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https://github.com/wassname/simpeg.git
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BFGS implementation in the notebook.
This commit is contained in:
Rowan Cockett
@@ -76,7 +76,7 @@ class IterationPrinters(object):
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itType = {"title": "itType", "value": lambda M: M._itType, "width": 8, "format": "%s"}
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aSet = {"title": "aSet", "value": lambda M: np.sum(M.activeSet(M.xc)), "width": 8, "format": "%d"}
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bSet = {"title": "bSet", "value": lambda M: np.sum(M.bindingSet(M.xc)), "width": 8, "format": "%d"}
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comment = {"title": "Comment", "value": lambda M: M.projComment, "width": 7, "format": "%s"}
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comment = {"title": "Comment", "value": lambda M: M.comment, "width": 12, "format": "%s"}
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beta = {"title": "beta", "value": lambda M: M.parent._beta, "width": 10, "format": "%1.2e"}
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phi_d = {"title": "phi_d", "value": lambda M: M.parent.phi_d, "width": 10, "format": "%1.2e"}
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@@ -106,6 +106,8 @@ class Minimize(object):
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debug = False
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debugLS = False
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comment = ''
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def __init__(self, **kwargs):
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self._id = int(np.random.rand()*1e6) # create a unique identifier to this program to be used in pubsub
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self.stoppers = [StoppingCriteria.tolerance_f, StoppingCriteria.moving_x, StoppingCriteria.tolerance_g, StoppingCriteria.norm_g, StoppingCriteria.iteration]
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@@ -525,7 +527,7 @@ class ProjectedGradient(Minimize, Remember):
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self.stopDoingPG = False
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self._itType = 'SD'
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self.projComment = ''
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self.comment = ''
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self.aSet_prev = self.activeSet(x0)
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@@ -600,7 +602,7 @@ class ProjectedGradient(Minimize, Remember):
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self.exploreCG = np.all(aSet == bSet) # explore conjugate gradient
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f_current_decrease = self.f_last - self.f
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self.projComment = ''
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self.comment = ''
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if self._iter < 1:
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# Note that this is reset on every CG iteration.
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self.f_decrease_max = -np.inf
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@@ -608,7 +610,7 @@ class ProjectedGradient(Minimize, Remember):
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self.f_decrease_max = max(self.f_decrease_max, f_current_decrease)
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self.stopDoingPG = f_current_decrease < 0.25 * self.f_decrease_max
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if self.stopDoingPG:
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self.projComment = 'Stop SD'
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self.comment = 'Stop SD'
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self.explorePG = False
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self.exploreCG = True
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# implement 3.8, MoreToraldo91
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@@ -0,0 +1,197 @@
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{
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"metadata": {
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"name": ""
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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"worksheets": [
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{
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"cells": [
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"import SimPEG\n",
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"from SimPEG import Solver\n",
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"from SimPEG.mesh import TensorMesh\n",
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"from SimPEG.regularization import Regularization\n",
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"import SimPEG.inverse as inverse\n",
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"from SimPEG.inverse import Minimize, Remember, IterationPrinters\n",
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"import numpy as np\n",
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"import scipy.sparse as sp"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 1
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"FUN = SimPEG.tests.Rosenbrock\n",
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"FUN = SimPEG.tests.getQuadratic(sp.csr_matrix(([100,1],([0,1],[0,1])),shape=(2,2)),np.array([-5,-5]),100)\n",
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"\n",
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"\n",
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"class BFGS(Minimize, Remember):\n",
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" name = 'BFGS'\n",
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" nbfgs = 10\n",
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" \n",
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" @property\n",
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" def H0(self):\n",
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" \"\"\"\n",
