stgevc.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

	    if (ilall) {
		ilcomp = TRUE_;
	    } else if (ilcplx) {
		ilcomp = select[je] || select[je - 1];
	    } else {
		ilcomp = select[je];
	    }
	    if (! ilcomp) {
		goto L500;
	    }

/*           Decide if (a) singular pencil, (b) real eigenvalue, or   
             (c) complex eigenvalue. */

	    if (! ilcplx) {
		if ((r__1 = a_ref(je, je), dabs(r__1)) <= safmin && (r__2 = 
			b_ref(je, je), dabs(r__2)) <= safmin) {

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

		    --ieig;
		    i__1 = *n;
		    for (jr = 1; jr <= i__1; ++jr) {
			vr_ref(jr, ieig) = 0.f;
/* L230: */
		    }
		    vr_ref(ieig, ieig) = 1.f;
		    goto L500;
		}
	    }

/*           Clear vector */

	    i__1 = nw - 1;
	    for (jw = 0; jw <= i__1; ++jw) {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
		    work[(jw + 2) * *n + jr] = 0.f;
/* L240: */
		}
/* L250: */
	    }

/*           Compute coefficients in  ( a A - b B ) x = 0   
                a  is  ACOEF   
                b  is  BCOEFR + i*BCOEFI */

	    if (! ilcplx) {

/*              Real eigenvalue   

   Computing MAX */
		r__3 = (r__1 = a_ref(je, je), dabs(r__1)) * ascale, r__4 = (
			r__2 = b_ref(je, je), dabs(r__2)) * bscale, r__3 = 
			max(r__3,r__4);
		temp = 1.f / dmax(r__3,safmin);
		salfar = temp * a_ref(je, je) * ascale;
		sbeta = temp * b_ref(je, je) * bscale;
		acoef = sbeta * ascale;
		bcoefr = salfar * bscale;
		bcoefi = 0.f;

/*              Scale to avoid underflow */

		scale = 1.f;
		lsa = dabs(sbeta) >= safmin && dabs(acoef) < small;
		lsb = dabs(salfar) >= safmin && dabs(bcoefr) < small;
		if (lsa) {
		    scale = small / dabs(sbeta) * dmin(anorm,big);
		}
		if (lsb) {
/* Computing MAX */
		    r__1 = scale, r__2 = small / dabs(salfar) * dmin(bnorm,
			    big);
		    scale = dmax(r__1,r__2);
		}
		if (lsa || lsb) {
/* Computing MIN   
   Computing MAX */
		    r__3 = 1.f, r__4 = dabs(acoef), r__3 = max(r__3,r__4), 
			    r__4 = dabs(bcoefr);
		    r__1 = scale, r__2 = 1.f / (safmin * dmax(r__3,r__4));
		    scale = dmin(r__1,r__2);
		    if (lsa) {
			acoef = ascale * (scale * sbeta);
		    } else {
			acoef = scale * acoef;
		    }
		    if (lsb) {
			bcoefr = bscale * (scale * salfar);
		    } else {
			bcoefr = scale * bcoefr;
		    }
		}
		acoefa = dabs(acoef);
		bcoefa = dabs(bcoefr);

/*              First component is 1 */

		work[(*n << 1) + je] = 1.f;
		xmax = 1.f;

/*              Compute contribution from column JE of A and B to sum   
                (See "Further Details", above.) */

		i__1 = je - 1;
		for (jr = 1; jr <= i__1; ++jr) {
		    work[(*n << 1) + jr] = bcoefr * b_ref(jr, je) - acoef * 
			    a_ref(jr, je);
/* L260: */
		}
	    } else {

/*              Complex eigenvalue */

		r__1 = safmin * 100.f;
		slag2_(&a_ref(je - 1, je - 1), lda, &b_ref(je - 1, je - 1), 
			ldb, &r__1, &acoef, &temp, &bcoefr, &temp2, &bcoefi);
		if (bcoefi == 0.f) {
		    *info = je - 1;
		    return 0;
		}

