slaein.c

提供矩阵类的函数库

/* ** */
    } else {

/*        Complex eigenvalue. */

	if (*noinit) {

/*           Set initial vector. */

	    i__1 = *n;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		vr[i__] = *eps3;
		vi[i__] = 0.f;
/* L130: */
	    }
	} else {

/*           Scale supplied initial vector. */

	    r__1 = snrm2_(n, &vr[1], &c__1);
	    r__2 = snrm2_(n, &vi[1], &c__1);
	    norm = slapy2_(&r__1, &r__2);
	    rec = *eps3 * rootn / dmax(norm,nrmsml);
	    sscal_(n, &rec, &vr[1], &c__1);
	    sscal_(n, &rec, &vi[1], &c__1);
/* ** */
	    opst += *n * 6 + 5;
/* ** */
	}

	if (*rightv) {

/*           LU decomposition with partial pivoting of B, replacing zero   
             pivots by EPS3.   

             The imaginary part of the (i,j)-th element of U is stored in   
             B(j+1,i). */

	    b_ref(2, 1) = -(*wi);
	    i__1 = *n;
	    for (i__ = 2; i__ <= i__1; ++i__) {
		b_ref(i__ + 1, 1) = 0.f;
/* L140: */
	    }

	    i__1 = *n - 1;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		absbii = slapy2_(&b_ref(i__, i__), &b_ref(i__ + 1, i__));
		ei = h___ref(i__ + 1, i__);
		if (absbii < dabs(ei)) {

/*                 Interchange rows and eliminate. */

		    xr = b_ref(i__, i__) / ei;
		    xi = b_ref(i__ + 1, i__) / ei;
		    b_ref(i__, i__) = ei;
		    b_ref(i__ + 1, i__) = 0.f;
		    i__2 = *n;
		    for (j = i__ + 1; j <= i__2; ++j) {
			temp = b_ref(i__ + 1, j);
			b_ref(i__ + 1, j) = b_ref(i__, j) - xr * temp;
			b_ref(j + 1, i__ + 1) = b_ref(j + 1, i__) - xi * temp;
			b_ref(i__, j) = temp;
			b_ref(j + 1, i__) = 0.f;
/* L150: */
		    }
		    b_ref(i__ + 2, i__) = -(*wi);
		    b_ref(i__ + 1, i__ + 1) = b_ref(i__ + 1, i__ + 1) - xi * *
			    wi;
		    b_ref(i__ + 2, i__ + 1) = b_ref(i__ + 2, i__ + 1) + xr * *
			    wi;
/* ** */
		    opst += (*n - i__ << 2) + 6;
/* ** */
		} else {

/*                 Eliminate without interchanging rows. */

		    if (absbii == 0.f) {
			b_ref(i__, i__) = *eps3;
			b_ref(i__ + 1, i__) = 0.f;
			absbii = *eps3;
		    }
		    ei = ei / absbii / absbii;
		    xr = b_ref(i__, i__) * ei;
		    xi = -b_ref(i__ + 1, i__) * ei;
		    i__2 = *n;
		    for (j = i__ + 1; j <= i__2; ++j) {
			b_ref(i__ + 1, j) = b_ref(i__ + 1, j) - xr * b_ref(
				i__, j) + xi * b_ref(j + 1, i__);
			b_ref(j + 1, i__ + 1) = -xr * b_ref(j + 1, i__) - xi *
				 b_ref(i__, j);
/* L160: */
		    }
		    b_ref(i__ + 2, i__ + 1) = b_ref(i__ + 2, i__ + 1) - *wi;
/* ** */
		    opst += (*n - i__) * 7 + 4;
/* ** */
		}

/*              Compute 1-norm of offdiagonal elements of i-th row. */

		i__2 = *n - i__;
		i__3 = *n - i__;
		work[i__] = sasum_(&i__2, &b_ref(i__, i__ + 1), ldb) + sasum_(
			&i__3, &b_ref(i__ + 2, i__), &c__1);
/* ** */
		opst += (*n - i__ << 1) + 4;
/* **   
   L170: */
	    }
	    if (b_ref(*n, *n) == 0.f && b_ref(*n + 1, *n) == 0.f) {
		b_ref(*n, *n) = *eps3;
	    }
	    work[*n] = 0.f;

	    i1 = *n;
	    i2 = 1;
	    i3 = -1;
	} else {

/*           UL decomposition with partial pivoting of conjg(B),   
             replacing zero pivots by EPS3.   

