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t_hessian

PURPOSE ^

T_HESSIAN Numerical tests of 2nd derivative code.

SYNOPSIS ^

function t_hessian(quiet)

DESCRIPTION ^

T_HESSIAN  Numerical tests of 2nd derivative code.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function t_hessian(quiet)
0002 %T_HESSIAN  Numerical tests of 2nd derivative code.
0003 
0004 %   MATPOWER
0005 %   $Id: t_hessian.m 2229 2013-12-11 01:28:09Z ray $
0006 %   by Ray Zimmerman, PSERC Cornell
0007 %   Copyright (c) 2004-2010 by Power System Engineering Research Center (PSERC)
0008 %
0009 %   This file is part of MATPOWER.
0010 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0011 %
0012 %   MATPOWER is free software: you can redistribute it and/or modify
0013 %   it under the terms of the GNU General Public License as published
0014 %   by the Free Software Foundation, either version 3 of the License,
0015 %   or (at your option) any later version.
0016 %
0017 %   MATPOWER is distributed in the hope that it will be useful,
0018 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0019 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
0020 %   GNU General Public License for more details.
0021 %
0022 %   You should have received a copy of the GNU General Public License
0023 %   along with MATPOWER. If not, see <http://www.gnu.org/licenses/>.
0024 %
0025 %   Additional permission under GNU GPL version 3 section 7
0026 %
0027 %   If you modify MATPOWER, or any covered work, to interface with
0028 %   other modules (such as MATLAB code and MEX-files) available in a
0029 %   MATLAB(R) or comparable environment containing parts covered
0030 %   under other licensing terms, the licensors of MATPOWER grant
0031 %   you additional permission to convey the resulting work.
0032 
0033 if nargin < 1
0034     quiet = 0;
0035 end
0036 
0037 t_begin(44, quiet);
0038 
0039 casefile = 'case30';
0040 
0041 %% define named indices into bus, gen, branch matrices
0042 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0043     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0044 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0045     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0046     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0047 
0048 %% run powerflow to get solved case
0049 mpopt = mpoption('verbose', 0, 'out.all', 0);
0050 [baseMVA, bus, gen, branch, success, et] = runpf(casefile, mpopt);
0051 
0052 %% switch to internal bus numbering and build admittance matrices
0053 [i2e, bus, gen, branch] = ext2int(bus, gen, branch);
0054 [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch);
0055 Vm = bus(:, VM);
0056 Va = bus(:, VA) * pi/180;
0057 V = Vm .* exp(1j * Va);
0058 f = branch(:, F_BUS);       %% list of "from" buses
0059 t = branch(:, T_BUS);       %% list of "to" buses
0060 nl = length(f);
