From 15e01261722e90dc109d569d6a19633ffec5a754 Mon Sep 17 00:00:00 2001 From: Rowan Cockett Date: Tue, 12 Nov 2013 11:09:51 -0800 Subject: [PATCH] Updates to Optimization Framework. Testing. Bug Fixes. --- SimPEG/forward/DCProblem.py | 2 +- SimPEG/forward/Problem.py | 4 +- SimPEG/inverse/Optimize.py | 31 +- SimPEG/tests/TestUtils.py | 22 + SimPEG/tests/__init__.py | 2 +- SimPEG/tests/test_optimizers.py | 54 ++ notebooks/Bound Constraint Problem.ipynb | 1048 +++++++--------------- 7 files changed, 422 insertions(+), 741 deletions(-) create mode 100644 SimPEG/tests/test_optimizers.py diff --git a/SimPEG/forward/DCProblem.py b/SimPEG/forward/DCProblem.py index 132966a8..9ddb5332 100644 --- a/SimPEG/forward/DCProblem.py +++ b/SimPEG/forward/DCProblem.py @@ -16,7 +16,7 @@ class DCProblem(ModelTransforms.LogModel, Problem): """ def __init__(self, mesh): - super(DCProblem, self).__init__(mesh) + Problem.__init__(self, mesh) self.mesh.setCellGradBC('neumann') def reshapeFields(self, u): diff --git a/SimPEG/forward/Problem.py b/SimPEG/forward/Problem.py index 2e6831f7..cf22baae 100644 --- a/SimPEG/forward/Problem.py +++ b/SimPEG/forward/Problem.py @@ -140,7 +140,7 @@ class Problem(object): This can often be computed given a vector (i.e. J(v)) rather than stored, as J is a large dense matrix. """ - pass + raise NotImplementedError('J is not yet implemented.') def Jt(self, m, v, u=None): """ @@ -152,7 +152,7 @@ class Problem(object): Effect of transpose of J on a vector v. """ - pass + raise NotImplementedError('Jt is not yet implemented.') def J_approx(self, m, v, u=None): diff --git a/SimPEG/inverse/Optimize.py b/SimPEG/inverse/Optimize.py index bd26ea79..37c8b296 100644 --- a/SimPEG/inverse/Optimize.py +++ b/SimPEG/inverse/Optimize.py @@ -35,12 +35,12 @@ class StoppingCriteria(object): "left": lambda M: 1 if M._iter==0 else norm(M.xc-M.x_last), "right": lambda M: 0 if M._iter==0 else M.tolX*(1+norm(M.x0)), "stopType": "optimal"} - tolerance_g = { "str": "%d : |g| = %1.4e <= tolG = %1.4e", - "left": lambda M: norm(M.projection(M.g)), "right": lambda M: M.tolG, + tolerance_g = { "str": "%d : |proj(x-g)-x| = %1.4e <= tolG = %1.4e", + "left": lambda M: norm(M.projection(M.xc - M.g) - M.xc), "right": lambda M: M.tolG, "stopType": "optimal"} - norm_g = { "str": "%d : |g| = %1.4e <= 1e3*eps = %1.4e", - "left": lambda M: norm(M.g), "right": lambda M: 1e3*M.eps, + norm_g = { "str": "%d : |proj(x-g)-x| = %1.4e <= 1e3*eps = %1.4e", + "left": lambda M: norm(M.projection(M.xc - M.g) - M.xc), "right": lambda M: 1e3*M.eps, "stopType": "critical"} bindingSet = { "str": "%d : probSize = %3d <= bindingSet = %3d", @@ -65,7 +65,7 @@ class IterationPrinters(object): iteration = {"title": "#", "value": lambda M: M._iter, "width": 5, "format": "%3d"} f = {"title": "f", "value": lambda M: M.f, "width": 10, "format": "%1.2e"} - norm_g = {"title": "|g|", "value": lambda M: norm(M.g), "width": 10, "format": "%1.2e"} + norm_g = {"title": "|proj(x-g)-x|", "value": lambda M: norm(M.projection(M.xc - M.g) - M.xc), "width": 15, "format": "%1.2e"} totalLS = {"title": "LS", "value": lambda M: M._iterLS, "width": 5, "format": "%d"} iterationLS = {"title": "#", "value": lambda M: (M._iter, M._iterLS), "width": 5, "format": "%3d.%d"} @@ -436,11 +436,12 @@ class Minimize(object): if self.debug: print 'doEndIteration is calling self.'+method getattr(self,method)(xt) - # store old values self.f_last = self.f self.x_last, self.xc = self.xc, xt self._iter += 1 + if self.debug: self.printDone() + class Remember(object): @@ -500,8 +501,8 @@ class ProjectedGradient(Minimize, Remember): maxIterCG = 10 tolCG = 1e-3 - lower = -0.4 - upper = 0.9 + lower = -np.inf + upper = np.inf def __init__(self,**kwargs): super(ProjectedGradient, self).