dstebz.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

	latime_1.ops = latime_1.ops + (*n - 1) * 5 + 23;
	i__1 = *n - 1;
	for (j = 1; j <= i__1; ++j) {
	    tmp2 = sqrt(work[j]);
/* Computing MAX */
	    d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
	    gu = max(d__1,d__2);
/* Computing MIN */
	    d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
	    gl = min(d__1,d__2);
	    tmp1 = tmp2;
/* L20: */
	}

/* Computing MAX */
	d__1 = gu, d__2 = d__[*n] + tmp1;
	gu = max(d__1,d__2);
/* Computing MIN */
	d__1 = gl, d__2 = d__[*n] - tmp1;
	gl = min(d__1,d__2);
/* Computing MAX */
	d__1 = abs(gl), d__2 = abs(gu);
	tnorm = max(d__1,d__2);
	gl = gl - tnorm * 2. * ulp * *n - pivmin * 4.;
	gu = gu + tnorm * 2. * ulp * *n + pivmin * 2.;

/*        Compute Iteration parameters */

	itmax = (integer) ((log(tnorm + pivmin) - log(pivmin)) / log(2.)) + 2;
	if (*abstol <= 0.) {
	    atoli = ulp * tnorm;
	} else {
	    atoli = *abstol;
	}

	work[*n + 1] = gl;
	work[*n + 2] = gl;
	work[*n + 3] = gu;
	work[*n + 4] = gu;
	work[*n + 5] = gl;
	work[*n + 6] = gu;
	iwork[1] = -1;
	iwork[2] = -1;
	iwork[3] = *n + 1;
	iwork[4] = *n + 1;
	iwork[5] = *il - 1;
	iwork[6] = *iu;

	dlaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, &pivmin, 
		&d__[1], &e[1], &work[1], &iwork[5], &work[*n + 1], &work[*n 
		+ 5], &iout, &iwork[1], &w[1], &iblock[1], &iinfo);

	if (iwork[6] == *iu) {
	    wl = work[*n + 1];
	    wlu = work[*n + 3];
	    nwl = iwork[1];
	    wu = work[*n + 4];
	    wul = work[*n + 2];
	    nwu = iwork[4];
	} else {
	    wl = work[*n + 2];
	    wlu = work[*n + 4];
	    nwl = iwork[2];
	    wu = work[*n + 3];
	    wul = work[*n + 1];
	    nwu = iwork[3];
	}

	if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
	    *info = 4;
	    return 0;
	}
    } else {

/*        RANGE='A' or 'V' -- Set ATOLI */

	latime_1.ops = latime_1.ops + 3 + (*n - 2 << 1);
/* Computing MAX */
	d__3 = abs(d__[1]) + abs(e[1]), d__4 = (d__1 = d__[*n], abs(d__1)) + (
		d__2 = e[*n - 1], abs(d__2));
	tnorm = max(d__3,d__4);

	i__1 = *n - 1;
	for (j = 2; j <= i__1; ++j) {
/* Computing MAX */
	    d__4 = tnorm, d__5 = (d__1 = d__[j], abs(d__1)) + (d__2 = e[j - 1]
		    , abs(d__2)) + (d__3 = e[j], abs(d__3));
	    tnorm = max(d__4,d__5);
/* L30: */
	}

	if (*abstol <= 0.) {
	    atoli = ulp * tnorm;
	} else {
	    atoli = *abstol;
	}

	if (irange == 2) {
	    wl = *vl;
	    wu = *vu;
	} else {
	    wl = 0.;
	    wu = 0.;
	}
    }

/*     Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU.   
       NWL accumulates the number of eigenvalues .le. WL,   
       NWU accumulates the number of eigenvalues .le. WU */

    *m = 0;
    iend = 0;
    *info = 0;
    nwl = 0;
    nwu = 0;

    i__1 = *nsplit;
    for (jb = 1; jb <= i__1; ++jb) {
	ioff = iend;
	ibegin = ioff + 1;
	iend = isplit[jb];
	in = iend - ioff;

	if (in == 1) {

/*           Special Case -- IN=1 */

	    latime_1.ops += 4;
	    if (irange == 1 || wl >= d__[ibegin] - pivmin) {
		++nwl;
	    }
	    if (irange == 1 || wu >= d__[ibegin] - pivmin) {
		++nwu;
	    }
	    if (irange == 1 || wl < d__[ibegin] - pivmin && wu >= d__[ibegin] 
		    - pivmin) {
		++(*m);
		w[*m] = d__[ibegin];
		iblock[*m] = jb;
	    }
	} else {

/*           General Case -- IN > 1   

             Compute Gershgorin Interval   
             and use it as the initial interval */

	    gu = d__[ibegin];
	    gl = d__[ibegin];
	    tmp1 = 0.;

	    latime_1.ops = latime_1.ops + (iend - ibegin << 2) + 13;
	    i__2 = iend - 1;
	    for (j = ibegin; j <= i__2; ++j) {
		tmp2 = (d__1 = e[j], abs(d__1));
/* Computing MAX */
		d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
		gu = max(d__1,d__2);
/* Computing MIN */
		d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
		gl = min(d__1,d__2);
		tmp1 = tmp2;
/* L40: */
	    }

/* Computing MAX */
	    d__1 = gu, d__2 = d__[iend] + tmp1;
	    gu = max(d__1,d__2);
/* Computing MIN */
	    d__1 = gl, d__2 = d__[iend] - tmp1;
	    gl = min(d__1,d__2);
/* Computing MAX */
	    d__1 = abs(gl), d__2 = abs(gu);
	    bnorm = max(d__1,d__2);
	    gl = gl - bnorm * 2. * ulp * in - pivmin * 2.;
	    gu = gu + bnorm * 2. * ulp * in + pivmin * 2.;