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" Approximate Hessian used in preconditioning the problem.\n",
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" \n",
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" Must be a SimPEG.Solver\n",
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" \"\"\"\n",
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" _H0 = getattr(self,'_H0',None)\n",
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" if _H0 is None:\n",
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" return Solver(sp.identity(self.xc.size).tocsc())\n",
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" return _H0\n",
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" @H0.setter\n",
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" def H0(self, value):\n",
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" self._H0 = value\n",
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" \n",
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" def _startup_BFGS(self,x0):\n",
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" self._bfgscnt = -1\n",
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" self._bfgsY = np.zeros((x0.size, self.nbfgs))\n",
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" self._bfgsS = np.zeros((x0.size, self.nbfgs))\n",
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" if not np.any([p is IterationPrinters.comment for p in self.printers]):\n",
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" self.printers.append(IterationPrinters.comment)\n",
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" \n",
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" def bfgs(self,n,d):\n",
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" nn = min(self._bfgsS.shape[1],n)\n",
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" ktop = nn\n",
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" d = self.bfgsrec(ktop,n,nn,self._bfgsS,self._bfgsY,d)\n",
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" return d\n",
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"\n",
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" def bfgsrec(self,k,n,nn,S,Y,d):\n",
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" \"\"\"BFGS recursion\"\"\"\n",
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" if k < 0:\n",
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" d = self.H0.solve(d)\n",
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" else:\n",
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" khat = mod(n-nn+k,nn)\n",
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" gamma = np.vdot(S[:,khat],d)/np.vdot(Y[:,khat],S[:,khat])\n",
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" d = d - gamma*Y[:,khat]\n",
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" d = self.bfgsrec(k-1,n,nn,S,Y,d)\n",
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" d = d + (gamma - np.vdot(Y[:,khat],d)/np.vdot(Y[:,khat],S[:,khat]))*S[:,khat]\n",
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" \n",
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" return d\n",
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" \n",
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" def findSearchDirection(self):\n",
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" return self.bfgs(self._bfgscnt,-self.g)\n",
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" \n",
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" def _doEndIteration_BFGS(self, xt):\n",
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" if self._iter is 0: \n",
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" self.g_last = self.g\n",
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" return\n",
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" \n",
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" yy = self.g - self.g_last;\n",
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" ss = self.xc - xt;\n",
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" self.g_last = self.g\n",
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" \n",
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" if yy.dot(ss) > 0:\n",
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" self._bfgscnt += 1\n",
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" ktop = np.mod(self._bfgscnt,self.nbfgs)\n",
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" self._bfgsY[:,ktop] = yy\n",
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" self._bfgsS[:,ktop] = ss\n",
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" self.comment = ''\n",
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" else:\n",
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" self.comment = 'Skip BFGS'\n",
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" \n",
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"\n",
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"\n",
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"x0 = np.array([1,0])\n",
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"opt = BFGS()\n",
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"xopt = opt.minimize(FUN,x0)\n",
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"print xopt\n",
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"opt = inverse.GaussNewton()\n",
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"xopt = opt.minimize(FUN,x0)\n",
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"print xopt\n",
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"opt = inverse.SteepestDescent()\n",
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"xopt = opt.minimize(FUN,x0)\n",
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"print xopt"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"===================== BFGS =====================\n",
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" # f |proj(x-g)-x| LS Comment \n",
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"-----------------------------------------------\n",
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" 0 1.45e+02 9.51e+01 0 \n",
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" 1 1.14e+02 5.37e+01 6 \n",
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" 2 1.04e+02 3.04e+01 6 \n",