__init__(**kwargs) @@ -568,7 +569,9 @@ class ProjectedGradient(Minimize, Remember): p = -self.g else: if self.debug: print 'findSearchDirection.CG: doingCG' - self.f_decrease_max = -np.inf # Reset the max decrease each time you do a CG iteration + # Reset the max decrease each time you do a CG iteration + self.f_decrease_max = -np.inf + self._itType = '.CG.' iSet = self.inactiveSet(self.xc) # The inactive set (free variables) @@ -598,15 +601,12 @@ class ProjectedGradient(Minimize, Remember): f_current_decrease = self.f_last - self.f self.projComment = '' -# print f_current_decrease if self._iter < 1: + # Note that this is reset on every CG iteration. self.f_decrease_max = -np.inf else: - # Note that I reset this if we do a CG iteration. self.f_decrease_max = max(self.f_decrease_max, f_current_decrease) self.stopDoingPG = f_current_decrease < 0.25 * self.f_decrease_max -# print 'f_decrease_max: ', self.f_decrease_max -# print 'stopDoingSD: ', self.stopDoingSD if self.stopDoingPG: self.projComment = 'Stop SD' self.explorePG = False @@ -615,7 +615,10 @@ class ProjectedGradient(Minimize, Remember): #self.eta_2 * max_decrease where max decrease # if true go to CG # don't do too many steps of PG in a row. - if self.debug: self.printDone() + + if self.debug: print 'doEndIteration.ProjGrad, f_current_decrease: ', f_current_decrease + if self.debug: print 'doEndIteration.ProjGrad, f_decrease_max: ', self.f_decrease_max + if self.debug: print 'doEndIteration.ProjGrad, stopDoingSD: ', self.stopDoingSD class GaussNewton(Minimize, Remember): name = 'Gauss Newton' diff --git a/SimPEG/tests/TestUtils.py b/SimPEG/tests/TestUtils.py index 48ec2ae8..1cc2bbae 100644 --- a/SimPEG/tests/TestUtils.py +++ b/SimPEG/tests/TestUtils.py @@ -275,6 +275,28 @@ def checkDerivative(fctn, x0, num=7, plotIt=True, dx=None): return passTest + +def getQuadratic(A, b): + """ + Given A and b, this returns a quadratic, Q + + .. math:: + + \mathbf{Q( x ) = 0.5 x A x + b x} + """ + def Quadratic(x, return_g=True, return_H=True): + f = 0.5 * x.dot( A.dot(x)) + b.dot( x ) + out = (f,) + if return_g: + g = A.dot(x) + b + out += (g,) + if return_H: + H = A + out += (H,) + return out if len(out) > 1 else out[0] + return Quadratic + + if __name__ == '__main__': def simplePass(x): diff --git a/SimPEG/tests/__init__.py b/SimPEG/tests/__init__.py index f896cfd0..d082562d 100644 --- a/SimPEG/tests/__init__.py +++ b/SimPEG/tests/__init__.py @@ -1,2 +1,2 @@ import TestUtils -from TestUtils import checkDerivative, Rosenbrock, OrderTest +from TestUtils import checkDerivative, Rosenbrock, OrderTest, getQuadratic diff --git a/SimPEG/tests/test_optimizers.py b/SimPEG/tests/test_optimizers.py new file mode 100644 index 00000000..6fff75d3 --- /dev/null +++ b/SimPEG/tests/test_optimizers.py @@ -0,0 +1,54 @@ +import unittest +from SimPEG import Solver +from SimPEG.mesh import TensorMesh +from SimPEG.utils import sdiag +import numpy as np +import scipy.sparse as sp +from SimPEG import inverse +from SimPEG.tests import getQuadratic, Rosenbrock + +TOL = 1e-2 + +class TestOptimizers(unittest.TestCase): + + def setUp(self): + self.A = sp.identity(2).tocsr() + self.b = np.array([-5,-5]) + + def test_GN_Rosenbrock(self): + GN = inverse.GaussNewton() + xopt = GN.minimize(Rosenbrock,np.array([0,0])) + x_true = np.array([1.,1.]) + print 'xopt: ', xopt + print 'x_true: ', x_true + self.assertTrue(np.linalg.norm(xopt-x_true,2) < TOL, True) + + def test_GN_quadratic(self): + GN = inverse.GaussNewton() + xopt = GN.minimize(getQuadratic(self.A,self.b),np.array([0,0])) + x_true = np.array([5.,5.]) + print 'xopt: ', xopt + print 'x_true: ', x_true + self.assertTrue(np.linalg.norm(xopt-x_true,2) < TOL, True) + + def test_ProjGradient_quadraticBounded(self): + PG = inverse.ProjectedGradient() + PG.lower, PG.upper = -2, 2 + xopt = PG.minimize(getQuadratic(self.A,self.b),np.array([0,0])) + x_true = np.array([2.,2.]) + print 'xopt: ', xopt + print 'x_true: ', x_true + self.assertTrue(np.linalg.norm(xopt-x_true,2) < TOL, True) + + def test_ProjGradient_quadratic1Bound(self): + myB = np.array([-5,1]) + PG = inverse.ProjectedGradient() + PG.lower, PG.upper = -2, 2 + xopt = PG.minimize(getQuadratic(self.A,myB),np.array([0,0])) + x_true = np.array([2.,-1.]) + print 'xopt: ', xopt + print 'x_true: ', x_true + self.assertTrue(np.linalg.norm(xopt-x_true,2) < TOL, True) + +if __name__ == '__main__': + unittest.main() diff --git a/notebooks/Bound Constraint Problem.ipynb b/notebooks/Bound Constraint Problem.ipynb index fa512d2b..efaa487c 100644 --- a/notebooks/Bound Constraint Problem.ipynb +++ b/notebooks/Bound Constraint Problem.ipynb @@ -34,14 +34,18 @@ "M = prob.mesh\n", "\n", "reg = Regularization(M)\n", - "opt = inverse.InexactGaussNewton(maxIter=100,debug=False,LSreduction=0.3,maxIterLS=50)\n", - "inv = inverse.Inversion(prob,reg,opt,beta0=1e-4,maxIter=2)\n", + "opt = inverse.InexactGaussNewton(maxIter=100,maxStep=0.2,debug=False,LSreduction=0.3,maxIterLS=50)\n", + "opt.remember('f', ('norm_g', lambda M:np.linalg.norm(M.g)))\n", + "inv = inverse.Inversion(prob,reg,opt,beta0=1e-4,maxIter=2,debug=False)\n", "m0 = np.zeros_like(m_true)\n", "\n", "mrec = inv.run(m0)\n", "\n", "plt.plot(M.vectorCCx, m_true, 'b-')\n", - "plt.plot(M.vectorCCx, mrec, 'r-')" + "plt.plot(M.vectorCCx, mrec, 'r-')\n", + "\n", + "figure()\n", + "plot(opt.recall('f'))\n" ], "language": "python", "metadata": {}, @@ -50,58 +54,13 @@ "output_type": "stream", "stream": "stdout", "text": [ - "=================== Inexact Gauss Newton ===================\n", - " # beta phi_d phi_m f |g| LS \n", - "------------------------------------------------------------\n", - " 0 1.00e-04 9.53e+02 0.00e+00 9.53e+02 8.99e+03 0 \n", - " 1 1.00e-04 6.23e-01 2.62e+04 3.24e+00 1.53e+01 0 \n", - " 2 1.00e-04 8.70e-02 2.29e+04 2.37e+00 1.15e+02 0 \n", - " 3 1.00e-04 4.58e-02 2.28e+04 2.32e+00 1.02e+00 0 \n", - " 4 1.00e-04 3.59e-02 2.27e+04 2.31e+00 1.49e+01 0 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 5 1.00e-04 2.80e-02 2.27e+04 2.30e+00 5.71e-01 0 \n", - " 6 1.00e-04 2.46e-02 2.27e+04 2.30e+00 1.50e+01 0 \n", - " 7 1.00e-04 2.17e-02 2.27e+04 2.29e+00 3.62e-01 0 \n", - " 8 1.00e-04 2.05e-02 2.27e+04 2.29e+00 2.61e-01 0 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 9 1.00e-04 1.91e-02 2.27e+04 2.29e+00 2.59e-01 0 \n", - " 10 1.00e-04 1.85e-02 2.27e+04 2.29e+00 1.98e-01 0 \n", - " 11 1.00e-04 1.76e-02 2.27e+04 2.29e+00 2.06e-01 0 \n", - " 12 1.00e-04 1.73e-02 2.27e+04 2.29e+00 1.64e-01 0 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 13 1.00e-04 1.66e-02 2.27e+04 2.29e+00 1.74e-01 0 \n", - " 14 1.00e-04 1.63e-02 2.27e+04 2.29e+00 2.93e-01 0 \n", - " 15 1.00e-04 1.58e-02 2.27e+04 2.29e+00 1.51e-01 0 \n", - " 16 1.00e-04 1.56e-02 2.27e+04 2.29e+00 1.22e-01 0 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 17 1.00e-04 1.51e-02 2.27e+04 2.29e+00 1.33e-01 0 \n", - " 18 1.00e-04 1.50e-02 2.27e+04 