[37] | 1 | % * This code was used in the following articles:
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| 2 | % * [1] Learning 3-D Scene Structure from a Single Still Image,
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| 3 | % * Ashutosh Saxena, Min Sun, Andrew Y. Ng,
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| 4 | % * In ICCV workshop on 3D Representation for Recognition (3dRR-07), 2007.
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| 5 | % * (best paper)
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| 6 | % * [2] 3-D Reconstruction from Sparse Views using Monocular Vision,
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| 7 | % * Ashutosh Saxena, Min Sun, Andrew Y. Ng,
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| 8 | % * In ICCV workshop on Virtual Representations and Modeling
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| 9 | % * of Large-scale environments (VRML), 2007.
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| 10 | % * [3] 3-D Depth Reconstruction from a Single Still Image,
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| 11 | % * Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng.
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| 12 | % * International Journal of Computer Vision (IJCV), Aug 2007.
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| 13 | % * [6] Learning Depth from Single Monocular Images,
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| 14 | % * Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng.
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| 15 | % * In Neural Information Processing Systems (NIPS) 18, 2005.
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| 16 | % *
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| 17 | % * These articles are available at:
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| 18 | % * http://make3d.stanford.edu/publications
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| 19 | % *
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| 20 | % * We request that you cite the papers [1], [3] and [6] in any of
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| 21 | % * your reports that uses this code.
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| 22 | % * Further, if you use the code in image3dstiching/ (multiple image version),
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| 23 | % * then please cite [2].
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| 24 | % *
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| 25 | % * If you use the code in third_party/, then PLEASE CITE and follow the
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| 26 | % * LICENSE OF THE CORRESPONDING THIRD PARTY CODE.
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| 27 | % *
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| 28 | % * Finally, this code is for non-commercial use only. For further
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| 29 | % * information and to obtain a copy of the license, see
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| 30 | % *
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| 31 | % * http://make3d.stanford.edu/publications/code
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| 32 | % *
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| 33 | % * Also, the software distributed under the License is distributed on an
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| 34 | % * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
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| 35 | % * express or implied. See the License for the specific language governing
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| 36 | % * permissions and limitations under the License.
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| 37 | % *
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| 38 | % */
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| 39 | function [x,status,history] = L1Barrier_wo_Constrain(Para,method,ptol,pmaxi, VERBOSE) |
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| 40 | %function [x,status,history] = L1Barrier_wo_Constrain(A,b,t_0,method,ptol,pmaxi) |
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| 41 | % |
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| 42 | % Fast L1 - norm Solver |
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| 43 | % |
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| 44 | % L1 - norm Solver Solves problems of the following form: |
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| 45 | % |
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| 46 | % minimize | A*x - b|L1 |
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| 47 | % |
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| 48 | % where variable is x and problem data are A and b. |
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| 49 | % |
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| 50 | % INPUT |
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| 51 | % |
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| 52 | % A : mxn matrix; input data. each column corresponds to each feature |
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| 53 | % b : m vector; class label |
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| 54 | % |
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| 55 | % method : string; search direction method type |
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| 56 | % 'cg' : conjugate gradients method, 'pcg' |
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| 57 | % 'pcg' : preconditioned conjugate gradients method |
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| 58 | % 'exact': exact method (default value) |
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| 59 | % ptol : scalar; pcg relative tolerance. if empty, use adaptive rule. |
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| 60 | % pmaxi : scalar: pcg maximum iteration. if empty, use default value (500). |
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| 61 | % |
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| 62 | % OUTPUT |
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| 63 | % |
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| 64 | % x : n vector; |
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| 65 | % status : scalar; +1: success, -1: maxiter exceeded |
