zstedc.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

	    lwmin = *n * *n;
/* Computing 2nd power */
	    i__1 = *n;
	    lrwmin = *n * 3 + 1 + (*n << 1) * lgn + i__1 * i__1 * 3;
	    liwmin = *n * 6 + 6 + *n * 5 * lgn;
	} else if (icompz == 2) {
	    lwmin = 1;
/* Computing 2nd power */
	    i__1 = *n;
	    lrwmin = (*n << 2) + 1 + (i__1 * i__1 << 1);
	    liwmin = *n * 5 + 3;
	}
    }
    if (icompz < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) {
	*info = -6;
    } else if (*lwork < lwmin && ! lquery) {
	*info = -8;
    } else if (*lrwork < lrwmin && ! lquery) {
	*info = -10;
    } else if (*liwork < liwmin && ! lquery) {
	*info = -12;
    }

    if (*info == 0) {
	work[1].r = (doublereal) lwmin, work[1].i = 0.;
	rwork[1] = (doublereal) lrwmin;
	iwork[1] = liwmin;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZSTEDC", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    latime_1.itcnt = 0.;
    if (*n == 0) {
	return 0;
    }
    if (*n == 1) {
	if (icompz != 0) {
	    i__1 = z___subscr(1, 1);
	    z__[i__1].r = 1., z__[i__1].i = 0.;
	}
	return 0;
    }

    smlsiz = ilaenv_(&c__9, "ZSTEDC", " ", &c__0, &c__0, &c__0, &c__0, (
	    ftnlen)6, (ftnlen)1);

/*     If the following conditional clause is removed, then the routine   
       will use the Divide and Conquer routine to compute only the   
       eigenvalues, which requires (3N + 3N**2) real workspace and   
       (2 + 5N + 2N lg(N)) integer workspace.   
       Since on many architectures DSTERF is much faster than any other   
       algorithm for finding eigenvalues only, it is used here   
       as the default.   

       If COMPZ = 'N', use DSTERF to compute the eigenvalues. */

    if (icompz == 0) {
	dsterf_(n, &d__[1], &e[1], info);
	return 0;
    }

/*     If N is smaller than the minimum divide size (SMLSIZ+1), then   
       solve the problem with another solver. */

    if (*n <= smlsiz) {
	if (icompz == 0) {
	    dsterf_(n, &d__[1], &e[1], info);
	    return 0;
	} else if (icompz == 2) {
	    zsteqr_("I", n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], 
		    info);
	    return 0;
	} else {
	    zsteqr_("V", n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], 
		    info);
	    return 0;
	}
    }

/*     If COMPZ = 'I', we simply call DSTEDC instead. */

    if (icompz == 2) {
	dlaset_("Full", n, n, &c_b18, &c_b19, &rwork[1], n);
	ll = *n * *n + 1;
	i__1 = *lrwork - ll + 1;
	dstedc_("I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, &
		iwork[1], liwork, info);
	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = *n;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		i__3 = z___subscr(i__, j);
		i__4 = (j - 1) * *n + i__;
		z__[i__3].r = rwork[i__4], z__[i__3].i = 0.;
/* L10: */
	    }
/* L20: */
	}
	return 0;
    }

/*     From now on, only option left to be handled is COMPZ = 'V',   
       i.e. ICOMPZ = 1.   

       Scale. */

    orgnrm = dlanst_("M", n, &d__[1], &e[1]);
    if (orgnrm == 0.) {
	return 0;
    }

    eps = dlamch_("Epsilon");

    start = 1;

/*     while ( START <= N ) */

L30:
    if (start <= *n) {

/*     Let END be the position of the next subdiagonal entry such that   
       E( END ) <= TINY or END = N if no such subdiagonal exists.  The   
       matrix identified by the elements between START and END   
       constitutes an independent sub-problem. */

	end = start;
L40:
	if (end < *n) {
	    latime_1.ops += 4;
	    tiny = eps * sqrt((d__1 = d__[end], abs(d__1))) * sqrt((d__2 = 
		    d__[end + 1], abs(d__2)));
	    if ((d__1 = e[end], abs(d__1)) > tiny) {
		++end;
		goto L40;
	    }
	}

/*        (Sub) Problem determined.  Compute its size and solve it. */

	m = end - start + 1;
	if (m > smlsiz) {
	    *info = smlsiz;

/*           Scale. */

	    orgnrm = dlanst_("M", &m, &d__[start], &e[start]);
	    latime_1.ops = latime_1.ops + (m << 1) - 1;
	    dlascl_("G", &c__0, &c__0, &orgnrm, &c_b19, &m, &c__1, &d__[start]
		    , &m, info);
	    i__1 = m - 1;
	    i__2 = m - 1;
	    dlascl_("G", &c__0, &c__0, &orgnrm, &c_b19, &i__1, &c__1, &e[
		    start], &i__2, info);

	    zlaed0_(n, &m, &d__[start], &e[start], &z___ref(1, start), ldz, &
		    work[1], n, &rwork[1], &iwork[1], info);
	    if (*info > 0) {
		*info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % (m 
			+ 1) + start - 1;
		return 0;
	    }

/*           Scale back. */

	    latime_1.ops += m;
	    dlascl_("G", &c__0, &c__0, &c_b19, &orgnrm, &m, &c__1, &d__[start]
		    , &m, info);

	} else {
	    dsteqr_("I", &m, &d__[start], &e[start], &rwork[1], &m, &rwork[m *
		     m + 1], info);
	    latime_1.ops += (doublereal) (*n) * 4 * m * m;
	    zlacrm_(n, &m, &z___ref(1, start), ldz, &rwork[1], &m, &work[1], 
		    n, &rwork[m * m + 1]);
	    zlacpy_("A", n, &m, &work[1], n, &z___ref(1, start), ldz);
	    if (*info > 0) {
		*info = start * (*n + 1) + end;
		return 0;
	    }
	}

	start = end + 1;
	goto L30;
    }

/*     endwhile   

       If the problem split any number of times, then the eigenvalues   
       will not be properly ordered.  Here we permute the eigenvalues   
       (and the associated eigenvectors) into ascending order. */

    if (m != *n) {

/*        Use Selection Sort to minimize swaps of eigenvectors */

	i__1 = *n;
	for (ii = 2; ii <= i__1; ++ii) {
	    i__ = ii - 1;
	    k = i__;
	    p = d__[i__];
	    i__2 = *n;
	    for (j = ii; j <= i__2; ++j) {
		if (d__[j] < p) {
		    k = j;
		    p = d__[j];
		}
/* L50: */
	    }
	    if (k != i__) {
		d__[k] = d__[i__];
		d__[i__] = p;
		zswap_(n, &z___ref(1, i__), &c__1, &z___ref(1, k), &c__1);
	    }
/* L60: */
	}
    }

    work[1].r = (doublereal) lwmin, work[1].i = 0.;
    rwork[1] = (doublereal) lrwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of ZSTEDC */

} /* zstedc_ */

#undef z___ref
#undef z___subscr