csteqr.c

提供矩阵类的函数库

	m = lend;

L60:
	if (m < lend) {
	    e[m] = 0.f;
	}
	p = d__[l];
	if (m == l) {
	    goto L80;
	}

/*        If remaining matrix is 2-by-2, use SLAE2 or SLAEV2   
          to compute its eigensystem. */

	if (m == l + 1) {
	    if (icompz > 0) {
		latime_1.ops += 22;
		slaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
		work[l] = c__;
		work[*n - 1 + l] = s;
		latime_1.ops += *n * 12;
		clasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
			z___ref(1, l), ldz);
	    } else {
		latime_1.ops += 15;
		slae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
	    }
	    d__[l] = rt1;
	    d__[l + 1] = rt2;
	    e[l] = 0.f;
	    l += 2;
	    if (l <= lend) {
		goto L40;
	    }
	    goto L140;
	}

	if (jtot == nmaxit) {
	    goto L140;
	}
	++jtot;

/*        Form shift. */

	latime_1.ops += 12;
	g = (d__[l + 1] - p) / (e[l] * 2.f);
	r__ = slapy2_(&g, &c_b41);
	g = d__[m] - p + e[l] / (g + r_sign(&r__, &g));

	s = 1.f;
	c__ = 1.f;
	p = 0.f;

/*        Inner loop */

	mm1 = m - 1;
	latime_1.ops += (m - l) * 18;
	i__1 = l;
	for (i__ = mm1; i__ >= i__1; --i__) {
	    f = s * e[i__];
	    b = c__ * e[i__];
	    slartg_(&g, &f, &c__, &s, &r__);
	    if (i__ != m - 1) {
		e[i__ + 1] = r__;
	    }
	    g = d__[i__ + 1] - p;
	    r__ = (d__[i__] - g) * s + c__ * 2.f * b;
	    p = s * r__;
	    d__[i__ + 1] = g + p;
	    g = c__ * r__ - b;

/*           If eigenvectors are desired, then save rotations. */

	    if (icompz > 0) {
		work[i__] = c__;
		work[*n - 1 + i__] = -s;
	    }

/* L70: */
	}

/*        If eigenvectors are desired, then apply saved rotations. */

	if (icompz > 0) {
	    mm = m - l + 1;
	    latime_1.ops += *n * 12 * (mm - 1);
	    clasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &
		    z___ref(1, l), ldz);
	}

	latime_1.ops += 1;
	d__[l] -= p;
	e[l] = g;
	goto L40;

/*        Eigenvalue found. */

L80:
	d__[l] = p;

	++l;
	if (l <= lend) {
	    goto L40;
	}
	goto L140;

    } else {

/*        QR Iteration   

          Look for small superdiagonal element. */

L90:
	if (l != lend) {
	    lendp1 = lend + 1;
	    i__1 = lendp1;
	    for (m = l; m >= i__1; --m) {
		latime_1.ops += 4;
/* Computing 2nd power */
		r__2 = (r__1 = e[m - 1], dabs(r__1));
		tst = r__2 * r__2;
		if (tst <= eps2 * (r__1 = d__[m], dabs(r__1)) * (r__2 = d__[m 
			- 1], dabs(r__2)) + safmin) {
		    goto L110;
		}
/* L100: */
	    }
	}

	m = lend;

L110:
	if (m > lend) {
	    e[m - 1] = 0.f;
	}
	p = d__[l];
	if (m == l) {
	    goto L130;
	}

/*        If remaining matrix is 2-by-2, use SLAE2 or SLAEV2   
          to compute its eigensystem. */

	if (m == l - 1) {
	    if (icompz > 0) {
		latime_1.ops += 22;
		slaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
			;
		work[m] = c__;
		work[*n - 1 + m] = s;
		latime_1.ops += *n * 12;
		clasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
			z___ref(1, l - 1), ldz);
	    } else {
		latime_1.ops += 15;
		slae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
	    }
	    d__[l - 1] = rt1;
	    d__[l] = rt2;
	    e[l - 1] = 0.f;
	    l += -2;
	    if (l >= lend) {
		goto L90;
	    }
	    goto L140;
	}

	if (jtot == nmaxit) {
	    goto L140;
	}
	++jtot;

/*        Form shift. */

	latime_1.ops += 12;
	g = (d__[l - 1] - p) / (e[l - 1] * 2.f);
	r__ = slapy2_(&g, &c_b41);
	g = d__[m] - p + e[l - 1] / (g + r_sign(&r__, &g));

	s = 1.f;
	c__ = 1.f;
	p = 0.f;

/*        Inner loop */

	lm1 = l - 1;
	latime_1.ops += (l - m) * 18;
	i__1 = lm1;
	for (i__ = m; i__ <= i__1; ++i__) {
	    f = s * e[i__];
	    b = c__ * e[i__];
	    slartg_(&g, &f, &c__, &s, &r__);
	    if (i__ != m) {
		e[i__ - 1] = r__;
	    }
	    g = d__[i__] - p;
	    r__ = (d__[i__ + 1] - g) * s + c__ * 2.f * b;
	    p = s * r__;
	    d__[i__] = g + p;
	    g = c__ * r__ - b;

/*           If eigenvectors are desired, then save rotations. */

	    if (icompz > 0) {
		work[i__] = c__;
		work[*n - 1 + i__] = s;
	    }

/* L120: */
	}

/*        If eigenvectors are desired, then apply saved rotations. */

	if (icompz > 0) {
	    mm = l - m + 1;
	    latime_1.ops += *n * 12 * (mm - 1);
	    clasr_("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &
		    z___ref(1, m), ldz);
	}

	latime_1.ops += 1;
	d__[l] -= p;
	e[lm1] = g;
	goto L90;

/*        Eigenvalue found. */

L130:
	d__[l] = p;

	--l;
	if (l >= lend) {
	    goto L90;
	}
	goto L140;

    }

/*     Undo scaling if necessary */

L140:
    if (iscale == 1) {
	latime_1.ops = latime_1.ops + (lendsv - lsv << 1) + 1;
	i__1 = lendsv - lsv + 1;
	slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], 
		n, info);
	i__1 = lendsv - lsv;
	slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, 
		info);
    } else if (iscale == 2) {
	latime_1.ops = latime_1.ops + (lendsv - lsv << 1) + 1;
	i__1 = lendsv - lsv + 1;
	slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], 
		n, info);
	i__1 = lendsv - lsv;
	slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, 
		info);
    }

/*     Check for no convergence to an eigenvalue after a total   
       of N*MAXIT iterations. */

    if (jtot == nmaxit) {
	i__1 = *n - 1;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (e[i__] != 0.f) {
		++(*info);
	    }
/* L150: */
	}
	return 0;
    }
    goto L10;

/*     Order eigenvalues and eigenvectors. */

L160:
    if (icompz == 0) {

/*        Use Quick Sort */

	slasrt_("I", n, &d__[1], info);

    } else {

/*        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];
		}
/* L170: */
	    }
	    if (k != i__) {
		d__[k] = d__[i__];
		d__[i__] = p;
		cswap_(n, &z___ref(1, i__), &c__1, &z___ref(1, k), &c__1);
	    }
/* L180: */
	}
    }
    return 0;

/*     End of CSTEQR */

} /* csteqr_ */

#undef z___ref
#undef z___subscr