2.29e+00 1.07e-01 0 \n", - " 19 1.00e-04 1.46e-02 2.27e+04 2.29e+00 5.30e-01 0 \n", - " 20 1.00e-04 1.45e-02 2.27e+04 2.28e+00 9.43e-02 0 " + "====================== Inexact Gauss Newton ======================\n", + " # beta phi_d phi_m f |proj(x-g)-x| LS \n", + "-----------------------------------------------------------------\n", + " 0 1.00e-04 9.62e+02 0.00e+00 9.62e+02 1.02e+04 0 \n", + " 1 1.00e-04 6.63e+02 7.73e+02 6.63e+02 8.47e+03 0 \n", + " 2 1.00e-04 4.15e+02 4.39e+03 4.15e+02 6.63e+03 0 \n", + " 3 1.00e-04 2.26e+02 6.85e+03 2.27e+02 4.80e+03 0 " ] }, { @@ -109,59 +68,60 @@ "stream": "stdout", "text": [ "\n", + " 4 1.00e-04 9.74e+01 1.07e+04 9.84e+01 3.02e+03 0 \n", + " 5 1.00e-04 2.42e+01 1.64e+04 2.58e+01 1.35e+03 0 \n", + " 6 1.00e-04 1.06e+00 2.34e+04 3.39e+00 9.21e+00 0 \n", "------------------------- STOP! -------------------------\n", - "1 : |fc-fOld| = 2.2048e-04 <= tolF*(1+|f0|) = 9.5415e+01\n", - "1 : |xc-x_last| = 7.2682e-03 <= tolX*(1+|x0|) = 1.0000e-01\n", - "1 : |g| = 9.4320e-02 <= tolG = 1.0000e-01\n", - "0 : |g| = 9.4320e-02 <= 1e3*eps = 1.0000e-02\n", - "0 : maxIter = 100 <= iter = 20\n", + "1 : |fc-fOld| = 2.2421e+01 <= tolF*(1+|f0|) = 9.6325e+01\n", + "0 : |xc-x_last| = 2.1351e+00 <= tolX*(1+|x0|) = 1.0000e-01\n", + "0 : |proj(x-g)-x| = 9.2073e+00 <= tolG = 1.0000e-01\n", + "0 : |proj(x-g)-x| = 9.2073e+00 <= 1e3*eps = 1.0000e-02\n", + "0 : maxIter = 100 <= iter = 6\n", + "1 : phi_d = 1.0595e+00 <= phi_d_target = 2.0000e+01 \n", "------------------------- DONE! -------------------------\n", - "20" + "-------------------------STOP!-------------------------\n", + "0 : maxIter = 2 <= iter = 1\n", + "1 : phi_d = 1.0595e+00 <= phi_d_target = 2.0000e+01 \n", + "-------------------------DONE!-------------------------\n" ] }, { - "output_type": "stream", - "stream": "stdout", + "metadata": {}, + "output_type": "pyout", + "prompt_number": 3, "text": [ - "\n" + "[]" ] }, { "metadata": {}, "output_type": "display_data", - "png": 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+ "text": [ + "" ] } ], - "prompt_number": 17 + "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ - "def Quadratic(x, return_g=True, return_H=True):\n", - " A = sp.identity(2)\n", - " b = np.array([-5,-5])\n", - " f = 0.5 * x.dot( A.dot(x)) + b.dot( x )\n", - " out = (f,)\n", - " if return_g:\n", - " g = A.dot(x) + b\n", - " out += (g,)\n", - " if return_H:\n", - " H = A\n", - " out += (H,)\n", - " return out if len(out) > 1 else out[0]\n", - "\n", + "FUN = SimPEG.tests.getQuadratic(sp.identity(2),np.array([-5,-5]))\n", "# FUN = SimPEG.tests.Rosenbrock\n", - "FUN = Quadratic\n", "\n", "f = FUN(np.array([1,2]))\n", "print f\n", - "n = 50\n", - "l = -10\n", - "u = 10\n", + "n,l,u = 50,-10,10\n", "I = np.zeros((n,n))\n", "X = np.linspace(l,u,n)\n", "for i, x in enumerate(X):\n", @@ -184,7 +144,7 @@ "text": [ "(-12.5, array([-4., -3.]), <2x2 sparse matrix of type ''\n", "\twith 2 stored elements (1 diagonals) in DIAgonal format>)\n", - "======== Gauss Newton ========" + "=========== Gauss Newton ===========" ] }, { @@ -192,38 +152,30 @@ "stream": "stdout", "text": [ "\n", - " # f |g| LS \n", - "------------------------------\n", - " 0 0.00e+00 7.07e+00 0 \n", - " 1 -2.50e+01 0.00e+00 0 \n", + " # f |proj(x-g)-x| LS \n", + "-----------------------------------\n", + " 0 0.00e+00 7.07e+00 0 \n", + " 1 -2.50e+01 0.00e+00 0 \n", "------------------------- STOP! -------------------------\n", "0 : |fc-fOld| = 2.5000e+01 <= tolF*(1+|f0|) = 1.0000e-01\n", "0 : |xc-x_last| = 7.0711e+00 <= tolX*(1+|x0|) = 1.0000e-01\n", - "1 : |g| = 0.0000e+00 <= tolG = 1.0000e-01\n", - "1 : |g| = 0.0000e+00 <= 1e3*eps = 1.0000e-02\n", + "1 : |proj(x-g)-x| = 0.0000e+00 <= tolG = 1.0000e-01\n", + "1 : |proj(x-g)-x| = 0.0000e+00 <= 1e3*eps = 1.0000e-02\n", "0 : maxIter = 20 <= iter = 1\n", "------------------------- DONE! -------------------------\n", "[ 5. 