ztgevc.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

/*              ------------------- Begin Timing Code ------------------- */
		latime_1.ops += (doublereal) ((*n - je) * 36 + (*n - je << 3) 
			* (*n + 1 - je) + (*n + 1 - ibeg) * 3 + 1) + (
			doublereal) iopst;
/*              -------------------- End Timing Code -------------------- */
	    }
L140:
	    ;
	}
    }

/*     Right eigenvectors */

    if (compr) {
	ieig = im + 1;

/*        Main loop over eigenvalues */

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

		i__1 = a_subscr(je, je);
		i__2 = b_subscr(je, je);
		if ((d__2 = a[i__1].r, abs(d__2)) + (d__3 = d_imag(&a_ref(je, 
			je)), abs(d__3)) <= safmin && (d__1 = b[i__2].r, abs(
			d__1)) <= safmin) {

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

		    i__1 = *n;
		    for (jr = 1; jr <= i__1; ++jr) {
			i__2 = vr_subscr(jr, ieig);
			vr[i__2].r = 0., vr[i__2].i = 0.;
/* L150: */
		    }
		    i__1 = vr_subscr(ieig, ieig);
		    vr[i__1].r = 1., vr[i__1].i = 0.;
		    goto L250;
		}

/*              Non-singular eigenvalue:   
                Compute coefficients  a  and  b  in   

                ( a A - b B ) x  = 0   

   Computing MAX */
		i__1 = a_subscr(je, je);
		i__2 = b_subscr(je, je);
		d__4 = ((d__2 = a[i__1].r, abs(d__2)) + (d__3 = d_imag(&a_ref(
			je, je)), abs(d__3))) * ascale, d__5 = (d__1 = b[i__2]
			.r, abs(d__1)) * bscale, d__4 = max(d__4,d__5);
		temp = 1. / max(d__4,safmin);
		i__1 = a_subscr(je, je);
		z__2.r = temp * a[i__1].r, z__2.i = temp * a[i__1].i;
		z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
		salpha.r = z__1.r, salpha.i = z__1.i;
		i__1 = b_subscr(je, je);
		sbeta = temp * b[i__1].r * bscale;
		acoeff = sbeta * ascale;
		z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
		bcoeff.r = z__1.r, bcoeff.i = z__1.i;

/*              Scale to avoid underflow */

		lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
		lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), 
			abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3)) 
			+ (d__4 = d_imag(&bcoeff), abs(d__4)) < small;

		scale = 1.;
		if (lsa) {
		    scale = small / abs(sbeta) * min(anorm,big);
		}
		if (lsb) {
/* Computing MAX */
		    d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
			     + (d__2 = d_imag(&salpha), abs(d__2))) * min(
			    bnorm,big);
		    scale = max(d__3,d__4);
		}
		if (lsa || lsb) {
/* Computing MIN   
   Computing MAX */
		    d__5 = 1., d__6 = abs(acoeff), d__5 = max(d__5,d__6), 
			    d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = 
			    d_imag(&bcoeff), abs(d__2));
		    d__3 = scale, d__4 = 1. / (safmin * max(d__5,d__6));
		    scale = min(d__3,d__4);
		    if (lsa) {
			acoeff = ascale * (scale * sbeta);
		    } else {
			acoeff = scale * acoeff;
		    }
		    if (lsb) {
			z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
			z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
			bcoeff.r = z__1.r, bcoeff.i = z__1.i;
		    } else {
			z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
			bcoeff.r = z__1.r, bcoeff.i = z__1.i;
		    }
/*                 ----------------- Begin Timing Code ------------------   
                   Calculation of SALPHA through DMIN */
		    iopst = 34;
		} else {
		    iopst = 20;
/*                 ------------------ End Timing Code ------------------- */
		}

		acoefa = abs(acoeff);
		bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
			bcoeff), abs(d__2));
		xmax = 1.;
		i__1 = *n;
		for (jr = 1; jr <= i__1; ++jr) {
		    i__2 = jr;
		    work[i__2].r = 0., work[i__2].i = 0.;
/* L160: */
		}
		i__1 = je;
		work[i__1].r = 1., work[i__1].i = 0.;
/* Computing MAX */
		d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, 
			d__1 = max(d__1,d__2);
		dmin__ = max(d__1,safmin);

/*              Triangular solve of  (a A - b B) x = 0  (columnwise)   

                WORK(1:j-1) contains sums w,   
                WORK(j+1:JE) contains x */

		i__1 = je - 1;
		for (jr = 1; jr <= i__1; ++jr) {
		    i__2 = jr;
		    i__3 = a_subscr(jr, je);
		    z__2.r = acoeff * a[i__3].r, z__2.i = acoeff * a[i__3].i;
		    i__4 = b_subscr(jr, je);
		    z__3.r = bcoeff.r * b[i__4].r - bcoeff.i * b[i__4].i, 
			    z__3.i = bcoeff.r * b[i__4].i + bcoeff.i * b[i__4]
			    .r;
		    z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
		    work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L170: */
		}
		i__1 = je;
		work[i__1].r = 1., work[i__1].i = 0.;

		for (j = je - 1; j >= 1; --j) {

/*                 Form x(j) := - w(j) / d   
                   with scaling and perturbation of the denominator */

		    i__1 = a_subscr(j, j);
		    z__2.r = acoeff * a[i__1].r, z__2.i = acoeff * a[i__1].i;
		    i__2 = b_subscr(j, j);
		    z__3.r = bcoeff.r * b[i__2].r - bcoeff.i * b[i__2].i, 
			    z__3.i = bcoeff.r * b[i__2].i + bcoeff.i * b[i__2]
			    .r;
		    z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
		    d__.r = z__1.r, d__.i = z__1.i;
		    if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
			    d__2)) <= dmin__) {
			z__1.r = dmin__, z__1.i = 0.;
			d__.r = z__1.r, d__.i = z__1.i;
		    }

