'''
Created on Sep 4, 2017
@author: franzefn
'''
from argparse import ArgumentParser
import matplotlib.pylab as plt
import numpy as np
import cvxopt
import quadprog
from cvxopt.base import matrix
from pysgpp import (GridType_Bspline, GridType_BsplineBoundary,
GridType_BsplineClenshawCurtis, GridType_Linear,
GridType_LinearBoundary, GridType_LinearClenshawCurtis,
GridType_LinearClenshawCurtisBoundary,
GridType_LinearL0Boundary, GridType_ModBspline,
GridType_ModBsplineClenshawCurtis,
GridType_ModLinearClenshawCurtis,
GridType_ModPolyClenshawCurtis, GridType_Poly,
GridType_PolyBoundary, GridType_PolyClenshawCurtis,
GridType_PolyClenshawCurtisBoundary)
from pysgpp.extensions.datadriven.uq.dists import J, Normal
from pysgpp.extensions.datadriven.uq.dists.SGDEdist import SGDEdist
from pysgpp.extensions.datadriven.uq.operations.sparse_grid import (createGrid,
dehierarchize)
from pysgpp.extensions.datadriven.uq.plot.colors import insert_legend
from pysgpp.extensions.datadriven.uq.plot.plot1d import plotDensity1d, plotSG1d
from pysgpp.extensions.datadriven.uq.plot.plot2d import plotDensity2d, plotSG2d
from pysgpp.pysgpp_swig import (DataMatrix, DataVector, DensitySystemMatrix,
Grid,
MakePositiveCandidateSearchAlgorithm_Intersections,
MakePositiveInterpolationAlgorithm_InterpolateBoundaries1d,
RegularGridConfiguration,
createOperationLaplace,
createOperationLaplaceExplicit,
createOperationLTwoDotProduct,
createOperationMakePositive,
createOperationMultipleEval,
createOperationMultipleEvalNaive)
multipleEvalNaiveGridTypes = [GridType_Bspline,
GridType_BsplineClenshawCurtis,
GridType_BsplineBoundary,
GridType_ModBsplineClenshawCurtis,
GridType_ModBspline,
GridType_LinearClenshawCurtis,
GridType_LinearClenshawCurtisBoundary,
GridType_ModLinearClenshawCurtis,
GridType_PolyClenshawCurtis,
GridType_PolyClenshawCurtisBoundary,
GridType_ModPolyClenshawCurtis]
def getSamples():
return [[2.82323528526134293060e-01, 4.44821979348490936790e-01], \
[6.59563641710053216727e-01, 5.18168023604723249065e-01], \
[4.66204974971183350174e-01, 4.95399047706179262995e-01], \
[6.03526748539960355977e-01, 2.43268593292003454387e-01], \
[5.62533284596697602531e-01, 4.13446014803317773989e-01], \
[4.63253051381150471322e-01, 5.27242448822871967451e-01], \
[4.63228561454141485321e-01, 4.79068206886379688303e-01], \
[6.15016438560158529292e-01, 7.65841887254424591447e-01], \
[3.27390132759550089858e-01, 6.03578470511489939554e-01], \
[5.35401593038080436671e-01, 5.09572598797057851883e-01], \
[5.79763581036643715905e-01, 4.88509624749233817287e-01], \
[4.65176953338734489041e-01, 4.03396701047219141678e-01], \
[5.52854915372480326674e-01, 4.43624000760940717658e-01], \
[5.60710066030899234590e-01, 5.66610999883632948659e-01], \
[4.74441318074539153393e-01, 4.48279077549398552449e-01], \
[5.79704674489956550687e-01, 4.00429209403681540813e-01], \
[3.27418832211618604511e-01, 2.64694071058703350730e-01], \
[4.68272041096344959765e-01, 5.00686521541746643038e-01], \
[4.49396918966004310647e-01, 4.00441220113194606967e-01], \
[6.03754938081578762521e-01, 4.55931072222370947777e-01], \
[5.54996201469469818690e-01, 5.93871279984109601280e-01], \
[3.99711447601519165307e-01, 5.87033198350718321556e-01], \
[3.55432928275846271582e-01, 4.71746827190755335657e-01], \
[4.03990862343044987437e-01, 4.97874665282332817817e-01], \
[6.22513676177041563875e-01, 5.55383787785616034327e-01], \
[6.06734863458273654402e-01, 4.48026905189891244685e-01], \
[3.44689894316432154930e-01, 5.51499335564391124365e-01], \
[6.76901723651494480194e-01, 6.09192043743277511503e-01], \