5.]\n" ] }, - { - "output_type": "stream", - "stream": "stderr", - "text": [ - "/Users/rowan/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/sparse/linalg/dsolve/linsolve.py:87: SparseEfficiencyWarning: spsolve requires A be CSC or CSR matrix format\n", - " warn('spsolve requires A be CSC or CSR matrix format', SparseEfficiencyWarning)\n" - ] - }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ - "" + "" ] } ], - "prompt_number": 3 + "prompt_number": 5 }, { "cell_type": "code", @@ -231,10 +183,9 @@ "input": [ "opt = inverse.ProjectedGradient(maxIter=50,maxStep=np.inf, maxIterLS=20, debug=False)\n", "opt.remember('f')\n", - "opt.lower = np.array([-2,-1])\n", - "opt.upper = np.array([2,10])\n", - "opt.minimize(FUN,np.array([50,0]))\n", - "plot(opt.recall('f'))" + "opt.lower = -2\n", + "opt.upper = 2\n", + "opt.minimize(FUN,np.array([0,0]))" ], "language": "python", "metadata": {}, @@ -243,95 +194,31 @@ "output_type": "stream", "stream": "stdout", "text": [ - "===================== Projected Gradient =====================\n", - " # f |g| LS itType aSet bSet Comment\n", - "-------------------------------------------------------------\n", - " 0 -8.00e+00 5.83e+00 0 SD 1 1 \n", - " 1 -2.05e+01 3.00e+00 0 SD 1 1 \n", - " 2 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 3 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 4 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 5 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 6 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 7 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 8 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 9 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 10 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 11 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 12 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 13 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 14 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 15 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 16 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 17 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 18 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 19 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 20 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 21 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 22 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 23 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 24 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 25 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 26 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 27 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 28 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 29 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 30 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 31 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 32 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 33 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 34 -2.05e+01 3.00e+00 0 .CG. 1 1 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 35 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 36 