0061 nb = length(V);
0062 Cf = sparse(1:nl, f, ones(nl, 1), nl, nb);      %% connection matrix for line & from buses
0063 Ct = sparse(1:nl, t, ones(nl, 1), nl, nb);      %% connection matrix for line & to buses
0064 pert = 1e-8;
0065 
0066 %%-----  check d2Sbus_dV2 code  -----
0067 t = ' - d2Sbus_dV2 (complex power injections)';
0068 lam = 10 * rand(nb, 1);
0069 num_Haa = zeros(nb, nb);
0070 num_Hav = zeros(nb, nb);
0071 num_Hva = zeros(nb, nb);
0072 num_Hvv = zeros(nb, nb);
0073 [dSbus_dVm, dSbus_dVa] = dSbus_dV(Ybus, V);
0074 [Haa, Hav, Hva, Hvv] = d2Sbus_dV2(Ybus, V, lam);
0075 for i = 1:nb
0076     Vap = V;
0077     Vap(i) = Vm(i) * exp(1j * (Va(i) + pert));
0078     [dSbus_dVm_ap, dSbus_dVa_ap] = dSbus_dV(Ybus, Vap);
0079     num_Haa(:, i) = (dSbus_dVa_ap - dSbus_dVa).' * lam / pert;
0080     num_Hva(:, i) = (dSbus_dVm_ap - dSbus_dVm).' * lam / pert;
0081 
0082     Vmp = V;
0083     Vmp(i) = (Vm(i) + pert) * exp(1j * Va(i));
0084     [dSbus_dVm_mp, dSbus_dVa_mp] = dSbus_dV(Ybus, Vmp);
0085     num_Hav(:, i) = (dSbus_dVa_mp - dSbus_dVa).' * lam / pert;
0086     num_Hvv(:, i) = (dSbus_dVm_mp - dSbus_dVm).' * lam / pert;
0087 end
0088 
0089 t_is(full(Haa), num_Haa, 4, ['Haa' t]);
0090 t_is(full(Hav), num_Hav, 4, ['Hav' t]);
0091 t_is(full(Hva), num_Hva, 4, ['Hva' t]);
0092 t_is(full(Hvv), num_Hvv, 4, ['Hvv' t]);
0093 
0094 %%-----  check d2Sbr_dV2 code  -----
0095 t = ' - d2Sbr_dV2 (complex power flows)';
0096 lam = 10 * rand(nl, 1);
0097 % lam = [1; zeros(nl-1, 1)];
0098 num_Gfaa = zeros(nb, nb);
0099 num_Gfav = zeros(nb, nb);
0100 num_Gfva = zeros(nb, nb);
0101 num_Gfvv = zeros(nb, nb);
0102 num_Gtaa = zeros(nb, nb);
0103 num_Gtav = zeros(nb, nb);
0104 num_Gtva = zeros(nb, nb);
0105 num_Gtvv = zeros(nb, nb);
0106 [dSf_dVa, dSf_dVm, dSt_dVa, dSt_dVm, Sf, St] = dSbr_dV(branch, Yf, Yt, V);
0107 [Gfaa, Gfav, Gfva, Gfvv] = d2Sbr_dV2(Cf, Yf, V, lam);
0108 [Gtaa, Gtav, Gtva, Gtvv] = d2Sbr_dV2(Ct, Yt, V, lam);
0109 for i = 1:nb
0110     Vap = V;
0111     Vap(i) = Vm(i) * exp(1j * (Va(i) + pert));
0112     [dSf_dVa_ap, dSf_dVm_ap, dSt_dVa_ap, dSt_dVm_ap, Sf_ap, St_ap] = ...
0113         dSbr_dV(branch, Yf, Yt, Vap);
0114     num_Gfaa(:, i) = (dSf_dVa_ap - dSf_dVa).' * lam / pert;
0115     num_Gfva(:, i) = (dSf_dVm_ap - dSf_dVm).' * lam / pert;
0116     num_Gtaa(:, i) = (dSt_dVa_ap - dSt_dVa).' * lam / pert;
0117     num_Gtva(:, i) = (dSt_dVm_ap - dSt_dVm).' * lam / pert;
0118 
0119     Vmp = V;
0120     Vmp(i) = (Vm(i) + pert) * exp(1j * Va(i));
0121     [dSf_dVa_mp, dSf_dVm_mp, dSt_dVa_mp, dSt_dVm_mp, Sf_mp, St_mp] = ...
0122         dSbr_dV(branch, Yf, Yt, Vmp);
0123     num_Gfav(:, i) = (dSf_dVa_mp - dSf_dVa).' * lam / pert;
0124     num_Gfvv(:, i) = (dSf_dVm_mp - dSf_dVm).' * lam / pert;
0125     num_Gtav(:, i) = (dSt_dVa_mp - dSt_dVa).' * lam / pert;
0126     num_Gtvv(:, i) = (dSt_dVm_mp - dSt_dVm).' * lam / pert;
0127 end
