvdc */
    }

/*        this section of the program inspects for */
/*        negligible elements in the s and e arrays.  on */
/*        completion the variables kase and l are set as follows. */

/*           kase = 1     if s(m) and e(l-1) are negligible and l.lt.m */
/*           kase = 2     if s(l) is negligible and l.lt.m */
/*           kase = 3     if e(l-1) is negligible, l.lt.m, and */
/*                        s(l), ..., s(m) are not negligible (qr step). */
/*           kase = 4     if e(m-1) is negligible (convergence). */

    for (l = m; l > 0; --l) {
        test = z_abs(&s[l-1]) + z_abs(&s[l]);
        ztest = test + z_abs(&e[l-1]);
        if (fsm_ieee_doubles_equal(&ztest, &test)) {
/* WAS: if (ztest == test) { */
            e[l-1].r = 0., e[l-1].i = 0.;
            break; /* last l */
        }
    }
    if (l == m) { /* kase = 4 */ /*        convergence. */

/*           make the singular value  positive */

        if (s[l].r < 0.) {
            s[l].r = -s[l].r, s[l].i = -s[l].i;
            if (wantv) {
                zscal_(p, &c_m1, &v[l* *ldv], &c__1);
            }
        }

/*           order the singular value. */

        while (l != mm && s[l].r < s[l+1].r) {
            t.r = s[l].r, t.i = s[l].i;
            s[l].r = s[l+1].r, s[l].i = s[l+1].i;
            s[l+1].r = t.r, s[l+1].i = t.i;
            if (wantv && l < *p-1) {
                zswap_(p, &v[l* *ldv], &c__1, &v[(l+1)* *ldv], &c__1);
            }
            if (wantu && l < *n-1) {
                zswap_(n, &u[l* *ldu], &c__1, &u[(l+1)* *ldu], &c__1);
            }
            ++l;
        }
        iter = 0;
        --m;
        goto L400;
    }
    for (ls = m; ls >= l; --ls) {
        test = 0.;
        if (ls != m) {
            test += z_abs(&e[ls]);
        }
        if (ls != l) {
            test += z_abs(&e[ls-1]);
        }
        ztest = test + z_abs(&s[ls]);
        if (fsm_ieee_doubles_equal(&ztest, &test)) {
/* WAS: if (ztest == test) { */
            s[ls].r = 0., s[ls].i = 0.;
            break; /* last ls */
        }
    }
    if (ls == l-1) { /* kase = 3 */ /*        perform one qr step. */

/*           calculate the shift. */

        scale =            z_abs(&s[m]),
        scale = max(scale, z_abs(&s[m-1])),
        scale = max(scale, z_abs(&e[m-1])),
        scale = max(scale, z_abs(&s[l])),
        scale = max(scale, z_abs(&e[l]));
        sm = s[m].r / scale;
        smm1 = s[m-1].r / scale;
        emm1 = e[m-1].r / scale;
        sl = s[l].r / scale;
        el = e[l].r / scale;
        b = ((smm1+sm) * (smm1-sm) + emm1*emm1) / 2.;
        c = sm * emm1; c *= c;
        shift = 0.;
        if (b != 0. || c != 0.) {
            shift = sqrt(b*b + c);
            if (b < 0.) {
                shift = -shift;
            }
            shift = c / (b + shift);
        }
        f = (sl + sm) * (sl - sm) + shift;
        g = sl * el;

/*           chase zeros. */

        for (k = l; k < m; ++k) {
            drotg_(&f, &g, &cs, &sn);
            if (k != l) {
                e[k-1].r = f, e[k-1].i = 0.;
            }
            f      = cs * s[k].r + sn * e[k].r;
            e[k].r = cs * e[k].r - sn * s[k].r,
            e[k].i = cs * e[k].i - sn * s[k].i;
            g = sn * s[k+1].r;
            s[k+1].r *= cs, s[k+1].i *= cs;
            if (wantv) {
                zdrot_(p, &v[k* *ldv], &c__1, &v[(k+1)* *ldv], &c__1, &cs, &sn);
            }
            drotg_(&f, &g, &cs, &sn);
            s[k].r = f, s[k].i = 0.;
            f        =  cs * e[k].r + sn * s[k+1].r;
            s[k+1].r = -sn * e[k].r + cs * s[k+1].r,
            s[k+1].i = -sn * e[k].i + cs * s[k+1].i;
            g = sn * e[k+1].r;
            e[k+1].r *= cs, e[k+1].i *= cs;
            if (wantu && k < *n-1) {
                zdrot_(n, &u[k* *ldu], &c__1, &u[(k+1)* *ldu], &c__1, &cs, &sn);
            }
        }
        e[m-1].r = f, e[m-1].i = 0.;
        ++iter;
    }
    else if (ls == m) { /* kase = 1 */ /*        deflate negligible s(m). */
        f = e[m-1].r;
        e[m-1].r = 0., e[m-1].i = 0.;
        for (k = m-1; k >= l; --k) {
            t1 = s[k].r;
            drotg_(&t1, &f, &cs, &sn);
            s[k].r = t1, s[k].i = 0.;
            if (k != l) {
                f = -sn * e[k-1].r;
                e[k-1].r *= cs, e[k-1].i *= cs;
            }
            if (wantv) {
                zdrot_(p, &v[k* *ldv], &c__1, &v[m* *ldv], &c__1, &cs, &sn);
            }
        }
    }
    else { /* kase = 2 */ /*        split at negligible s(l). */
        /* l = ls + 1; */
        f = e[ls].r;
        e[ls].r = 0., e[ls].i = 0.;
        for (k = ls+1; k <= m; ++k) {
            t1 = s[k].r;
            drotg_(&t1, &f, &cs, &sn);
            s[k].r = t1, s[k].i = 0.;
            f = -sn * e[k].r;
            e[k].r *= cs, e[k].i *= cs;
            if (wantu) {
                zdrot_(n, &u[k* *ldu], &c__1, &u[ls* *ldu], &c__1, &cs, &sn);
            }
        }
    }
    goto L400;

} /* zsvdc_ */

int fsm_ieee_doubles_equal(const double *x, const double *y)
{
  return *x == *y;
}