/*              Scale to avoid over/underflow */

		acoefa = dabs(acoef);
		bcoefa = dabs(bcoefr) + dabs(bcoefi);
		scale = 1.f;
		if (acoefa * ulp < safmin && acoefa >= safmin) {
		    scale = safmin / ulp / acoefa;
		}
		if (bcoefa * ulp < safmin && bcoefa >= safmin) {
/* Computing MAX */
		    r__1 = scale, r__2 = safmin / ulp / bcoefa;
		    scale = dmax(r__1,r__2);
		}
		if (safmin * acoefa > ascale) {
		    scale = ascale / (safmin * acoefa);
		}
		if (safmin * bcoefa > bscale) {
/* Computing MIN */
		    r__1 = scale, r__2 = bscale / (safmin * bcoefa);
		    scale = dmin(r__1,r__2);
		}
		if (scale != 1.f) {
		    acoef = scale * acoef;
		    acoefa = dabs(acoef);
		    bcoefr = scale * bcoefr;
		    bcoefi = scale * bcoefi;
		    bcoefa = dabs(bcoefr) + dabs(bcoefi);
		}

/*              Compute first two components of eigenvector   
                and contribution to sums */

		temp = acoef * a_ref(je, je - 1);
		temp2r = acoef * a_ref(je, je) - bcoefr * b_ref(je, je);
		temp2i = -bcoefi * b_ref(je, je);
		if (dabs(temp) >= dabs(temp2r) + dabs(temp2i)) {
		    work[(*n << 1) + je] = 1.f;
		    work[*n * 3 + je] = 0.f;
		    work[(*n << 1) + je - 1] = -temp2r / temp;
		    work[*n * 3 + je - 1] = -temp2i / temp;
		} else {
		    work[(*n << 1) + je - 1] = 1.f;
		    work[*n * 3 + je - 1] = 0.f;
		    temp = acoef * a_ref(je - 1, je);
		    work[(*n << 1) + je] = (bcoefr * b_ref(je - 1, je - 1) - 
			    acoef * a_ref(je - 1, je - 1)) / temp;
		    work[*n * 3 + je] = bcoefi * b_ref(je - 1, je - 1) / temp;
		}

/* Computing MAX */
		r__5 = (r__1 = work[(*n << 1) + je], dabs(r__1)) + (r__2 = 
			work[*n * 3 + je], dabs(r__2)), r__6 = (r__3 = work[(*
			n << 1) + je - 1], dabs(r__3)) + (r__4 = work[*n * 3 
			+ je - 1], dabs(r__4));
		xmax = dmax(r__5,r__6);

/*              Compute contribution from columns JE and JE-1   
                of A and B to the sums. */

		creala = acoef * work[(*n << 1) + je - 1];
		cimaga = acoef * work[*n * 3 + je - 1];
		crealb = bcoefr * work[(*n << 1) + je - 1] - bcoefi * work[*n 
			* 3 + je - 1];
		cimagb = bcoefi * work[(*n << 1) + je - 1] + bcoefr * work[*n 
			* 3 + je - 1];
		cre2a = acoef * work[(*n << 1) + je];
		cim2a = acoef * work[*n * 3 + je];
		cre2b = bcoefr * work[(*n << 1) + je] - bcoefi * work[*n * 3 
			+ je];
		cim2b = bcoefi * work[(*n << 1) + je] + bcoefr * work[*n * 3 
			+ je];
		i__1 = je - 2;
		for (jr = 1; jr <= i__1; ++jr) {
		    work[(*n << 1) + jr] = -creala * a_ref(jr, je - 1) + 
			    crealb * b_ref(jr, je - 1) - cre2a * a_ref(jr, je)
			     + cre2b * b_ref(jr, je);
		    work[*n * 3 + jr] = -cimaga * a_ref(jr, je - 1) + cimagb *
			     b_ref(jr, je - 1) - cim2a * a_ref(jr, je) + 
			    cim2b * b_ref(jr, je);
/* L270: */
		}
	    }

/* Computing MAX */
	    r__1 = ulp * acoefa * anorm, r__2 = ulp * bcoefa * bnorm, r__1 = 
		    max(r__1,r__2);
	    dmin__ = dmax(r__1,safmin);

/*           Columnwise triangular solve of  (a A - b B)  x = 0 */

	    il2by2 = FALSE_;
/*           ------------------- Begin Timing Code ---------------------- */
	    opst = 0.f;
	    in2by2 = 0;
/*           -------------------- End Timing Code ----------------------- */
	    for (j = je - nw; j >= 1; --j) {
/*              ------------------- Begin Timing Code ------------------- */
		opssca = (real) (nw * je + 1);
/*              -------------------- End Timing Code --------------------   