0128 
0129 t_is(full(Gfaa), num_Gfaa, 4, ['Gfaa' t]);
0130 t_is(full(Gfav), num_Gfav, 4, ['Gfav' t]);
0131 t_is(full(Gfva), num_Gfva, 4, ['Gfva' t]);
0132 t_is(full(Gfvv), num_Gfvv, 4, ['Gfvv' t]);
0133 
0134 t_is(full(Gtaa), num_Gtaa, 4, ['Gtaa' t]);
0135 t_is(full(Gtav), num_Gtav, 4, ['Gtav' t]);
0136 t_is(full(Gtva), num_Gtva, 4, ['Gtva' t]);
0137 t_is(full(Gtvv), num_Gtvv, 4, ['Gtvv' t]);
0138 
0139 %%-----  check d2Ibr_dV2 code  -----
0140 t = ' - d2Ibr_dV2 (complex currents)';
0141 lam = 10 * rand(nl, 1);
0142 % lam = [1; zeros(nl-1, 1)];
0143 num_Gfaa = zeros(nb, nb);
0144 num_Gfav = zeros(nb, nb);
0145 num_Gfva = zeros(nb, nb);
0146 num_Gfvv = zeros(nb, nb);
0147 num_Gtaa = zeros(nb, nb);
0148 num_Gtav = zeros(nb, nb);
0149 num_Gtva = zeros(nb, nb);
0150 num_Gtvv = zeros(nb, nb);
0151 [dIf_dVa, dIf_dVm, dIt_dVa, dIt_dVm, If, It] = dIbr_dV(branch, Yf, Yt, V);
0152 [Gfaa, Gfav, Gfva, Gfvv] = d2Ibr_dV2(Yf, V, lam);
0153 [Gtaa, Gtav, Gtva, Gtvv] = d2Ibr_dV2(Yt, V, lam);
0154 for i = 1:nb
0155     Vap = V;
0156     Vap(i) = Vm(i) * exp(1j * (Va(i) + pert));
0157     [dIf_dVa_ap, dIf_dVm_ap, dIt_dVa_ap, dIt_dVm_ap, If_ap, It_ap] = ...
0158         dIbr_dV(branch, Yf, Yt, Vap);
0159     num_Gfaa(:, i) = (dIf_dVa_ap - dIf_dVa).' * lam / pert;
0160     num_Gfva(:, i) = (dIf_dVm_ap - dIf_dVm).' * lam / pert;
0161     num_Gtaa(:, i) = (dIt_dVa_ap - dIt_dVa).' * lam / pert;
0162     num_Gtva(:, i) = (dIt_dVm_ap - dIt_dVm).' * lam / pert;
0163 
0164     Vmp = V;
0165     Vmp(i) = (Vm(i) + pert) * exp(1j * Va(i));
0166     [dIf_dVa_mp, dIf_dVm_mp, dIt_dVa_mp, dIt_dVm_mp, If_mp, It_mp] = ...
0167         dIbr_dV(branch, Yf, Yt, Vmp);
0168     num_Gfav(:, i) = (dIf_dVa_mp - dIf_dVa).' * lam / pert;
0169     num_Gfvv(:, i) = (dIf_dVm_mp - dIf_dVm).' * lam / pert;
0170     num_Gtav(:, i) = (dIt_dVa_mp - dIt_dVa).' * lam / pert;
0171     num_Gtvv(:, i) = (dIt_dVm_mp - dIt_dVm).' * lam / pert;
0172 end
0173 
0174 t_is(full(Gfaa), num_Gfaa, 4, ['Gfaa' t]);
0175 t_is(full(Gfav), num_Gfav, 4, ['Gfav' t]);
0176 t_is(full(Gfva), num_Gfva, 4, ['Gfva' t]);
0177 t_is(full(Gfvv), num_Gfvv, 4, ['Gfvv' t]);
0178 
0179 t_is(full(Gtaa), num_Gtaa, 4, ['Gtaa' t]);
0180 t_is(full(Gtav), num_Gtav, 4, ['Gtav' t]);
0181 t_is(full(Gtva), num_Gtva, 4, ['Gtva' t]);
0182 t_is(full(Gtvv), num_Gtvv, 4, ['Gtvv' t]);
0183 
0184 %%-----  check d2ASbr_dV2 code  -----
0185 t = ' - d2ASbr_dV2 (squared apparent power flows)';
0186 lam = 10 * rand(nl, 1);
0187 % lam = [1; zeros(nl-1, 1)];
0188 num_Gfaa = zeros(nb, nb);
0189 num_Gfav = zeros(nb, nb);
0190 num_Gfva = zeros(nb, nb);
0191 num_Gfvv = zeros(nb, nb);
0192 num_Gtaa = zeros(nb, nb);
0193 num_Gtav = zeros(nb, nb);
0194 num_Gtva = zeros(nb, nb);
0195 num_Gtvv = zeros(nb, nb);
0196 [dSf_dVa, dSf_dVm, dSt_dVa, dSt_dVm, Sf, St] = dSbr_dV(branch, Yf, Yt, V);
0197 [dAf_dVa, dAf_dVm, dAt_dVa, dAt_dVm] = ...