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| 66 | % history : |
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| 67 | % row 1) phi |
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| 68 | % row 2) norm(gradient of phi) |
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| 69 | % row 3) cumulative cg iterations |
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| 70 | % |
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| 71 | % USAGE EXAMPLE |
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| 72 | % |
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| 73 | % [x,status] = l2_logreg(A,b,lambda,'pcg'); |
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| 74 | % |
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| 75 | |
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| 76 | % Written by Kwangmoo Koh <deneb1@stanford.edu> |
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| 77 | % adopted by Min Sun |
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| 78 | |
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| 79 | %------------------------------------------------------------ |
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| 80 | % INITIALIZE |
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| 81 | %------------------------------------------------------------ |
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| 82 | global A D p b; |
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| 83 | |
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| 84 | % LOG BARRIER METHOD |
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| 85 | MAX_LOGB_ITER = 100; |
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| 86 | EPSILON_GAP = 2e-4; |
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| 87 | MU_t = 100; % for t -- log barrier. Changed ASH |
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| 88 | %if(isempty(t_0)) t_0 = 1; end |
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| 89 | t_0 = 1; |
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| 90 | t = t_0; |
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| 91 | |
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| 92 | |
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| 93 | % NEWTON PARAMETERS |
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| 94 | MAX_TNT_ITER = 100; % maximum (truncated) Newton iteration |
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| 95 | ABSTOL = 1e-8; % terminates when the norm of gradient < ABSTOL |
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| 96 | EPSILON = 1e-7; % terminate when lambdasqr_by_2 < EPSILON |
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| 97 | StopNorm = 0; % set to 0 using newton decrement |
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| 98 | |
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| 99 | % LINE SEARCH PARAMETERS |
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| 100 | ALPHA = 0.01; % minimum fraction of decrease in norm(gradient) |
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| 101 | BETA = 0.5; % stepsize decrease factor |
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| 102 | MAX_LS_ITER = 50; % maximum backtracking line search iteration |
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| 103 | Eps = -1e-50; % gap for inequality |
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| 104 | normg_Flag = 1; % if evaluate function set normg_Flag = 1 |
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| 105 | |
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| 106 | [m,n] = size(A); % problem size: m examples, n features |
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| 107 | A2 = A.^2; |
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| 108 | |
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| 109 | |
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| 110 | %if(isempty(pmaxi)) pcgmaxi = 500; else pcgmaxi = pmaxi; end |
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| 111 | %if(isempty(ptol )) pcgtol = 1e-4; else pcgtol = ptol; end |
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| 112 | pcgmaxi = 500; |
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| 113 | pcgtol = 1e-4; |
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| 114 | |
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| 115 | % INITIALIZE |
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| 116 | pobj = Inf; s = inf; pitr = 0 ; pflg = 0 ; prelres = 0; pcgiter = 0; |
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| 117 | history = []; |
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| 118 | status = -1; |
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| 119 | % feasible starting point |
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| 120 | |
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| 121 | |
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| 122 | x = zeros(n,1); dx = zeros(n,1); |
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| 123 | y = max( abs( A*x-b))-Eps- (-1e-2); dy = zeros(m,1); |
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| 124 | |
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| 125 | |
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| 126 | % check is x y feasible start |
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| 127 | % if max(A*(x) - (y)-b)< 0 && max(-A*(x) - (y)+b) < 0 |
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| 128 | % disp('Feasible start'); |
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| 129 | % end |
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| 130 | |
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| 131 | |
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| 132 | %------------------------------------------------------------ |
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| 133 | % LOG BARRIER OUTER LOOP |
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| 134 | %------------------------------------------------------------ |
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| 135 | %for lbiter = 1:MAX_LOGB_ITER |
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| 136 | %while true |
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| 137 | % return; |
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| 138 | %end |