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 37 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 38 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 39 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 40 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 41 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 42 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 43 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 44 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 45 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 46 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 47 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 48 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 49 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", - " 50 -2.05e+01 3.00e+00 0 .CG. 1 1 \n", + "======================= Projected Gradient =======================\n", + " # f |proj(x-g)-x| LS itType aSet bSet Comment\n", + "------------------------------------------------------------------\n", + " 0 0.00e+00 2.83e+00 0 SD 0 0 \n", + " 1 -1.60e+01 0.00e+00 0 SD 2 2 \n", "------------------------- STOP! -------------------------\n", - "1 : |fc-fOld| = 0.0000e+00 <= tolF*(1+|f0|) = 9.0000e-01\n", - "1 : |xc-x_last| = 0.0000e+00 <= tolX*(1+|x0|) = 3.0000e-01\n", - "0 : |g| = 2.0000e+00 <= tolG = 1.0000e-01\n", - "0 : |g| = 3.0000e+00 <= 1e3*eps = 1.0000e-02\n", - "1 : maxIter = 50 <= iter = 50\n", - "0 : probSize = 2 <= bindingSet = 1\n", + "0 : |fc-fOld| = 1.6000e+01 <= tolF*(1+|f0|) = 1.0000e-01\n", + "0 : |xc-x_last| = 2.8284e+00 <= tolX*(1+|x0|) = 1.0000e-01\n", + "1 : |proj(x-g)-x| = 0.0000e+00 <= tolG = 1.0000e-01\n", + "1 : |proj(x-g)-x| = 0.0000e+00 <= 1e3*eps = 1.0000e-02\n", + "0 : maxIter = 50 <= iter = 1\n", + "1 : probSize = 2 <= bindingSet = 2\n", "------------------------- DONE! -------------------------\n" ] }, { "metadata": {}, "output_type": "pyout", - "prompt_number": 4, + "prompt_number": 7, "text": [ - "[]" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" + "array([ 2., 2.])" ] } ], - "prompt_number": 4 + "prompt_number": 7 }, { "cell_type": "code", @@ -340,7 +227,8 @@ "opt = inverse.ProjectedGradient(maxIter=50, maxStep=0.3,debug=False, maxIterLS=20, tolCG=1e-5, maxIterCG=1000)\n", "opt.lower, opt.upper = -0.4, 0.9\n", "opt.remember('f', 'xc', ('norm_g', lambda M: np.linalg.norm(M.g)), 'phi_d', 'phi_m')\n", - "inv = inverse.Inversion(prob,reg,opt,beta0=1e-4)\n", + "inv = inverse.Inversion(prob,reg,opt,beta0=1e-3,debug=False)\n", + "inv.remember(('phi_d',lambda I:I.opt.recall('phi_d')),('phi_m',lambda I:I.opt.recall('phi_m')))\n", "m0 = np.zeros_like(m_true)\n", "mrecB = inv.run(m0)" ], @@ -351,12 +239,12 @@ "output_type": "stream", "stream": "stdout", "text": [ - "==================================== Projected Gradient ====================================\n", - " # beta phi_d phi_m f |g| LS itType aSet bSet Comment\n", - "-------------------------------------------------------------------------------------------\n", - " 0 1.00e-04 9.78e+02 0.00e+00 9.78e+02 7.08e+03 0 SD 0 0 \n", - " 1 1.00e-04 9.48e+02 3.40e-02 9.48e+02 2.32e+02 8 SD 0 0 \n", - " 2 1.00e-04 5.30e+02 1.47e+03 5.30e+02 1.73e+02 0 .CG. 0 0 " + "====================================== Projected Gradient ======================================\n", + " # beta phi_d phi_m f |proj(x-g)-x| LS itType aSet bSet Comment\n", + "------------------------------------------------------------------------------------------------\n", + " 0 1.00e-03 9.62e+02 0.00e+00 9.62e+02 2.14e+01 0 SD 0 0 \n", + " 