0198                         dAbr_dV(dSf_dVa, dSf_dVm, dSt_dVa, dSt_dVm, Sf, St);
0199 [Gfaa, Gfav, Gfva, Gfvv] = d2ASbr_dV2(dSf_dVa, dSf_dVm, Sf, Cf, Yf, V, lam);
0200 [Gtaa, Gtav, Gtva, Gtvv] = d2ASbr_dV2(dSt_dVa, dSt_dVm, St, Ct, Yt, V, lam);
0201 for i = 1:nb
0202     Vap = V;
0203     Vap(i) = Vm(i) * exp(1j * (Va(i) + pert));
0204     [dSf_dVa_ap, dSf_dVm_ap, dSt_dVa_ap, dSt_dVm_ap, Sf_ap, St_ap] = ...
0205         dSbr_dV(branch, Yf, Yt, Vap);
0206     [dAf_dVa_ap, dAf_dVm_ap, dAt_dVa_ap, dAt_dVm_ap] = ...
0207         dAbr_dV(dSf_dVa_ap, dSf_dVm_ap, dSt_dVa_ap, dSt_dVm_ap, Sf_ap, St_ap);
0208     num_Gfaa(:, i) = (dAf_dVa_ap - dAf_dVa).' * lam / pert;
0209     num_Gfva(:, i) = (dAf_dVm_ap - dAf_dVm).' * lam / pert;
0210     num_Gtaa(:, i) = (dAt_dVa_ap - dAt_dVa).' * lam / pert;
0211     num_Gtva(:, i) = (dAt_dVm_ap - dAt_dVm).' * lam / pert;
0212 
0213     Vmp = V;
0214     Vmp(i) = (Vm(i) + pert) * exp(1j * Va(i));
0215     [dSf_dVa_mp, dSf_dVm_mp, dSt_dVa_mp, dSt_dVm_mp, Sf_mp, St_mp] = ...
0216         dSbr_dV(branch, Yf, Yt, Vmp);
0217     [dAf_dVa_mp, dAf_dVm_mp, dAt_dVa_mp, dAt_dVm_mp] = ...
0218         dAbr_dV(dSf_dVa_mp, dSf_dVm_mp, dSt_dVa_mp, dSt_dVm_mp, Sf_mp, St_mp);
0219     num_Gfav(:, i) = (dAf_dVa_mp - dAf_dVa).' * lam / pert;
0220     num_Gfvv(:, i) = (dAf_dVm_mp - dAf_dVm).' * lam / pert;
0221     num_Gtav(:, i) = (dAt_dVa_mp - dAt_dVa).' * lam / pert;
0222     num_Gtvv(:, i) = (dAt_dVm_mp - dAt_dVm).' * lam / pert;
0223 end
0224 
0225 t_is(full(Gfaa), num_Gfaa, 2, ['Gfaa' t]);
0226 t_is(full(Gfav), num_Gfav, 2, ['Gfav' t]);
0227 t_is(full(Gfva), num_Gfva, 2, ['Gfva' t]);
0228 t_is(full(Gfvv), num_Gfvv, 2, ['Gfvv' t]);
0229 
0230 t_is(full(Gtaa), num_Gtaa, 2, ['Gtaa' t]);
0231 t_is(full(Gtav), num_Gtav, 2, ['Gtav' t]);
0232 t_is(full(Gtva), num_Gtva, 2, ['Gtva' t]);
0233 t_is(full(Gtvv), num_Gtvv, 2, ['Gtvv' t]);
0234 
0235 %%-----  check d2ASbr_dV2 code  -----
0236 t = ' - d2ASbr_dV2 (squared real power flows)';
0237 lam = 10 * rand(nl, 1);
0238 % lam = [1; zeros(nl-1, 1)];
0239 num_Gfaa = zeros(nb, nb);
0240 num_Gfav = zeros(nb, nb);
0241 num_Gfva = zeros(nb, nb);
0242 num_Gfvv = zeros(nb, nb);
0243 num_Gtaa = zeros(nb, nb);
0244 num_Gtav = zeros(nb, nb);
0245 num_Gtva = zeros(nb, nb);
0246 num_Gtvv = zeros(nb, nb);
0247 [dSf_dVa, dSf_dVm, dSt_dVa, dSt_dVm, Sf, St] = dSbr_dV(branch, Yf, Yt, V);
0248 [dAf_dVa, dAf_dVm, dAt_dVa, dAt_dVm] = ...