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" 3 8.83e+01 1.37e+01 0 \n",
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" 4 8.76e+01 5.97e+00 0 Skip BFGS \n",
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" 5 8.74e+01 2.61e+00 0 Skip BFGS \n",
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" 6 8.74e+01 1.14e+00 0 Skip BFGS \n",
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" 7 8.74e+01 5.01e-01 0 Skip BFGS \n",
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" 8 8.74e+01 2.19e-01 0 Skip BFGS \n",
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" 9 8.74e+01 9.60e-02 0 Skip BFGS \n",
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"------------------------- STOP! -------------------------\n",
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"1 : |fc-fOld| = 1.9437e-04 <= tolF*(1+|f0|) = 1.4600e+01\n",
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"1 : |xc-x_last| = 1.2663e-03 <= tolX*(1+|x0|) = 2.0000e-01\n",
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"1 : |proj(x-g)-x| = 9.5952e-02 <= tolG = 1.0000e-01\n",
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"0 : |proj(x-g)-x| = 9.5952e-02 <= 1e3*eps = 1.0000e-02\n",
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"0 : maxIter = 20 <= iter = 9\n",
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"------------------------- DONE! -------------------------\n",
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"[ 0.05095952 4.99977449]\n",
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"=========== Gauss Newton ===========\n",
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" # f |proj(x-g)-x| LS \n",
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"-----------------------------------\n",
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" 0 1.45e+02 9.51e+01 0 \n",
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" 1 8.74e+01 4.44e-15 0 \n",
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"------------------------- STOP! -------------------------\n",
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"0 : |fc-fOld| = 5.7625e+01 <= tolF*(1+|f0|) = 1.4600e+01\n",
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"0 : |xc-x_last| = 5.0894e+00 <= tolX*(1+|x0|) = 2.0000e-01\n",
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"1 : |proj(x-g)-x| = 4.4409e-15 <= tolG = 1.0000e-01\n",
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"1 : |proj(x-g)-x| = 4.4409e-15 <= 1e3*eps = 1.0000e-02\n",
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"0 : maxIter = 20 <= iter = 1\n",
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"------------------------- DONE! -------------------------\n",
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"[ 0.05 5. ]\n",
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"========= Steepest Descent =========\n",
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" # f |proj(x-g)-x| LS \n",
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"-----------------------------------\n",
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" 0 1.45e+02 9.51e+01 0 \n",
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" 1 1.14e+02 5.37e+01 6 \n",
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" 2 1.04e+02 3.04e+01 6 \n",
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" 3 1.00e+02 1.76e+01 6 \n",
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" 4 9.88e+01 1.06e+01 6 \n",
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" 5 9.82e+01 7.07e+00 6 \n",
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" 6 9.80e+01 1.22e+01 5 \n",
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" 7 9.73e+01 7.77e+00 6 \n",
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" 8 9.68e+01 5.64e+00 6 \n",
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" 9 9.65e+01 8.72e+00 5 \n",
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" 10 9.60e+01 5.97e+00 6 \n",
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" 11 9.58e+01 9.98e+00 5 \n",
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" 12 9.53e+01 6.48e+00 6 \n",
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" 13 9.53e+01 1.16e+01 5 \n",
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" 14 9.46e+01 7.20e+00 6 \n",
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" 15 9.43e+01 5.07e+00 6 \n",
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" 16 9.41e+01 8.17e+00 5 \n",
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" 17 9.37e+01 5.43e+00 6 \n",
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" 18 9.36e+01 9.42e+00 5 \n",
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" 19 9.32e+01 5.98e+00 6 \n",
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" 20 9.29e+01 4.32e+00 6 \n",
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"------------------------- STOP! -------------------------\n",
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"1 : |fc-fOld| = 2.5913e-01 <= tolF*(1+|f0|) = 1.4600e+01\n",
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"1 : |xc-x_last| = 9.3379e-02 <= tolX*(1+|x0|) = 2.0000e-01\n",
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"0 : |proj(x-g)-x| = 4.3246e+00 <= tolG = 1.0000e-01\n",
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"0 : |proj(x-g)-x| = 4.3246e+00 <= 1e3*eps = 1.0000e-02\n",
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"1 : maxIter = 20 <= iter = 20\n",
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"------------------------- DONE! -------------------------\n",
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"[ 0.07777107 1.6849632 ]\n"
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]
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}
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],
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"prompt_number": 14
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}
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],
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"metadata": {}
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}
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]
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}
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