                If a 2-by-2 block, is in position j-1:j, wait until   
                next iteration to process it (when it will be j:j+1) */

		if (! il2by2 && j > 1) {
		    if (a_ref(j, j - 1) != 0.f) {
			il2by2 = TRUE_;
/*                    -------------- Begin Timing Code ----------------- */
			++in2by2;
/*                    --------------- End Timing Code ------------------- */
			goto L370;
		    }
		}
		bdiag[0] = b_ref(j, j);
		if (il2by2) {
		    na = 2;
		    bdiag[1] = b_ref(j + 1, j + 1);
		} else {
		    na = 1;
		}

/*              Compute x(j) (and x(j+1), if 2-by-2 block) */

		slaln2_(&c_false, &na, &nw, &dmin__, &acoef, &a_ref(j, j), 
			lda, bdiag, &bdiag[1], &work[(*n << 1) + j], n, &
			bcoefr, &bcoefi, sum, &c__2, &scale, &temp, &iinfo);
		if (scale < 1.f) {

		    i__1 = nw - 1;
		    for (jw = 0; jw <= i__1; ++jw) {
			i__2 = je;
			for (jr = 1; jr <= i__2; ++jr) {
			    work[(jw + 2) * *n + jr] = scale * work[(jw + 2) *
				     *n + jr];
/* L280: */
			}
/* L290: */
		    }
		}
/* Computing MAX */
		r__1 = scale * xmax;
		xmax = dmax(r__1,temp);
/*              ------------------ Begin Timing Code ----------------- */
		opst += opssca;
/*              ------------------- End Timing Code ------------------ */

		i__1 = nw;
		for (jw = 1; jw <= i__1; ++jw) {
		    i__2 = na;
		    for (ja = 1; ja <= i__2; ++ja) {
			work[(jw + 1) * *n + j + ja - 1] = sum_ref(ja, jw);
/* L300: */
		    }
/* L310: */
		}

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

		if (j > 1) {

/*                 Check whether scaling is necessary for sum. */

		    xscale = 1.f / dmax(1.f,xmax);
		    temp = acoefa * work[j] + bcoefa * work[*n + j];
		    if (il2by2) {
/* Computing MAX */
			r__1 = temp, r__2 = acoefa * work[j + 1] + bcoefa * 
				work[*n + j + 1];
			temp = dmax(r__1,r__2);
		    }
/* Computing MAX */
		    r__1 = max(temp,acoefa);
		    temp = dmax(r__1,bcoefa);
		    if (temp > bignum * xscale) {

			i__1 = nw - 1;
			for (jw = 0; jw <= i__1; ++jw) {
			    i__2 = je;
			    for (jr = 1; jr <= i__2; ++jr) {
				work[(jw + 2) * *n + jr] = xscale * work[(jw 
					+ 2) * *n + jr];
/* L320: */
			    }
/* L330: */
			}
			xmax *= xscale;
/*                    ----------------- Begin Timing Code --------------- */
			opst += opssca;
/*                    ------------------ End Timing Code ---------------- */
		    }

/*                 Compute the contributions of the off-diagonals of   
                   column j (and j+1, if 2-by-2 block) of A and B to the   
                   sums. */


		    i__1 = na;
		    for (ja = 1; ja <= i__1; ++ja) {
			if (ilcplx) {
			    creala = acoef * work[(*n << 1) + j + ja - 1];
			    cimaga = acoef * work[*n * 3 + j + ja - 1];
			    crealb = bcoefr * work[(*n << 1) + j + ja - 1] - 
				    bcoefi * work[*n * 3 + j + ja - 1];
			    cimagb = bcoefi * work[(*n << 1) + j + ja - 1] + 
				    bcoefr * work[*n * 3 + j + ja - 1];
			    i__2 = j - 1;
			    for (jr = 1; jr <= i__2; ++jr) {
				work[(*n << 1) + jr] = work[(*n << 1) + jr] - 
					creala * a_ref(jr, j + ja - 1) + 
					crealb * b_ref(jr, j + ja - 1);
				work[*n * 3 + jr] = work[*n * 3 + jr] - 
					cimaga * a_ref(jr, j + ja - 1) + 
					cimagb * b_ref(jr, j + ja - 1);
/* L340: */
			    }
			} else {
			    creala = acoef * work[(*n << 1) + j + ja - 1];
			    crealb = bcoefr * work[(*n << 1) + j + ja - 1];
			    i__2 = j - 1;
			    for (jr = 1; jr <= i__2; ++jr) {
				work[(*n << 1) + jr] = work[(*n << 1) + jr] - 
					creala * a_ref(jr, j + ja - 1) + 
					crealb * b_ref(jr, j + ja - 1);
/* L350: */
			    }
			}
/* L360: */
		    }
		}

		il2by2 = FALSE_;
L370:
		;
	    }

/*           Copy eigenvector to VR, back transforming if   
             HOWMNY='B'. */

	    ieig -= nw;
	    if (ilback) {

		i__1 = nw - 1;
		for (jw = 0; jw <= i__1; ++jw) {
		    i__2 = *n;
		    for (jr = 1; jr <= i__2; ++jr) {
			work[(jw + 4) * *n + jr] = work[(jw + 2) * *n + 1] * 
				vr_ref(jr, 1);
/* L380: */
		    }