1 1.00e-03 9.53e+02 8.49e-03 9.53e+02 2.18e+01 9 SD 0 0 \n", + " 2 1.00e-03 5.32e+02 1.42e+03 5.33e+02 2.20e+01 0 .CG. 0 0 " ] }, { @@ -364,7 +252,7 @@ "stream": "stdout", "text": [ "\n", - " 3 1.00e-04 2.32e+02 5.87e+03 2.33e+02 1.15e+02 0 .CG. 0 0 " + " 3 1.00e-03 2.32e+02 5.66e+03 2.38e+02 2.26e+01 0 .CG. 0 0 " ] }, { @@ -372,7 +260,7 @@ "stream": "stdout", "text": [ "\n", - " 4 1.00e-04 1.30e+02 9.16e+03 1.31e+02 1.19e+03 1 .CG. 21 21 " + " 4 1.00e-03 1.29e+02 8.85e+03 1.38e+02 2.30e+01 1 .CG. 0 0 " ] }, { @@ -380,8 +268,7 @@ "stream": "stdout", "text": [ "\n", - " 5 1.00e-04 1.29e+02 9.16e+03 1.30e+02 6.04e+02 10 SD 21 0 \n", - " 6 1.00e-04 6.84e+01 1.30e+04 6.97e+01 2.64e+03 1 .CG. 59 59 " + " 5 1.00e-03 1.10e+02 9.74e+03 1.20e+02 2.15e+01 3 .CG. 22 22 " ] }, { @@ -389,8 +276,8 @@ "stream": "stdout", "text": [ "\n", - " 7 1.00e-04 6.47e+01 1.30e+04 6.60e+01 9.40e+02 9 SD 59 0 \n", - " 8 1.00e-04 5.79e+01 1.39e+04 5.93e+01 1.83e+03 3 .CG. 89 85 " + " 6 1.00e-03 1.09e+02 9.74e+03 1.19e+02 2.36e+01 10 SD 22 0 Stop SD\n", + " 7 1.00e-03 7.65e+01 1.33e+04 8.98e+01 2.21e+01 1 .CG. 85 75 " ] }, { @@ -398,9 +285,10 @@ "stream": "stdout", "text": [ "\n", - " 9 1.00e-04 5.78e+01 1.39e+04 5.92e+01 1.75e+03 9 SD 85 7 \n", - " 10 1.00e-04 5.68e+01 1.39e+04 5.81e+01 1.17e+03 10 SD 11 8 Stop SD\n", - " 11 1.00e-04 5.67e+01 1.39e+04 5.81e+01 1.18e+03 12 .CG. 89 86 " + " 8 1.00e-03 5.11e+01 1.33e+04 6.44e+01 2.38e+01 9 SD 75 3 \n", + " 9 1.00e-03 5.07e+01 1.33e+04 6.41e+01 2.11e+01 12 SD 4 4 \n", + " 10 1.00e-03 5.06e+01 1.33e+04 6.40e+01 2.20e+01 12 SD 17 9 Stop SD\n", + " 11 1.00e-03 5.04e+01 1.34e+04 6.37e+01 2.05e+01 8 .CG. 85 81 " ] }, { @@ -408,8 +296,10 @@ "stream": "stdout", "text": [ "\n", - " 12 1.00e-04 5.61e+01 1.39e+04 5.75e+01 6.03e+02 10 SD 86 15 Stop SD\n", - " 13 1.00e-04 3.93e+01 2.72e+04 4.20e+01 6.11e+03 0 .CG. 216 157 " + " 12 1.00e-03 5.03e+01 1.34e+04 6.37e+01 1.65e+01 13 SD 81 26 \n", + " 13 1.00e-03 5.03e+01 1.34e+04 6.37e+01 1.67e+01 15 SD 30 30 \n", + " 14 1.00e-03 5.03e+01 1.34e+04 6.36e+01 1.42e+01 15 SD 84 84 Stop SD\n", + " 15 1.00e-03 2.65e+01 2.26e+04 4.91e+01 2.52e+01 0 .CG. 190 50 " ] }, { @@ -417,132 +307,24 @@ "stream": "stdout", "text": [ "\n", - " 14 1.00e-04 1.76e+01 2.72e+04 2.03e+01 9.85e+02 8 SD 157 6 \n", - " 15 1.00e-04 1.71e+01 2.72e+04 1.99e+01 4.69e+02 11 SD 8 8 \n", - " 16 1.00e-04 1.71e+01 2.72e+04 1.98e+01 4.28e+02 11 SD 62 22 Stop SD\n", - " 17 1.00e-04 1.71e+01 2.71e+04 1.98e+01 4.04e+02 7 .CG. 199 165 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 18 1.00e-04 1.70e+01 2.71e+04 1.97e+01 4.59e+01 12 SD 165 164 \n", - " 19 1.00e-04 1.70e+01 2.71e+04 1.97e+01 4.57e+01 15 SD 176 176 \n", - " 20 1.00e-04 1.70e+01 2.71e+04 1.97e+01 6.65e+01 14 SD 183 182 Stop SD\n", - " 21 1.00e-04 1.69e+01 2.72e+04 1.97e+01 2.83e+02 8 .CG. 213 86 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 22 1.00e-04 1.69e+01 2.72e+04 1.96e+01 7.42e+01 13 SD 86 73 \n", - " 23 1.00e-04 1.69e+01 2.72e+04 1.96e+01 4.78e+01 14 SD 187 187 \n", - " 24 1.00e-04 1.69e+01 2.72e+04 1.96e+01 4.35e+01 15 SD 210 209 Stop SD\n", - " 25 1.00e-04 9.31e+00 3.57e+04 1.29e+01 9.48e+02 1 .CG. 235 80 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 26 1.00e-04 8.92e+00 3.57e+04 1.25e+01 4.85e+02 11 SD 80 13 \n", - " 27 1.00e-04 8.88e+00 3.57e+04 1.24e+01 4.15e+02 11 SD 48 21 Stop SD\n", - " 28 1.00e-04 8.80e+00 3.56e+04 1.24e+01 9.73e+01 8 .CG. 209 180 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 29 1.00e-04 8.80e+00 3.56e+04 1.24e+01 2.17e+01 14 SD 180 180 \n", - " 30 