[5.29252594074292481707e-01, 4.53921891869377369666e-01], \
[6.21287272061460837946e-01, 4.67386131667262283429e-01], \
[4.73474737535302225844e-01, 3.31366215716122680668e-01], \
[4.22058515319797489251e-01, 5.85655288984127553320e-01], \
[6.09157879244109023986e-01, 5.01029785281102313377e-01], \
[4.08589882279565885792e-01, 5.76247323139115308344e-01], \
[5.27615405966234463087e-01, 4.88837230398926847474e-01], \
[5.05141336533592610891e-01, 5.29409262848938855228e-01], \
[5.83778799053734198665e-01, 5.69872955233921119067e-01], \
[3.80508858545986206057e-01, 5.33938511026411433136e-01], \
[4.26989163363941104379e-01, 4.99783224537833747902e-01], \
[2.77657079118135974305e-01, 4.48032704403153514416e-01], \
[5.64447645543315279504e-01, 6.13323413563593433651e-01], \
[5.41492740515424397785e-01, 6.40342091101794630426e-01], \
[4.82003121732528960752e-01, 5.99363609581597511777e-01], \
[6.54269883937702245724e-01, 6.36467895969205832429e-01], \
[4.13590985767662233652e-01, 3.94731815928818730033e-01], \
[5.31066662541306078182e-01, 5.59649085735584139734e-01], \
[4.89172644290206848350e-01, 3.17628608093783459942e-01], \
[6.00813427026992252777e-01, 6.91555157222830896302e-01], \
[5.20366674074399515604e-01, 5.25855130987863517156e-01], \
[5.15689487911333621639e-01, 4.18563819379177304292e-01], \
[5.93054938632196937398e-01, 3.58492937309348502772e-01], \
[6.05703007289590589224e-01, 3.83423415212446272449e-01], \
[4.22073773434940346938e-01, 6.92815098137713025750e-01], \
[4.93668205111681746011e-01, 4.52106280723475362215e-01], \
[5.57959981775731583831e-01, 4.53986342751327820455e-01], \
[6.38690202622400393651e-01, 4.87626280731206285246e-01], \
[5.63926911955586529501e-01, 5.50628075675901773600e-01], \
[4.28419599266742279209e-01, 2.32220711641033195072e-01], \
[6.37011600755025386711e-01, 6.24416097625345223321e-01], \
[6.40698172583570979555e-01, 5.28949168799838220778e-01], \
[4.01058572553777969993e-01, 4.37153522488303469817e-01], \
[3.73896274277693285715e-01, 6.90767775324495514333e-01], \
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[5.18329759739195705670e-01, 3.02503597582994332438e-01], \
[6.95709753576134848352e-01, 3.92430421318656519336e-01], \
[6.38230477821175590236e-01, 5.80589438908979960097e-01], \
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[6.91745911035581806381e-01, 4.98786989511684097920e-01], \
[5.14125769230070583937e-01, 4.82871890303890938245e-01], \
[5.78016208854188029420e-01, 5.60769660778909218024e-01], \
[6.10301708480958993164e-01, 5.45145744677789423349e-01], \
[5.82137698464616826222e-01, 5.58503940193971093464e-01], \
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[4.71527404574930919523e-01, 7.31342887685912046436e-01], \
[6.22772896559283695161e-01, 6.15645963635931270375e-01], \
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[4.89598011977145419760e-01, 3.78784451965257062955e-01], \
[3.73197100303855000547e-01, 6.19562739874333301415e-01], \
[4.00550098625487349668e-01, 5.87784979624894399208e-01], \
[3.49267829106193694599e-01, 4.98573225989105639488e-01], \
[5.62488007322521577080e-01, 5.51361362935091969817e-01], \
[4.01358784366038279234e-01, 6.17134088036450090264e-01], \
[4.13022710165810214011e-01, 3.30168982468085014936e-01], \
[4.64686246389388879496e-01, 4.67906452780505632827e-01], \
[5.51991766853311194296e-01, 4.37705763014801241262e-01], \
[3.88102610313420248733e-01, 3.83832234823609286245e-01], \
[3.98737528640876526254e-01, 5.37444369976832647673e-01], \
[5.95328375175443347267e-01, 5.73431423038284870941e-01], \
