Mercurial > hg > octave-nkf
diff scripts/control/util/zgscal.m @ 7132:b01db194c526
[project @ 2007-11-08 16:17:34 by jwe]
author | jwe |
---|---|
date | Thu, 08 Nov 2007 16:17:34 +0000 |
parents | f084ba47812b |
children |
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--- a/scripts/control/util/zgscal.m +++ b/scripts/control/util/zgscal.m @@ -44,27 +44,27 @@ nmp = n+m+p; ## x_0 = x_{-1} = 0, r_0 = z - x = zeros(nmp,1); + x = zeros (nmp, 1); xk1 = x; xk2 = x; rk1 = z; k = 0; ## construct balancing least squares problem - F = eye(nmp); - for kk=1:nmp - F(1:nmp,kk) = zgfmul(a,b,c,d,F(:,kk)); + F = eye (nmp); + for kk = 1:nmp + F(1:nmp,kk) = zgfmul (a, b, c, d, F(:,kk)); endfor - [U,H,k1] = krylov(F,z,nmp,1e-12,1); - if(!issquare(H)) - if(columns(H) != k1) - error("zgscal(tzero): k1=%d, columns(H)=%d",k1,columns(H)); - elseif(rows(H) != k1+1) - error("zgscal: k1=%d, rows(H) = %d",k1,rows(H)); - elseif ( norm(H(k1+1,:)) > 1e-12*norm(H,"inf") ) + [U, H, k1] = krylov (F, z, nmp, 1e-12, 1); + if (! issquare (H)) + if (columns (H) != k1) + error ("zgscal(tzero): k1=%d, columns(H)=%d", k1, columns (H)); + elseif (rows (H) != k1+1) + error ("zgscal: k1=%d, rows(H) = %d", k1, rows (H)); + elseif (norm (H(k1+1,:)) > 1e-12*norm (H, "inf")) zgscal_last_row_of_H = H(k1+1,:) - error("zgscal: last row of H nonzero (norm(H)=%e)",norm(H,"inf")) + error ("zgscal: last row of H nonzero (norm(H)=%e)", norm (H, "inf")) endif H = H(1:k1,1:k1); U = U(:,1:k1); @@ -72,8 +72,8 @@ ## tridiagonal H can still be rank deficient, so do permuted qr ## factorization - [qq,rr,pp] = qr(H); # H = qq*rr*pp' - nn = rank(rr); + [qq, rr, pp] = qr (H); # H = qq*rr*pp' + nn = rank (rr); qq = qq(:,1:nn); rr = rr(1:nn,:); # rr may not be square, but "\" does least xx = U*pp*(rr\qq'*(U'*z)); # squares solution, so this works @@ -86,38 +86,41 @@ ## so for now I'm solving it with the krylov routine. ## initialize residual error norm - rnorm = norm(rk1,1); + rnorm = norm (rk1, 1); xnorm = 0; - fnorm = 1e-12 * norm([a,b;c,d],1); + fnorm = 1e-12 * norm ([a, b; c, d], 1); - ## dummy defines for MATHTOOLS compiler - gamk2 = 0; omega1 = 0; ztmz2 = 0; + gamk2 = 0; + omega1 = 0; + ztmz2 = 0; ## do until small changes to x len_x = length(x); - while ((k < 2*len_x) & (xnorm> 0.5) & (rnorm>fnorm))|(k == 0) - k = k+1; + while ((k < 2*len_x && xnorm > 0.5 && rnorm > fnorm) || k == 0) + k++; ## solve F_d z_{k-1} = r_{k-1} - zk1= zgfslv(n,m,p,rk1); + zk1= zgfslv (n, m, p, rk1); ## Generalized CG iteration ## gamk1 = (zk1'*F_d*zk1)/(zk1'*F*zk1); ztMz1 = zk1'*rk1; - gamk1 = ztMz1/(zk1'*zgfmul(a,b,c,d,zk1)); + gamk1 = ztMz1/(zk1'*zgfmul (a, b, c, d, zk1)); - if(rem(k,len_x) == 1) omega = 1; - else omega = 1/(1-gamk1*ztMz1/(gamk2*omega1*ztmz2)); + if (rem (k, len_x) == 1) + omega = 1; + else + omega = 1/(1-gamk1*ztMz1/(gamk2*omega1*ztmz2)); endif ## store x in xk2 to save space xk2 = xk2 + omega*(gamk1*zk1 + xk1 - xk2); ## compute new residual error: rk = z - F xk, check end conditions - rk1 = z - zgfmul(a,b,c,d,xk2); - rnorm = norm(rk1); - xnorm = max(abs(xk1 - xk2)); + rk1 = z - zgfmul (a, b, c, d, xk2); + rnorm = norm (rk1); + xnorm = max (abs (xk1 - xk2)); ## printf("zgscal: k=%d, gamk1=%e, gamk2=%e, \nztMz1=%e ztmz2=%e\n", ... ## k,gamk1, gamk2, ztMz1, ztmz2); @@ -129,21 +132,22 @@ gamk2 = gamk1; omega1 = omega; ztmz2 = ztMz1; - [xk1,xk2] = swap(xk1,xk2); + [xk1, xk2] = swap (xk1, xk2); endwhile x = xk2; ## check convergence - if (xnorm> 0.5 & rnorm>fnorm) - warning("zgscal(tzero): GCG iteration failed; solving with pinv"); + if (xnorm> 0.5 && rnorm > fnorm) + warning ("zgscal(tzero): GCG iteration failed; solving with pinv"); ## perform brute force least squares; construct F - Am = eye(nmp); - for ii=1:nmp - Am(:,ii) = zgfmul(a,b,c,d,Am(:,ii)); + Am = eye (nmp); + for ii = 1:nmp + Am(:,ii) = zgfmul (a, b, c, d, Am(:,ii)); endfor ## now solve with qr factorization - x = pinv(Am)*z; + x = pinv (Am) * z; endif + endfunction