/*                 A series of compiler directives to defeat   
                   vectorization for the next loop */


		    i__2 = je;
		    for (jc = 2; jc <= i__2; ++jc) {
			i__3 = *n;
			for (jr = 1; jr <= i__3; ++jr) {
			    work[(jw + 4) * *n + jr] += work[(jw + 2) * *n + 
				    jc] * vr_ref(jr, jc);
/* L390: */
			}
/* L400: */
		    }
/* L410: */
		}

		i__1 = nw - 1;
		for (jw = 0; jw <= i__1; ++jw) {
		    i__2 = *n;
		    for (jr = 1; jr <= i__2; ++jr) {
			vr_ref(jr, ieig + jw) = work[(jw + 4) * *n + jr];
/* L420: */
		    }
/* L430: */
		}

		iend = *n;
	    } else {
		i__1 = nw - 1;
		for (jw = 0; jw <= i__1; ++jw) {
		    i__2 = *n;
		    for (jr = 1; jr <= i__2; ++jr) {
			vr_ref(jr, ieig + jw) = work[(jw + 2) * *n + jr];
/* L440: */
		    }
/* L450: */
		}

		iend = je;
	    }

/*           Scale eigenvector */

	    xmax = 0.f;
	    if (ilcplx) {
		i__1 = iend;
		for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
		    r__3 = xmax, r__4 = (r__1 = vr_ref(j, ieig), dabs(r__1)) 
			    + (r__2 = vr_ref(j, ieig + 1), dabs(r__2));
		    xmax = dmax(r__3,r__4);
/* L460: */
		}
	    } else {
		i__1 = iend;
		for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
		    r__2 = xmax, r__3 = (r__1 = vr_ref(j, ieig), dabs(r__1));
		    xmax = dmax(r__2,r__3);
/* L470: */
		}
	    }

	    if (xmax > safmin) {
		xscale = 1.f / xmax;
		i__1 = nw - 1;
		for (jw = 0; jw <= i__1; ++jw) {
		    i__2 = iend;
		    for (jr = 1; jr <= i__2; ++jr) {
			vr_ref(jr, ieig + jw) = xscale * vr_ref(jr, ieig + jw)
				;
/* L480: */
		    }
/* L490: */
		}
	    }

/*           ------------------- Begin Timing Code ----------------------   
             Opcounts for each eigenvector   

                                  Real                Complex   
             Initialization       8--16 + 3*(JE-1)    71--87+16+14*(JE-2)   

             Solve (per iter)     NA*(5 + 7*(NA-1))   NA*(17 + 17*(NA-1))   
                                  + scaling           + scaling   
             column add (per iter)   
                                  2 + 5*NA            2 + 11*NA   
                                  + 4*NA*(J-1)        + 8*NA*(J-1)   
                                  + scaling           + scaling   
             iteration:           J=JE-1,...,1        J=JE-2,...,1   

             Back xform           2*N*JE - N          4*N*JE - 2*N   
             Scaling (w/back x.)  N                   3*N   
             Scaling (w/o back)   JE                  3*JE */

	    if (! ilcplx) {
		opst += (real) (((je << 1) + 11) * (je - 1) + 12 + (in2by2 << 
			3));
		if (ilback) {
		    opst += (real) ((*n << 1) * je);
		} else {
		    opst += (real) je;
		}
	    } else {
		opst += (real) (((je << 2) + 32) * (je - 2) + 95 + in2by2 * 
			24);
		if (ilback) {
		    opst += (real) ((*n << 2) * je + *n);
		} else {
		    opst += (real) (je * 3);
		}
	    }
	    latime_1.ops += opst;

/*           -------------------- End Timing Code ----------------------- */

L500:
	    ;
	}
    }

    return 0;

/*     End of STGEVC */

} /* stgevc_ */

#undef sum_ref
#undef vr_ref
#undef vl_ref
#undef b_ref
#undef a_ref
#undef sumb_ref
#undef suma_ref