0249                         dAbr_dV(real(dSf_dVa), real(dSf_dVm), real(dSt_dVa), real(dSt_dVm), real(Sf), real(St));
0250 [Gfaa, Gfav, Gfva, Gfvv] = d2ASbr_dV2(real(dSf_dVa), real(dSf_dVm), real(Sf), Cf, Yf, V, lam);
0251 [Gtaa, Gtav, Gtva, Gtvv] = d2ASbr_dV2(real(dSt_dVa), real(dSt_dVm), real(St), Ct, Yt, V, lam);
0252 for i = 1:nb
0253     Vap = V;
0254     Vap(i) = Vm(i) * exp(1j * (Va(i) + pert));
0255     [dSf_dVa_ap, dSf_dVm_ap, dSt_dVa_ap, dSt_dVm_ap, Sf_ap, St_ap] = ...
0256         dSbr_dV(branch, Yf, Yt, Vap);
0257     [dAf_dVa_ap, dAf_dVm_ap, dAt_dVa_ap, dAt_dVm_ap] = ...
0258         dAbr_dV(real(dSf_dVa_ap), real(dSf_dVm_ap), real(dSt_dVa_ap), real(dSt_dVm_ap), real(Sf_ap), real(St_ap));
0259     num_Gfaa(:, i) = (dAf_dVa_ap - dAf_dVa).' * lam / pert;
0260     num_Gfva(:, i) = (dAf_dVm_ap - dAf_dVm).' * lam / pert;
0261     num_Gtaa(:, i) = (dAt_dVa_ap - dAt_dVa).' * lam / pert;
0262     num_Gtva(:, i) = (dAt_dVm_ap - dAt_dVm).' * lam / pert;
0263 
0264     Vmp = V;
0265     Vmp(i) = (Vm(i) + pert) * exp(1j * Va(i));
0266     [dSf_dVa_mp, dSf_dVm_mp, dSt_dVa_mp, dSt_dVm_mp, Sf_mp, St_mp] = ...
0267         dSbr_dV(branch, Yf, Yt, Vmp);
0268     [dAf_dVa_mp, dAf_dVm_mp, dAt_dVa_mp, dAt_dVm_mp] = ...
0269         dAbr_dV(real(dSf_dVa_mp), real(dSf_dVm_mp), real(dSt_dVa_mp), real(dSt_dVm_mp), real(Sf_mp), real(St_mp));
0270     num_Gfav(:, i) = (dAf_dVa_mp - dAf_dVa).' * lam / pert;
0271     num_Gfvv(:, i) = (dAf_dVm_mp - dAf_dVm).' * lam / pert;
0272     num_Gtav(:, i) = (dAt_dVa_mp - dAt_dVa).' * lam / pert;
0273     num_Gtvv(:, i) = (dAt_dVm_mp - dAt_dVm).' * lam / pert;
0274 end
0275 
0276 t_is(full(Gfaa), num_Gfaa, 2, ['Gfaa' t]);
0277 t_is(full(Gfav), num_Gfav, 2, ['Gfav' t]);
0278 t_is(full(Gfva), num_Gfva, 2, ['Gfva' t]);
0279 t_is(full(Gfvv), num_Gfvv, 2, ['Gfvv' t]);
0280 
0281 t_is(full(Gtaa), num_Gtaa, 2, ['Gtaa' t]);
0282 t_is(full(Gtav), num_Gtav, 2, ['Gtav' t]);
0283 t_is(full(Gtva), num_Gtva, 2, ['Gtva' t]);
0284 t_is(full(Gtvv), num_Gtvv, 2, ['Gtvv' t]);
0285 
0286 %%-----  check d2AIbr_dV2 code  -----
0287 t = ' - d2AIbr_dV2 (squared current magnitudes)';
0288 lam = 10 * rand(nl, 1);
0289 % lam = [1; zeros(nl-1, 1)];
0290 num_Gfaa = zeros(nb, nb);
0291 num_Gfav = zeros(nb, nb);
0292 num_Gfva = zeros(nb, nb);
0293 num_Gfvv = zeros(nb, nb);
0294 num_Gtaa = zeros(nb, nb);
0295 num_Gtav = zeros(nb, nb);
0296 num_Gtva = zeros(nb, nb);
0297 num_Gtvv = zeros(nb, nb);
0298 [dIf_dVa, dIf_dVm, dIt_dVa, dIt_dVm, If, It] = dIbr_dV(branch, Yf, Yt, V);
0299 [dAf_dVa, dAf_dVm, dAt_dVa, dAt_dVm] = ...