		    if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
			    d__2)) < 1.) {
			i__1 = j;
			if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
				&work[j]), abs(d__2)) >= bignum * ((d__3 = 
				d__.r, abs(d__3)) + (d__4 = d_imag(&d__), abs(
				d__4)))) {
			    i__1 = j;
			    temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
				    d__2 = d_imag(&work[j]), abs(d__2)));
			    i__1 = je;
			    for (jr = 1; jr <= i__1; ++jr) {
				i__2 = jr;
				i__3 = jr;
				z__1.r = temp * work[i__3].r, z__1.i = temp * 
					work[i__3].i;
				work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L180: */
			    }
/*                       -------------- Begin Timing Code --------------- */
			    iopst = iopst + (je << 1) + 5;
			} else {
			    iopst += 3;
/*                       --------------- End Timing Code ---------------- */
			}
		    }

		    i__1 = j;
		    i__2 = j;
		    z__2.r = -work[i__2].r, z__2.i = -work[i__2].i;
		    zladiv_(&z__1, &z__2, &d__);
		    work[i__1].r = z__1.r, work[i__1].i = z__1.i;

		    if (j > 1) {

/*                    w = w + x(j)*(a A(*,j) - b B(*,j) ) with scaling */

			i__1 = j;
			if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
				&work[j]), abs(d__2)) > 1.) {
			    i__1 = j;
			    temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
				    d__2 = d_imag(&work[j]), abs(d__2)));
			    if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >= 
				    bignum * temp) {
				i__1 = je;
				for (jr = 1; jr <= i__1; ++jr) {
				    i__2 = jr;
				    i__3 = jr;
				    z__1.r = temp * work[i__3].r, z__1.i = 
					    temp * work[i__3].i;
				    work[i__2].r = z__1.r, work[i__2].i = 
					    z__1.i;
/* L190: */
				}
/*                          ------------- Begin Timing Code ------------- */
				iopst = iopst + (je << 1) + 6;
			    } else {
				iopst += 6;
/*                          -------------- End Timing Code -------------- */
			    }
			}

			i__1 = j;
			z__1.r = acoeff * work[i__1].r, z__1.i = acoeff * 
				work[i__1].i;
			ca.r = z__1.r, ca.i = z__1.i;
			i__1 = j;
			z__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[
				i__1].i, z__1.i = bcoeff.r * work[i__1].i + 
				bcoeff.i * work[i__1].r;
			cb.r = z__1.r, cb.i = z__1.i;
			i__1 = j - 1;
			for (jr = 1; jr <= i__1; ++jr) {
			    i__2 = jr;
			    i__3 = jr;
			    i__4 = a_subscr(jr, j);
			    z__3.r = ca.r * a[i__4].r - ca.i * a[i__4].i, 
				    z__3.i = ca.r * a[i__4].i + ca.i * a[i__4]
				    .r;
			    z__2.r = work[i__3].r + z__3.r, z__2.i = work[
				    i__3].i + z__3.i;
			    i__5 = b_subscr(jr, j);
			    z__4.r = cb.r * b[i__5].r - cb.i * b[i__5].i, 
				    z__4.i = cb.r * b[i__5].i + cb.i * b[i__5]
				    .r;
			    z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - 
				    z__4.i;
			    work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L200: */
			}
		    }
/* L210: */
		}

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

		if (ilback) {
		    zgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1],
			     &c__1, &c_b1, &work[*n + 1], &c__1);
		    isrc = 2;
		    iend = *n;
/*                 ----------------- Begin Timing Code ------------------ */
		    iopst += (*n << 3) * je;
/*                 ------------------ End Timing Code ------------------- */
		} else {
		    isrc = 1;
		    iend = je;
		}

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

		xmax = 0.;
		i__1 = iend;
		for (jr = 1; jr <= i__1; ++jr) {
/* Computing MAX */
		    i__2 = (isrc - 1) * *n + jr;
		    d__3 = xmax, d__4 = (d__1 = work[i__2].r, abs(d__1)) + (
			    d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
			    d__2));
		    xmax = max(d__3,d__4);
/* L220: */
		}

		if (xmax > safmin) {
		    temp = 1. / xmax;
		    i__1 = iend;
		    for (jr = 1; jr <= i__1; ++jr) {
			i__2 = vr_subscr(jr, ieig);
			i__3 = (isrc - 1) * *n + jr;
			z__1.r = temp * work[i__3].r, z__1.i = temp * work[
				i__3].i;
			vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
/* L230: */
		    }
		} else {
		    iend = 0;
		}

		i__1 = *n;
		for (jr = iend + 1; jr <= i__1; ++jr) {
		    i__2 = vr_subscr(jr, ieig);
		    vr[i__2].r = 0., vr[i__2].i = 0.;
/* L240: */
		}

/*              ------------------- Begin Timing Code ------------------- */
		latime_1.ops += (doublereal) ((je - 2) * 30 + (je - 1 << 3) * 
			(je - 2) + iend * 3 + 22) + (doublereal) iopst;
/*              -------------------- End Timing Code -------------------- */
	    }
L250:
	    ;
	}
    }

    return 0;

/*     End of ZTGEVC */

} /* ztgevc_ */

#undef vr_ref
#undef vr_subscr
#undef vl_ref
#undef vl_subscr
#undef b_ref
#undef b_subscr
#undef a_ref
#undef a_subscr