ctgevc.c

提供矩阵类的函数库

    safmin = slamch_("Safe minimum");
    big = 1.f / safmin;
    slabad_(&safmin, &big);
    ulp = slamch_("Epsilon") * slamch_("Base");
    small = safmin * *n / ulp;
    big = 1.f / small;
    bignum = 1.f / (safmin * *n);

/*     Compute the 1-norm of each column of the strictly upper triangular   
       part of A and B to check for possible overflow in the triangular   
       solver. */

    i__1 = a_subscr(1, 1);
    anorm = (r__1 = a[i__1].r, dabs(r__1)) + (r__2 = r_imag(&a_ref(1, 1)), 
	    dabs(r__2));
    i__1 = b_subscr(1, 1);
    bnorm = (r__1 = b[i__1].r, dabs(r__1)) + (r__2 = r_imag(&b_ref(1, 1)), 
	    dabs(r__2));
    rwork[1] = 0.f;
    rwork[*n + 1] = 0.f;
    i__1 = *n;
    for (j = 2; j <= i__1; ++j) {
	rwork[j] = 0.f;
	rwork[*n + j] = 0.f;
	i__2 = j - 1;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    i__3 = a_subscr(i__, j);
	    rwork[j] += (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
		    a_ref(i__, j)), dabs(r__2));
	    i__3 = b_subscr(i__, j);
	    rwork[*n + j] += (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
		    b_ref(i__, j)), dabs(r__2));
/* L30: */
	}
/* Computing MAX */
	i__2 = a_subscr(j, j);
	r__3 = anorm, r__4 = rwork[j] + ((r__1 = a[i__2].r, dabs(r__1)) + (
		r__2 = r_imag(&a_ref(j, j)), dabs(r__2)));
	anorm = dmax(r__3,r__4);
/* Computing MAX */
	i__2 = b_subscr(j, j);
	r__3 = bnorm, r__4 = rwork[*n + j] + ((r__1 = b[i__2].r, dabs(r__1)) 
		+ (r__2 = r_imag(&b_ref(j, j)), dabs(r__2)));
	bnorm = dmax(r__3,r__4);
/* L40: */
    }

    ascale = 1.f / dmax(anorm,safmin);
    bscale = 1.f / dmax(bnorm,safmin);
/*     ---------------------- Begin Timing Code -------------------------   
   Computing 2nd power */
    i__1 = *n;
    latime_1.ops += (real) ((i__1 * i__1 << 1) + (*n << 1) + 6);
/*     ----------------------- End Timing Code --------------------------   

       Left eigenvectors */

    if (compl) {
	ieig = 0;

/*        Main loop over eigenvalues */

	i__1 = *n;
	for (je = 1; je <= i__1; ++je) {
	    if (ilall) {
		ilcomp = TRUE_;
	    } else {
		ilcomp = select[je];
	    }
	    if (ilcomp) {
		++ieig;

		i__2 = a_subscr(je, je);
		i__3 = b_subscr(je, je);
		if ((r__2 = a[i__2].r, dabs(r__2)) + (r__3 = r_imag(&a_ref(je,
			 je)), dabs(r__3)) <= safmin && (r__1 = b[i__3].r, 
			dabs(r__1)) <= safmin) {

/*                 Singular matrix pencil -- return unit eigenvector */

		    i__2 = *n;
		    for (jr = 1; jr <= i__2; ++jr) {
			i__3 = vl_subscr(jr, ieig);
			vl[i__3].r = 0.f, vl[i__3].i = 0.f;
/* L50: */
		    }
		    i__2 = vl_subscr(ieig, ieig);
		    vl[i__2].r = 1.f, vl[i__2].i = 0.f;
		    goto L140;
		}

/*              Non-singular eigenvalue:   
                Compute coefficients  a  and  b  in   
                     H   
                   y  ( a A - b B ) = 0   

   Computing MAX */
		i__2 = a_subscr(je, je);
		i__3 = b_subscr(je, je);
		r__4 = ((r__2 = a[i__2].r, dabs(r__2)) + (r__3 = r_imag(&
			a_ref(je, je)), dabs(r__3))) * ascale, r__5 = (r__1 = 
			b[i__3].r, dabs(r__1)) * bscale, r__4 = max(r__4,r__5)
			;
		temp = 1.f / dmax(r__4,safmin);
		i__2 = a_subscr(je, je);
		q__2.r = temp * a[i__2].r, q__2.i = temp * a[i__2].i;
		q__1.r = ascale * q__2.r, q__1.i = ascale * q__2.i;
		salpha.r = q__1.r, salpha.i = q__1.i;
		i__2 = b_subscr(je, je);
		sbeta = temp * b[i__2].r * bscale;
		acoeff = sbeta * ascale;
		q__1.r = bscale * salpha.r, q__1.i = bscale * salpha.i;
		bcoeff.r = q__1.r, bcoeff.i = q__1.i;