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| 139 | for LogBIter = 1:MAX_LOGB_ITER |
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| 140 | if VERBOSE |
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| 141 | disp(sprintf('%s %15s %10s %10s %10s %s %s %6s %10s %6s',... |
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| 142 | 'iter','primal obj','stepsize','norg(g)','lambdasqr','LSiter', 'LSiter_fea''p_flg','p_res','p_itr')); |
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| 143 | end |
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| 144 | %------------------------------------------------------------ |
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| 145 | % MAIN LOOP |
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| 146 | %------------------------------------------------------------ |
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| 147 | |
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| 148 | status = -1; % initalized to -1; |
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| 149 | % nt_hist = []; |
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| 150 | Ax_b = A*x - b; |
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| 151 | Ax_b_y = Ax_b + y; |
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| 152 | Neg_Ax_b_y = -Ax_b + y; |
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| 153 | g_1 = (1./Neg_Ax_b_y - 1./Ax_b_y); |
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| 154 | g_2 = (t - 1./Ax_b_y - 1./Neg_Ax_b_y); |
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| 155 | gradphi_x = (g_1'*A)'; |
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| 156 | for ntiter = 0:MAX_TNT_ITER |
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| 157 | D_1 = (1./Neg_Ax_b_y).^2; |
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| 158 | D_2 = (1./Ax_b_y).^2; |
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| 159 | D = 2./(y.^2 + Ax_b.^2 ); |
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| 160 | g = g_1 +(D_1-D_2).*(1./(D_1+D_2)).*g_2; |
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| 161 | gradphi_x_eli = (g'*A)'; |
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| 162 | |
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| 163 | %------------------------------------------------------------ |
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| 164 | % CALCULATE NEWTON STEP |
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| 165 | %------------------------------------------------------------ |
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| 166 | % switch lower(method) |
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| 167 | % case 'pcg' |
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| 168 | % p = 1./(A2'*D); |
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| 169 | % if (isempty(ptol)) pcgtol = min(0.1,norm(gradphi_x_eli)); end |
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| 170 | % [dx, pflg, prelres, pitr, presvec] = ... |
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| 171 | % pcg(@AXfunc,-gradphi_x_eli,pcgtol,pcgmaxi,@Mfunc,[],[]); |
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| 172 | % % A,D,[],1./(A2'*D)); |
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| 173 | % if (pitr == 0) pitr = pcgmaxi; end |
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| 174 | % |
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| 175 | % case 'cg' |
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| 176 | % if (isempty(ptol)) pcgtol = min(0.1,norm(gradphi_x_eli)); end |
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| 177 | % [dx, pflg, prelres, pitr, presvec] = ... |
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| 178 | % pcg(@AXfunc,-gradphi_x_eli,pcgtol,pcgmaxi,[],[],[]); |
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| 179 | % % A,D,[],[]); |
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| 180 | % if (pitr == 0) pitr = pcgmaxi; end |
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| 181 | % |
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| 182 | % otherwise % exact method |
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| 183 | % hessphi_x = A'*sparse(1:m,1:m,D)*A; |
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| 184 | hessphi_x = (sparse(1:m,1:m, D)*A)' * A; |
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| 185 | dx = -hessphi_x\gradphi_x_eli; |
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| 186 | % end |
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| 187 | dy = (1./(D_1 + D_2)) .*(-g_2 + (D_1 - D_2).*(A*dx)); |
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| 188 | %pcgiter = pcgiter+pitr; |
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| 189 | |
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| 190 | % function value and normg for back tracking line search or stoping critera |
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| 191 | normg = norm([gradphi_x; g_2]); |
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| 192 | |
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| 193 | phi = sum(y) - sum( log( [Ax_b_y; Neg_Ax_b_y]))/t; |
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| 194 | lambda_sqr = -gradphi_x'*dx - g_2'*dy; |
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| 195 | %------------------------------------------------------------ |
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| 196 | % BACKTRACKING LINE SEARCH |
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| 197 | %------------------------------------------------------------ |
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| 198 | s = 1; |
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| 199 | % if false % debug |
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| 200 | Delta = A*(dx) - (dy); |
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| 201 | Delta_Negdy = -A*(dx) - (dy); |
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| 202 | LSiter = 0; |
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| 203 | while any( (s*Delta - Neg_Ax_b_y) >= Eps) || any(( s*Delta_Negdy - Ax_b_y) >= Eps) |
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| 204 | s = BETA*s; |
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| 205 | LSiter = LSiter + 1; |