1.00e-04 8.80e+00 3.56e+04 1.24e+01 2.53e+01 16 SD 202 202 Stop SD\n", - " 31 1.00e-04 8.78e+00 3.57e+04 1.23e+01 2.11e+02 7 .CG. 235 105 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 32 1.00e-04 8.76e+00 3.57e+04 1.23e+01 1.41e+02 13 SD 105 56 \n", - " 33 1.00e-04 8.75e+00 3.57e+04 1.23e+01 8.27e+01 13 SD 183 157 \n", - " 34 1.00e-04 8.75e+00 3.57e+04 1.23e+01 1.89e+01 15 SD 182 182 \n", - " 35 1.00e-04 8.75e+00 3.57e+04 1.23e+01 7.51e+01 13 SD 233 208 \n", - " 36 1.00e-04 8.75e+00 3.57e+04 1.23e+01 2.09e+01 15 SD 208 208 Stop SD\n", - " 37 1.00e-04 8.75e+00 3.57e+04 1.23e+01 2.74e+01 13 .CG. 234 227 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 38 1.00e-04 8.75e+00 3.57e+04 1.23e+01 3.25e+01 15 SD 227 227 Stop SD\n", - " 39 1.00e-04 8.65e+00 3.60e+04 1.23e+01 3.73e+02 5 .CG. 236 91 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 40 1.00e-04 8.63e+00 3.60e+04 1.22e+01 3.37e+02 12 SD 91 26 \n", - " 41 1.00e-04 8.57e+00 3.60e+04 1.22e+01 1.14e+02 12 SD 141 78 Stop SD\n", - " 42 1.00e-04 8.57e+00 3.60e+04 1.22e+01 1.13e+02 14 .CG. 224 132 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 43 1.00e-04 8.57e+00 3.60e+04 1.22e+01 6.28e+01 14 SD 138 116 Stop SD\n", - " 44 1.00e-04 8.57e+00 3.60e+04 1.22e+01 6.34e+01 17 .CG. 214 192 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 45 1.00e-04 8.56e+00 3.60e+04 1.22e+01 4.77e+01 14 SD 208 201 Stop SD\n", - " 46 1.00e-04 8.56e+00 3.60e+04 1.22e+01 4.84e+01 16 .CG. 230 223 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 47 1.00e-04 8.56e+00 3.60e+04 1.22e+01 3.88e+01 15 SD 225 211 Stop SD\n", - " 48 1.00e-04 6.48e+00 4.91e+04 1.14e+01 1.51e+03 0 .CG. 264 170 " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - " 49 1.00e-04 5.17e+00 4.91e+04 1.01e+01 2.64e+02 10 SD 170 14 \n", - " 50 1.00e-04 5.14e+00 4.91e+04 1.00e+01 1.04e+02 13 SD 16 16 \n", + " 16 1.00e-03 1.51e+01 2.26e+04 3.77e+01 2.24e+01 10 SD 50 1 \n", "------------------------- STOP! -------------------------\n", - "1 : |fc-fOld| = 3.5178e-02 <= tolF*(1+|f0|) = 9.7931e+01\n", - "1 : |xc-x_last| = 4.3861e-04 <= tolX*(1+|x0|) = 1.0000e-01\n", - "0 : |g| = 1.7094e+01 <= tolG = 1.0000e-01\n", - "0 : |g| = 1.0410e+02 <= 1e3*eps = 1.0000e-02\n", - "1 : maxIter = 50 <= iter = 50\n", - "0 : probSize = 1000 <= bindingSet = 16\n", - "------------------------- DONE! -------------------------\n" + "1 : |fc-fOld| = 1.1392e+01 <= tolF*(1+|f0|) = 9.6325e+01\n", + "1 : |xc-x_last| = 3.4809e-03 <= tolX*(1+|x0|) = 1.0000e-01\n", + "0 : |proj(x-g)-x| = 2.2369e+01 <= tolG = 1.0000e-01\n", + "0 : |proj(x-g)-x| = 2.2369e+01 <= 1e3*eps = 1.0000e-02\n", + "0 : maxIter = 50 <= iter = 16\n", + "0 : probSize = 1000 <= bindingSet = 1\n", + "1 : phi_d = 1.5077e+01 <= phi_d_target = 2.0000e+01 \n", + "------------------------- DONE! -------------------------\n", + "-------------------------STOP!-------------------------\n", + "0 : maxIter = 10 <= iter = 1\n", + "1 : phi_d = 1.5077e+01 <= phi_d_target = 2.0000e+01 \n", + "-------------------------DONE!-------------------------\n" ] } ], - "prompt_number": 7 + "prompt_number": 8 }, { "cell_type": "code", @@ -567,7 +349,7 @@ { "html": [ "" ], "metadata": {}, "output_type": "pyout", - "prompt_number": 14, + "prompt_number": 9, "text": [ - "" + "" ] } ], - "prompt_number": 14 + "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ - "plot(opt.recall('phi_m'))" + "plot(opt.recall('phi_d'))" ], "language": "python", "metadata": {}, @@ -987,29 +597,21 @@ { "metadata": {}, "output_type": 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