/*              Scale to avoid underflow */

		lsa = dabs(sbeta) >= safmin && dabs(acoeff) < small;
		lsb = (r__1 = salpha.r, dabs(r__1)) + (r__2 = r_imag(&salpha),
			 dabs(r__2)) >= safmin && (r__3 = bcoeff.r, dabs(r__3)
			) + (r__4 = r_imag(&bcoeff), dabs(r__4)) < small;

		scale = 1.f;
		if (lsa) {
		    scale = small / dabs(sbeta) * dmin(anorm,big);
		}
		if (lsb) {
/* Computing MAX */
		    r__3 = scale, r__4 = small / ((r__1 = salpha.r, dabs(r__1)
			    ) + (r__2 = r_imag(&salpha), dabs(r__2))) * dmin(
			    bnorm,big);
		    scale = dmax(r__3,r__4);
		}
		if (lsa || lsb) {
/* Computing MIN   
   Computing MAX */
		    r__5 = 1.f, r__6 = dabs(acoeff), r__5 = max(r__5,r__6), 
			    r__6 = (r__1 = bcoeff.r, dabs(r__1)) + (r__2 = 
			    r_imag(&bcoeff), dabs(r__2));
		    r__3 = scale, r__4 = 1.f / (safmin * dmax(r__5,r__6));
		    scale = dmin(r__3,r__4);
		    if (lsa) {
			acoeff = ascale * (scale * sbeta);
		    } else {
			acoeff = scale * acoeff;
		    }
		    if (lsb) {
			q__2.r = scale * salpha.r, q__2.i = scale * salpha.i;
			q__1.r = bscale * q__2.r, q__1.i = bscale * q__2.i;
			bcoeff.r = q__1.r, bcoeff.i = q__1.i;
		    } else {
			q__1.r = scale * bcoeff.r, q__1.i = scale * bcoeff.i;
			bcoeff.r = q__1.r, bcoeff.i = q__1.i;
		    }
/*                 ----------------- Begin Timing Code ------------------   
                   Calculation of SALPHA through DMIN */
		    iopst = 34;
		} else {
		    iopst = 20;
/*                 ------------------ End Timing Code ------------------- */
		}

		acoefa = dabs(acoeff);
		bcoefa = (r__1 = bcoeff.r, dabs(r__1)) + (r__2 = r_imag(&
			bcoeff), dabs(r__2));
		xmax = 1.f;
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
		    i__3 = jr;
		    work[i__3].r = 0.f, work[i__3].i = 0.f;
/* L60: */
		}
		i__2 = je;
		work[i__2].r = 1.f, work[i__2].i = 0.f;
/* Computing MAX */
		r__1 = ulp * acoefa * anorm, r__2 = ulp * bcoefa * bnorm, 
			r__1 = max(r__1,r__2);
		dmin__ = dmax(r__1,safmin);

/*                                              H   
                Triangular solve of  (a A - b B)  y = 0   

                                        H   
                (rowwise in  (a A - b B) , or columnwise in a A - b B) */

		i__2 = *n;
		for (j = je + 1; j <= i__2; ++j) {

/*                 Compute   
                         j-1   
                   SUM = sum  conjg( a*A(k,j) - b*B(k,j) )*x(k)   
                         k=je   
                   (Scale if necessary) */

		    temp = 1.f / xmax;
		    if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum * 
			    temp) {
			i__3 = j - 1;
			for (jr = je; jr <= i__3; ++jr) {
			    i__4 = jr;
			    i__5 = jr;
			    q__1.r = temp * work[i__5].r, q__1.i = temp * 
				    work[i__5].i;
			    work[i__4].r = q__1.r, work[i__4].i = q__1.i;
/* L70: */
			}
			xmax = 1.f;
/*                    ---------------- Begin Timing Code ---------------- */
			iopst += j - je << 1;
/*                    ----------------- End Timing Code ----------------- */
		    }
		    suma.r = 0.f, suma.i = 0.f;
		    sumb.r = 0.f, sumb.i = 0.f;

		    i__3 = j - 1;
		    for (jr = je; jr <= i__3; ++jr) {
			r_cnjg(&q__3, &a_ref(jr, j));
			i__4 = jr;
			q__2.r = q__3.r * work[i__4].r - q__3.i * work[i__4]
				.i, q__2.i = q__3.r * work[i__4].i + q__3.i * 
				work[i__4].r;
			q__1.r = suma.r + q__2.r, q__1.i = suma.i + q__2.i;
			suma.r = q__1.r, suma.i = q__1.i;
			r_cnjg(&q__3, &b_ref(jr, j));
			i__4 = jr;
			q__2.r = q__3.r * work[i__4].r - q__3.i * work[i__4]
				.i, q__2.i = q__3.r * work[i__4].i + q__3.i * 
				work[i__4].r;
			q__1.r = sumb.r + q__2.r, q__1.i = sumb.i + q__2.i;
			sumb.r = q__1.r, sumb.i = q__1.i;
/* L80: */
		    }
		    q__2.r = acoeff * suma.r, q__2.i = acoeff * suma.i;
		    r_cnjg(&q__4, &bcoeff);
		    q__3.r = q__4.r * sumb.r - q__4.i * sumb.i, q__3.i = 
			    q__4.r * sumb.i + q__4.i * sumb.r;
		    q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
		    sum.r = q__1.r, sum.i = q__1.i;

