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comparison scripts/control/util/zgscal.m @ 7132:b01db194c526

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[project @ 2007-11-08 16:17:34 by jwe]
author jwe
date Thu, 08 Nov 2007 16:17:34 +0000
parents f084ba47812b
children
comparison
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7131:a184bc985c37 7132:b01db194c526
42 ## Givens rotations, diagonalized 2x2 block of F, gcg vector initialization 42 ## Givens rotations, diagonalized 2x2 block of F, gcg vector initialization
43 43
44 nmp = n+m+p; 44 nmp = n+m+p;
45 45
46 ## x_0 = x_{-1} = 0, r_0 = z 46 ## x_0 = x_{-1} = 0, r_0 = z
47 x = zeros(nmp,1); 47 x = zeros (nmp, 1);
48 xk1 = x; 48 xk1 = x;
49 xk2 = x; 49 xk2 = x;
50 rk1 = z; 50 rk1 = z;
51 k = 0; 51 k = 0;
52 52
53 ## construct balancing least squares problem 53 ## construct balancing least squares problem
54 F = eye(nmp); 54 F = eye (nmp);
55 for kk=1:nmp 55 for kk = 1:nmp
56 F(1:nmp,kk) = zgfmul(a,b,c,d,F(:,kk)); 56 F(1:nmp,kk) = zgfmul (a, b, c, d, F(:,kk));
57 endfor 57 endfor
58 58
59 [U,H,k1] = krylov(F,z,nmp,1e-12,1); 59 [U, H, k1] = krylov (F, z, nmp, 1e-12, 1);
60 if(!issquare(H)) 60 if (! issquare (H))
61 if(columns(H) != k1) 61 if (columns (H) != k1)
62 error("zgscal(tzero): k1=%d, columns(H)=%d",k1,columns(H)); 62 error ("zgscal(tzero): k1=%d, columns(H)=%d", k1, columns (H));
63 elseif(rows(H) != k1+1) 63 elseif (rows (H) != k1+1)
64 error("zgscal: k1=%d, rows(H) = %d",k1,rows(H)); 64 error ("zgscal: k1=%d, rows(H) = %d", k1, rows (H));
65 elseif ( norm(H(k1+1,:)) > 1e-12*norm(H,"inf") ) 65 elseif (norm (H(k1+1,:)) > 1e-12*norm (H, "inf"))
66 zgscal_last_row_of_H = H(k1+1,:) 66 zgscal_last_row_of_H = H(k1+1,:)
67 error("zgscal: last row of H nonzero (norm(H)=%e)",norm(H,"inf")) 67 error ("zgscal: last row of H nonzero (norm(H)=%e)", norm (H, "inf"))
68 endif 68 endif
69 H = H(1:k1,1:k1); 69 H = H(1:k1,1:k1);
70 U = U(:,1:k1); 70 U = U(:,1:k1);
71 endif 71 endif
72 72
73 ## tridiagonal H can still be rank deficient, so do permuted qr 73 ## tridiagonal H can still be rank deficient, so do permuted qr
74 ## factorization 74 ## factorization
75 [qq,rr,pp] = qr(H); # H = qq*rr*pp' 75 [qq, rr, pp] = qr (H); # H = qq*rr*pp'
76 nn = rank(rr); 76 nn = rank (rr);
77 qq = qq(:,1:nn); 77 qq = qq(:,1:nn);
78 rr = rr(1:nn,:); # rr may not be square, but "\" does least 78 rr = rr(1:nn,:); # rr may not be square, but "\" does least
79 xx = U*pp*(rr\qq'*(U'*z)); # squares solution, so this works 79 xx = U*pp*(rr\qq'*(U'*z)); # squares solution, so this works
80 ## xx1 = pinv(F)*z; 80 ## xx1 = pinv(F)*z;
81 ## zgscal_x_xx1_err = [xx,xx1,xx-xx1] 81 ## zgscal_x_xx1_err = [xx,xx1,xx-xx1]
84 ## the rest of this is left from the original zgscal; 84 ## the rest of this is left from the original zgscal;
85 ## I've had some numerical problems with the GCG algorithm, 85 ## I've had some numerical problems with the GCG algorithm,
86 ## so for now I'm solving it with the krylov routine. 86 ## so for now I'm solving it with the krylov routine.