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| 206 | end |
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| 207 | for lsiter = 1:MAX_LS_ITER |
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| 208 | new_x = x + s*dx; |
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| 209 | new_y = y + s*dy; |
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| 210 | Ax_b = A*new_x - b; |
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| 211 | Ax_b_y = Ax_b + new_y; |
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| 212 | Neg_Ax_b_y = -Ax_b + new_y; |
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| 213 | |
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| 214 | % if normg_Flag |
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| 215 | g_1 = (1./Neg_Ax_b_y - 1./Ax_b_y); |
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| 216 | g_2 = (t - 1./Ax_b_y - 1./Neg_Ax_b_y); |
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| 217 | gradphi_x = (g_1'*A)'; |
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| 218 | if (norm([gradphi_x; g_2])<=(1-ALPHA*s)*normg) break; end |
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| 219 | s = BETA*s; |
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| 220 | % else |
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| 221 | % % evaluate function value |
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| 222 | % new_phi = sum(y) - sum( log( [Anew_x_b_y; Neg_Anew_x_b_y]))/t; |
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| 223 | % if new_phi <= phi +ALPHA*s*[gradphi_x; g_2]'*[dx; dy] break; end |
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| 224 | % s = BETA*s; |
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| 225 | % end |
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| 226 | end |
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| 227 | % end |
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| 228 | x = new_x; |
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| 229 | % dx; |
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| 230 | % x'; |
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| 231 | y = new_y; |
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| 232 | % if VERBOSE |
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| 233 | % disp(sprintf('%4d %15.6e %10.2e %10.2e %10.2e %4d %3d %6d %10.2e %6d',... |
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| 234 | % ntiter,phi,s,normg, lambda_sqr/2, lsiter, LSiter, pflg,prelres,pitr)); |
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| 235 | % nt_hist = [nt_hist [phi; normg; pcgiter]]; |
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| 236 | % end |
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| 237 | %------------------------------------------------------------ |
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| 238 | % STOPPING CRITERION |
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| 239 | %------------------------------------------------------------ |
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| 240 | if (lsiter == MAX_LS_ITER) disp('MaxLSIter'); break; end |
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| 241 | if StopNorm |
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| 242 | if (normg < ABSTOL) |
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| 243 | status = 1; |
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| 244 | %disp('Absolute normg tolerance reached.'); |
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| 245 | % disp(sprintf('%d/%d',sum(abs((A2'*h)./(2*lambda))<0.5),n)); |
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| 246 | break; |
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| 247 | end |
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| 248 | else |
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| 249 | if (lambda_sqr/2 <= EPSILON) |
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| 250 | status = 1; |
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| 251 | %disp('Absolute Lambda tolerance reached.'); |
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| 252 | break; |
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| 253 | end |
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| 254 | end |
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| 255 | end |
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| 256 | if status == -1 disp('Error status -1'); end |
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| 257 | |
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| 258 | %-------------- decreasing the gap ------------- |
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| 259 | gap = m/t; |
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| 260 | disp(gap); |
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| 261 | %history=[history [length(nt_hist); gap]]; |
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| 262 | if gap< EPSILON_GAP break; end |
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| 263 | t = MU_t*t; |
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| 264 | |
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| 265 | end |
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| 266 | |
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| 267 | return; |
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| 268 | |
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| 269 | |
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| 270 | %------------------------------------------------------------ |
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| 271 | % CALL BACK FUNCTIONS FOR PCG |
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| 272 | %------------------------------------------------------------ |
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| 273 | function y = AXfunc(x) |
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| 274 | global A D; |
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| 275 | y = A'*(D.*(A*x)); |
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| 276 | |
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| 277 | function y = Mfunc(x) |
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| 278 | global p; |
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| 279 | y = x.*p; |
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