             The imaginary part of the (i,j)-th element of U is stored in   
             B(j+1,i). */

	    b_ref(*n + 1, *n) = *wi;
	    i__1 = *n - 1;
	    for (j = 1; j <= i__1; ++j) {
		b_ref(*n + 1, j) = 0.f;
/* L180: */
	    }

	    for (j = *n; j >= 2; --j) {
		ej = h___ref(j, j - 1);
		absbjj = slapy2_(&b_ref(j, j), &b_ref(j + 1, j));
		if (absbjj < dabs(ej)) {

/*                 Interchange columns and eliminate */

		    xr = b_ref(j, j) / ej;
		    xi = b_ref(j + 1, j) / ej;
		    b_ref(j, j) = ej;
		    b_ref(j + 1, j) = 0.f;
		    i__1 = j - 1;
		    for (i__ = 1; i__ <= i__1; ++i__) {
			temp = b_ref(i__, j - 1);
			b_ref(i__, j - 1) = b_ref(i__, j) - xr * temp;
			b_ref(j, i__) = b_ref(j + 1, i__) - xi * temp;
			b_ref(i__, j) = temp;
			b_ref(j + 1, i__) = 0.f;
/* L190: */
		    }
		    b_ref(j + 1, j - 1) = *wi;
		    b_ref(j - 1, j - 1) = b_ref(j - 1, j - 1) + xi * *wi;
		    b_ref(j, j - 1) = b_ref(j, j - 1) - xr * *wi;
/* ** */
		    opst += (j - 1 << 2) + 6;
/* ** */
		} else {

/*                 Eliminate without interchange. */

		    if (absbjj == 0.f) {
			b_ref(j, j) = *eps3;
			b_ref(j + 1, j) = 0.f;
			absbjj = *eps3;
		    }
		    ej = ej / absbjj / absbjj;
		    xr = b_ref(j, j) * ej;
		    xi = -b_ref(j + 1, j) * ej;
		    i__1 = j - 1;
		    for (i__ = 1; i__ <= i__1; ++i__) {
			b_ref(i__, j - 1) = b_ref(i__, j - 1) - xr * b_ref(
				i__, j) + xi * b_ref(j + 1, i__);
			b_ref(j, i__) = -xr * b_ref(j + 1, i__) - xi * b_ref(
				i__, j);
/* L200: */
		    }
		    b_ref(j, j - 1) = b_ref(j, j - 1) + *wi;
/* ** */
		    opst += (j - 1) * 7 + 4;
/* ** */
		}

/*              Compute 1-norm of offdiagonal elements of j-th column. */

		i__1 = j - 1;
		i__2 = j - 1;
		work[j] = sasum_(&i__1, &b_ref(1, j), &c__1) + sasum_(&i__2, &
			b_ref(j + 1, 1), ldb);
/* ** */
		opst += (j - 1 << 1) + 4;
/* **   
   L210: */
	    }
	    if (b_ref(1, 1) == 0.f && b_ref(2, 1) == 0.f) {
		b_ref(1, 1) = *eps3;
	    }
	    work[1] = 0.f;

	    i1 = 1;
	    i2 = *n;
	    i3 = 1;
	}

	i__1 = *n;
	for (its = 1; its <= i__1; ++its) {
	    scale = 1.f;
	    vmax = 1.f;
	    vcrit = *bignum;