/*                 Form x(j) = - SUM / conjg( a*A(j,j) - b*B(j,j) )   

                   with scaling and perturbation of the denominator */

		    i__3 = a_subscr(j, j);
		    q__3.r = acoeff * a[i__3].r, q__3.i = acoeff * a[i__3].i;
		    i__4 = b_subscr(j, j);
		    q__4.r = bcoeff.r * b[i__4].r - bcoeff.i * b[i__4].i, 
			    q__4.i = bcoeff.r * b[i__4].i + bcoeff.i * b[i__4]
			    .r;
		    q__2.r = q__3.r - q__4.r, q__2.i = q__3.i - q__4.i;
		    r_cnjg(&q__1, &q__2);
		    d__.r = q__1.r, d__.i = q__1.i;
		    if ((r__1 = d__.r, dabs(r__1)) + (r__2 = r_imag(&d__), 
			    dabs(r__2)) <= dmin__) {
			q__1.r = dmin__, q__1.i = 0.f;
			d__.r = q__1.r, d__.i = q__1.i;
		    }

		    if ((r__1 = d__.r, dabs(r__1)) + (r__2 = r_imag(&d__), 
			    dabs(r__2)) < 1.f) {
			if ((r__1 = sum.r, dabs(r__1)) + (r__2 = r_imag(&sum),
				 dabs(r__2)) >= bignum * ((r__3 = d__.r, dabs(
				r__3)) + (r__4 = r_imag(&d__), dabs(r__4)))) {
			    temp = 1.f / ((r__1 = sum.r, dabs(r__1)) + (r__2 =
				     r_imag(&sum), dabs(r__2)));
			    i__3 = j - 1;
			    for (jr = je; jr <= i__3; ++jr) {
				i__4 = jr;
				i__5 = jr;
				q__1.r = temp * work[i__5].r, q__1.i = temp * 
					work[i__5].i;
				work[i__4].r = q__1.r, work[i__4].i = q__1.i;
/* L90: */
			    }
			    xmax = temp * xmax;
			    q__1.r = temp * sum.r, q__1.i = temp * sum.i;
			    sum.r = q__1.r, sum.i = q__1.i;
/*                       -------------- Begin Timing Code --------------- */
			    iopst = iopst + (j - je << 1) + 5;
/*                       --------------- End Timing Code ---------------- */
			}
		    }
		    i__3 = j;
		    q__2.r = -sum.r, q__2.i = -sum.i;
		    cladiv_(&q__1, &q__2, &d__);
		    work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* Computing MAX */
		    i__3 = j;
		    r__3 = xmax, r__4 = (r__1 = work[i__3].r, dabs(r__1)) + (
			    r__2 = r_imag(&work[j]), dabs(r__2));
		    xmax = dmax(r__3,r__4);
/* L100: */
		}

/*              Back transform eigenvector if HOWMNY='B'. */

		if (ilback) {
		    i__2 = *n + 1 - je;
		    cgemv_("N", n, &i__2, &c_b2, &vl_ref(1, je), ldvl, &work[
			    je], &c__1, &c_b1, &work[*n + 1], &c__1);
		    isrc = 2;
		    ibeg = 1;
/*                 ----------------- Begin Timing Code ------------------ */
		    iopst += (*n << 3) * (*n + 1 - je);
/*                 ------------------ End Timing Code ------------------- */
		} else {
		    isrc = 1;
		    ibeg = je;
		}

/*              Copy and scale eigenvector into column of VL */

		xmax = 0.f;
		i__2 = *n;
		for (jr = ibeg; jr <= i__2; ++jr) {
/* Computing MAX */
		    i__3 = (isrc - 1) * *n + jr;
		    r__3 = xmax, r__4 = (r__1 = work[i__3].r, dabs(r__1)) + (
			    r__2 = r_imag(&work[(isrc - 1) * *n + jr]), dabs(
			    r__2));
		    xmax = dmax(r__3,r__4);
/* L110: */
		}

		if (xmax > safmin) {
		    temp = 1.f / xmax;
		    i__2 = *n;
		    for (jr = ibeg; jr <= i__2; ++jr) {
			i__3 = vl_subscr(jr, ieig);
			i__4 = (isrc - 1) * *n + jr;
			q__1.r = temp * work[i__4].r, q__1.i = temp * work[
				i__4].i;
			vl[i__3].r = q__1.r, vl[i__3].i = q__1.i;
/* L120: */
		    }
		} else {
		    ibeg = *n + 1;
		}

		i__2 = ibeg - 1;
		for (jr = 1; jr <= i__2; ++jr) {
		    i__3 = vl_subscr(jr, ieig);
		    vl[i__3].r = 0.f, vl[i__3].i = 0.f;
/* L130: */
		}

/*              ------------------- Begin Timing Code ------------------- */