87 87
88 ## initialize residual error norm 88 ## initialize residual error norm
89 rnorm = norm(rk1,1); 89 rnorm = norm (rk1, 1);
90 90
91 xnorm = 0; 91 xnorm = 0;
92 fnorm = 1e-12 * norm([a,b;c,d],1); 92 fnorm = 1e-12 * norm ([a, b; c, d], 1);
93 93
94 ## dummy defines for MATHTOOLS compiler 94 gamk2 = 0;
95 gamk2 = 0; omega1 = 0; ztmz2 = 0; 95 omega1 = 0;
96 ztmz2 = 0;
96 97
97 ## do until small changes to x 98 ## do until small changes to x
98 len_x = length(x); 99 len_x = length(x);
99 while ((k < 2*len_x) & (xnorm> 0.5) & (rnorm>fnorm))|(k == 0) 100 while ((k < 2*len_x && xnorm > 0.5 && rnorm > fnorm) || k == 0)
100 k = k+1; 101 k++;
101 102
102 ## solve F_d z_{k-1} = r_{k-1} 103 ## solve F_d z_{k-1} = r_{k-1}
103 zk1= zgfslv(n,m,p,rk1); 104 zk1= zgfslv (n, m, p, rk1);
104 105
105 ## Generalized CG iteration 106 ## Generalized CG iteration
106 ## gamk1 = (zk1'*F_d*zk1)/(zk1'*F*zk1); 107 ## gamk1 = (zk1'*F_d*zk1)/(zk1'*F*zk1);
107 ztMz1 = zk1'*rk1; 108 ztMz1 = zk1'*rk1;
108 gamk1 = ztMz1/(zk1'*zgfmul(a,b,c,d,zk1)); 109 gamk1 = ztMz1/(zk1'*zgfmul (a, b, c, d, zk1));
109 110
110 if(rem(k,len_x) == 1) omega = 1; 111 if (rem (k, len_x) == 1)
111 else omega = 1/(1-gamk1*ztMz1/(gamk2*omega1*ztmz2)); 112 omega = 1;
113 else
114 omega = 1/(1-gamk1*ztMz1/(gamk2*omega1*ztmz2));
112 endif 115 endif
113 116
114 ## store x in xk2 to save space 117 ## store x in xk2 to save space
115 xk2 = xk2 + omega*(gamk1*zk1 + xk1 - xk2); 118 xk2 = xk2 + omega*(gamk1*zk1 + xk1 - xk2);
116 119
117 ## compute new residual error: rk = z - F xk, check end conditions 120 ## compute new residual error: rk = z - F xk, check end conditions
118 rk1 = z - zgfmul(a,b,c,d,xk2); 121 rk1 = z - zgfmul (a, b, c, d, xk2);
119 rnorm = norm(rk1); 122 rnorm = norm (rk1);
120 xnorm = max(abs(xk1 - xk2)); 123 xnorm = max (abs (xk1 - xk2));
121 124
122 ## printf("zgscal: k=%d, gamk1=%e, gamk2=%e, \nztMz1=%e ztmz2=%e\n", ... 125 ## printf("zgscal: k=%d, gamk1=%e, gamk2=%e, \nztMz1=%e ztmz2=%e\n", ...
123 ## k,gamk1, gamk2, ztMz1, ztmz2); 126 ## k,gamk1, gamk2, ztMz1, ztmz2);
124 ## xk2_1_zk1 = [xk2 xk1 zk1] 127 ## xk2_1_zk1 = [xk2 xk1 zk1]
125 ## ABCD = [a,b;c,d] 128 ## ABCD = [a,b;c,d]
127 130
128 ## get ready for next iteration 131 ## get ready for next iteration
129 gamk2 = gamk1; 132 gamk2 = gamk1;
130 omega1 = omega; 133 omega1 = omega;
131 ztmz2 = ztMz1; 134 ztmz2 = ztMz1;
132 [xk1,xk2] = swap(xk1,xk2); 135 [xk1, xk2] = swap (xk1, xk2);
133 endwhile 136 endwhile
134 x = xk2; 137 x = xk2;
135 138
136 ## check convergence 139 ## check convergence
137 if (xnorm> 0.5 & rnorm>fnorm) 140 if (xnorm> 0.5 && rnorm > fnorm)
138 warning("zgscal(tzero): GCG iteration failed; solving with pinv"); 141 warning ("zgscal(tzero): GCG iteration failed; solving with pinv");
139 142
140 ## perform brute force least squares; construct F 143 ## perform brute force least squares; construct F
141 Am = eye(nmp); 144 Am = eye (nmp);
142 for ii=1:nmp 145 for ii = 1:nmp
143 Am(:,ii) = zgfmul(a,b,c,d,Am(:,ii)); 146 Am(:,ii) = zgfmul (a, b, c, d, Am(:,ii));
144 endfor 147 endfor
145 148
146 ## now solve with qr factorization 149 ## now solve with qr factorization
147 x = pinv(Am)*z; 150 x = pinv (Am) * z;
148 endif 151 endif
152
149 endfunction 153 endfunction