/*           Solve U*(xr,xi) = scale*(vr,vi) for a right eigenvector,   
               or U'*(xr,xi) = scale*(vr,vi) for a left eigenvector,   
             overwriting (xr,xi) on (vr,vi). */

	    i__2 = i2;
	    i__3 = i3;
	    for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) 
		    {

		if (work[i__] > vcrit) {
		    rec = 1.f / vmax;
		    sscal_(n, &rec, &vr[1], &c__1);
		    sscal_(n, &rec, &vi[1], &c__1);
		    scale *= rec;
		    vmax = 1.f;
		    vcrit = *bignum;
		}

		xr = vr[i__];
		xi = vi[i__];
		if (*rightv) {
		    i__4 = *n;
		    for (j = i__ + 1; j <= i__4; ++j) {
			xr = xr - b_ref(i__, j) * vr[j] + b_ref(j + 1, i__) * 
				vi[j];
			xi = xi - b_ref(i__, j) * vi[j] - b_ref(j + 1, i__) * 
				vr[j];
/* L220: */
		    }
		} else {
		    i__4 = i__ - 1;
		    for (j = 1; j <= i__4; ++j) {
			xr = xr - b_ref(j, i__) * vr[j] + b_ref(i__ + 1, j) * 
				vi[j];
			xi = xi - b_ref(j, i__) * vi[j] - b_ref(i__ + 1, j) * 
				vr[j];
/* L230: */
		    }
		}

		w = (r__1 = b_ref(i__, i__), dabs(r__1)) + (r__2 = b_ref(i__ 
			+ 1, i__), dabs(r__2));
		if (w > *smlnum) {
		    if (w < 1.f) {
			w1 = dabs(xr) + dabs(xi);
			if (w1 > w * *bignum) {
			    rec = 1.f / w1;
			    sscal_(n, &rec, &vr[1], &c__1);
			    sscal_(n, &rec, &vi[1], &c__1);
			    xr = vr[i__];
			    xi = vi[i__];
			    scale *= rec;
			    vmax *= rec;
			}
		    }

/*                 Divide by diagonal element of B. */

		    sladiv_(&xr, &xi, &b_ref(i__, i__), &b_ref(i__ + 1, i__), 
			    &vr[i__], &vi[i__]);
/* Computing MAX */
		    r__3 = (r__1 = vr[i__], dabs(r__1)) + (r__2 = vi[i__], 
			    dabs(r__2));
		    vmax = dmax(r__3,vmax);
		    vcrit = *bignum / vmax;
/* ** */
		    opst += 9;
/* ** */
		} else {
		    i__4 = *n;
		    for (j = 1; j <= i__4; ++j) {
			vr[j] = 0.f;
			vi[j] = 0.f;
/* L240: */
		    }
		    vr[i__] = 1.f;
		    vi[i__] = 1.f;
		    scale = 0.f;
		    vmax = 1.f;
		    vcrit = *bignum;
		}
/* L250: */
	    }
/* **   
             Increment op count for loop 260, assuming no scaling */
	    latime_1.ops += (*n << 2) * (*n - 1);
/* **   

             Test for sufficient growth in the norm of (VR,VI). */

	    vnorm = sasum_(n, &vr[1], &c__1) + sasum_(n, &vi[1], &c__1);
/* ** */
	    opst += *n << 1;
/* ** */
	    if (vnorm >= growto * scale) {
		goto L280;
	    }

/*           Choose a new orthogonal starting vector and try again. */

	    y = *eps3 / (rootn + 1.f);
	    vr[1] = *eps3;
	    vi[1] = 0.f;

	    i__3 = *n;
	    for (i__ = 2; i__ <= i__3; ++i__) {
		vr[i__] = y;
		vi[i__] = 0.f;
/* L260: */
	    }
	    vr[*n - its + 1] -= *eps3 * rootn;
/* ** */
	    opst += 4;
/* **   
   L270: */
	}

/*        Failure to find eigenvector in N iterations */

	*info = 1;

L280:

/*        Normalize eigenvector. */

	vnorm = 0.f;
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
	    r__3 = vnorm, r__4 = (r__1 = vr[i__], dabs(r__1)) + (r__2 = vi[
		    i__], dabs(r__2));
	    vnorm = dmax(r__3,r__4);
/* L290: */
	}
	r__1 = 1.f / vnorm;
	sscal_(n, &r__1, &vr[1], &c__1);
	r__1 = 1.f / vnorm;
	sscal_(n, &r__1, &vi[1], &c__1);
/* ** */
	opst += (*n << 2) + 1;
/* ** */

    }

/* **   
       Compute final op count */
    latime_1.ops += opst;
/* ** */
    return 0;

/*     End of SLAEIN */

} /* slaein_ */

#undef h___ref
#undef b_ref