0300                         dAbr_dV(dIf_dVa, dIf_dVm, dIt_dVa, dIt_dVm, If, It);
0301 [Gfaa, Gfav, Gfva, Gfvv] = d2AIbr_dV2(dIf_dVa, dIf_dVm, If, Yf, V, lam);
0302 [Gtaa, Gtav, Gtva, Gtvv] = d2AIbr_dV2(dIt_dVa, dIt_dVm, It, Yt, V, lam);
0303 for i = 1:nb
0304     Vap = V;
0305     Vap(i) = Vm(i) * exp(1j * (Va(i) + pert));
0306     [dIf_dVa_ap, dIf_dVm_ap, dIt_dVa_ap, dIt_dVm_ap, If_ap, It_ap] = ...
0307         dIbr_dV(branch, Yf, Yt, Vap);
0308     [dAf_dVa_ap, dAf_dVm_ap, dAt_dVa_ap, dAt_dVm_ap] = ...
0309         dAbr_dV(dIf_dVa_ap, dIf_dVm_ap, dIt_dVa_ap, dIt_dVm_ap, If_ap, It_ap);
0310     num_Gfaa(:, i) = (dAf_dVa_ap - dAf_dVa).' * lam / pert;
0311     num_Gfva(:, i) = (dAf_dVm_ap - dAf_dVm).' * lam / pert;
0312     num_Gtaa(:, i) = (dAt_dVa_ap - dAt_dVa).' * lam / pert;
0313     num_Gtva(:, i) = (dAt_dVm_ap - dAt_dVm).' * lam / pert;
0314 
0315     Vmp = V;
0316     Vmp(i) = (Vm(i) + pert) * exp(1j * Va(i));
0317     [dIf_dVa_mp, dIf_dVm_mp, dIt_dVa_mp, dIt_dVm_mp, If_mp, It_mp] = ...
0318         dIbr_dV(branch, Yf, Yt, Vmp);
0319     [dAf_dVa_mp, dAf_dVm_mp, dAt_dVa_mp, dAt_dVm_mp] = ...
0320         dAbr_dV(dIf_dVa_mp, dIf_dVm_mp, dIt_dVa_mp, dIt_dVm_mp, If_mp, It_mp);
0321     num_Gfav(:, i) = (dAf_dVa_mp - dAf_dVa).' * lam / pert;
0322     num_Gfvv(:, i) = (dAf_dVm_mp - dAf_dVm).' * lam / pert;
0323     num_Gtav(:, i) = (dAt_dVa_mp - dAt_dVa).' * lam / pert;
0324     num_Gtvv(:, i) = (dAt_dVm_mp - dAt_dVm).' * lam / pert;
0325 end
0326 
0327 t_is(full(Gfaa), num_Gfaa, 3, ['Gfaa' t]);
0328 t_is(full(Gfav), num_Gfav, 3, ['Gfav' t]);
0329 t_is(full(Gfva), num_Gfva, 3, ['Gfva' t]);
0330 t_is(full(Gfvv), num_Gfvv, 2, ['Gfvv' t]);
0331 
0332 t_is(full(Gtaa), num_Gtaa, 3, ['Gtaa' t]);
0333 t_is(full(Gtav), num_Gtav, 3, ['Gtav' t]);
0334 t_is(full(Gtva), num_Gtva, 3, ['Gtva' t]);
0335 t_is(full(Gtvv), num_Gtvv, 2, ['Gtvv' t]);
0336 
0337 t_end;
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