/*           Compute ATOLI for the current submatrix */

	    if (*abstol <= 0.) {
/* Computing MAX */
		d__1 = abs(gl), d__2 = abs(gu);
		atoli = ulp * max(d__1,d__2);
	    } else {
		atoli = *abstol;
	    }

	    if (irange > 1) {
		if (gu < wl) {
		    nwl += in;
		    nwu += in;
		    goto L70;
		}
		gl = max(gl,wl);
		gu = min(gu,wu);
		if (gl >= gu) {
		    goto L70;
		}
	    }

/*           Set Up Initial Interval */

	    work[*n + 1] = gl;
	    work[*n + in + 1] = gu;
	    dlaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, &
		    pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
		    work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
		    w[*m + 1], &iblock[*m + 1], &iinfo);

	    nwl += iwork[1];
	    nwu += iwork[in + 1];
	    iwoff = *m - iwork[1];

/*           Compute Eigenvalues */

	    latime_1.ops += 8;
	    itmax = (integer) ((log(gu - gl + pivmin) - log(pivmin)) / log(2.)
		    ) + 2;
	    dlaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, &
		    pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
		    work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
		     &w[*m + 1], &iblock[*m + 1], &iinfo);

/*           Copy Eigenvalues Into W and IBLOCK   
             Use -JB for block number for unconverged eigenvalues. */

	    latime_1.ops += iout << 1;
	    i__2 = iout;
	    for (j = 1; j <= i__2; ++j) {
		tmp1 = (work[j + *n] + work[j + in + *n]) * .5;

/*              Flag non-convergence. */

		if (j > iout - iinfo) {
		    ncnvrg = TRUE_;
		    ib = -jb;
		} else {
		    ib = jb;
		}
		i__3 = iwork[j + in] + iwoff;
		for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
		    w[je] = tmp1;
		    iblock[je] = ib;
/* L50: */
		}
/* L60: */
	    }

	    *m += im;
	}
L70:
	;
    }

/*     If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU   
       If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */

    if (irange == 3) {
	im = 0;
	idiscl = *il - 1 - nwl;
	idiscu = nwu - *iu;

	if (idiscl > 0 || idiscu > 0) {
	    i__1 = *m;
	    for (je = 1; je <= i__1; ++je) {
		if (w[je] <= wlu && idiscl > 0) {
		    --idiscl;
		} else if (w[je] >= wul && idiscu > 0) {
		    --idiscu;
		} else {
		    ++im;
		    w[im] = w[je];
		    iblock[im] = iblock[je];
		}
/* L80: */
	    }
	    *m = im;
	}
	if (idiscl > 0 || idiscu > 0) {

/*           Code to deal with effects of bad arithmetic:   
             Some low eigenvalues to be discarded are not in (WL,WLU],   
             or high eigenvalues to be discarded are not in (WUL,WU]   
             so just kill off the smallest IDISCL/largest IDISCU   
             eigenvalues, by simply finding the smallest/largest   
             eigenvalue(s).   

             (If N(w) is monotone non-decreasing, this should never   
                 happen.) */

	    if (idiscl > 0) {
		wkill = wu;
		i__1 = idiscl;
		for (jdisc = 1; jdisc <= i__1; ++jdisc) {
		    iw = 0;
		    i__2 = *m;
		    for (je = 1; je <= i__2; ++je) {
			if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
			    iw = je;
			    wkill = w[je];
			}
/* L90: */
		    }
		    iblock[iw] = 0;
/* L100: */
		}
	    }
	    if (idiscu > 0) {

		wkill = wl;
		i__1 = idiscu;
		for (jdisc = 1; jdisc <= i__1; ++jdisc) {
		    iw = 0;
		    i__2 = *m;
		    for (je = 1; je <= i__2; ++je) {
			if (iblock[je] != 0 && (w[je] > wkill || iw == 0)) {
			    iw = je;
			    wkill = w[je];
			}
/* L110: */
		    }
		    iblock[iw] = 0;
/* L120: */
		}
	    }
	    im = 0;
	    i__1 = *m;
	    for (je = 1; je <= i__1; ++je) {
		if (iblock[je] != 0) {
		    ++im;
		    w[im] = w[je];
		    iblock[im] = iblock[je];
		}
/* L130: */
	    }
	    *m = im;
	}
	if (idiscl < 0 || idiscu < 0) {
	    toofew = TRUE_;
	}
    }

/*     If ORDER='B', do nothing -- the eigenvalues are already sorted   
          by block.   
       If ORDER='E', sort the eigenvalues from smallest to largest */

    if (iorder == 1 && *nsplit > 1) {
	i__1 = *m - 1;
	for (je = 1; je <= i__1; ++je) {
	    ie = 0;
	    tmp1 = w[je];
	    i__2 = *m;
	    for (j = je + 1; j <= i__2; ++j) {
		if (w[j] < tmp1) {
		    ie = j;
		    tmp1 = w[j];
		}
/* L140: */
	    }

	    if (ie != 0) {
		itmp1 = iblock[ie];
		w[ie] = w[je];
		iblock[ie] = iblock[je];
		w[je] = tmp1;
		iblock[je] = itmp1;
	    }
/* L150: */
	}
    }

    *info = 0;
    if (ncnvrg) {
	++(*info);
    }
    if (toofew) {
	*info += 2;
    }
    return 0;

/*     End of DSTEBZ */

} /* dstebz_ */