[3.88257497550217323123e-01, 5.14059858486109133580e-01], \
[5.04863140527336495822e-01, 4.51446458435778519291e-01], \
[6.50265146807304184051e-01, 4.97782757622688531995e-01], \
[4.59280355521878014269e-01, 3.57802042670019915249e-01], \
[3.54394444075298409302e-01, 5.46100202971736670143e-01], \
[7.37412852658540396433e-01, 4.92660349856638535293e-01], \
[4.76657325437819634484e-01, 3.61396895660130113015e-01], \
[6.41492925325354845789e-01, 4.16953750816718815564e-01], \
[4.80866463579334491030e-01, 4.68369788378654172689e-01], \
[6.11865961032596272773e-01, 5.09582969454834944223e-01], \
[4.44827028399928714464e-01, 6.17326138336828589281e-01], \
[3.80508802213145536086e-01, 4.28587677359055563286e-01], \
[5.60075969674214801941e-01, 5.42736346706122918526e-01], \
[5.99355966896555125700e-01, 4.96673975483510166118e-01], \
[4.03259510059256920389e-01, 4.77701048005833683874e-01], \
[6.86264916278657488569e-01, 3.92872315673204075548e-01], \
[5.59938065113621763480e-01, 3.44857178221207760771e-01], \
[4.62755221970736430048e-01, 5.49344080836453474426e-01], \
[5.15243864211035407230e-01, 4.94415406474638607914e-01], \
[5.70059649609089613698e-01, 4.53297955862518253678e-01], \
[4.26286288659527723421e-01, 5.18763418144311816427e-01], \
[4.96943189810205743218e-01, 5.67516579489903860711e-01], \
[3.84680437156342813765e-01, 4.89137684250132764863e-01], \
[4.68588192437881356778e-01, 4.62113207143274307143e-01], \
[6.12957578334281660837e-01, 4.49838986476400526371e-01], \
[5.97615180788182653870e-01, 4.92699340479273995008e-01], \
[4.47282354674083393320e-01, 5.77007470669912869710e-01], \
[5.86833157036939501161e-01, 4.92517923056862427789e-01], \
[3.10556918879802801303e-01, 4.95004141718429213626e-01]]
def loadMatrixFromOperation(numGridPoints, op):
alpha = DataVector(numGridPoints)
alpha.setAll(0.0)
result = DataVector(numGridPoints)
ans = np.ndarray((numGridPoints, numGridPoints))
for i in range(numGridPoints):
alpha[i] = 1.0
op.mult(alpha, result)
ans[:, i] = result.array()
alpha[i] = 0.0
return ans
def computeMassMatrix(grid):
return A, loadMatrixFromOperation(grid.getSize(), A)
def computeInterpolationMatrix(grid):
gridStorage = grid.getStorage()
numDims = gridStorage.getDimension()
grid_points = np.ndarray((gridStorage.getSize(),
numDims))
x = DataVector(numDims)
for i in range(gridStorage.getSize()):
gridStorage.getCoordinates(gridStorage.getPoint(i), x)
grid_points[i, :] = x.array()
grid_points_vec = DataMatrix(grid_points)
if grid.getType() in multipleEvalNaiveGridTypes:
else:
return loadMatrixFromOperation(grid.getSize(), B_op)
def computeRegularizationMatrix(grid):
m = DataMatrix(grid.getStorage().getSize(), grid.getStorage().getSize())
C_matrix = loadMatrixFromOperation(grid.getSize(), C)
m.sub(DataMatrix(C_matrix))
print(m)
return C, C_matrix
def cvxopt_solve_qp(P, q, G=None, h=None, A=None, b=None):
P = .5 * (P + P.T)
args = [matrix(P), matrix(q)]
if G is not None:
args.extend([matrix(G), matrix(h)])
if A is not None:
args.extend([matrix(A), matrix(b)])
sol = cvxopt.solvers.qp(*args)
if 'optimal' not in sol['status']:
return None
print(sol)
print("P", P)
print("G", G)
print("G", matrix(G))
alpha = np.array(sol['x']).reshape((P.shape[1],))
print(np.dot(G, alpha))
print("q", q)
return np.array(sol['x']).reshape((P.shape[1],))
def quadprog_solve_qp(P, q, G=None, h=None, A=None, b=None):
qp_G = .5 * (P + P.T)
qp_a = -q
if A is not None:
qp_C = -np.vstack([A, G]).T
qp_b = -np.hstack([b, h])
meq = A.shape[0]
else:
qp_C = -G.T
qp_b = -h
meq = 0
print("qp_G", qp_G)
print("qp_a", qp_a)
print("qp_C", qp_C)
print("qp_b", qp_b)
x, f, _, iterations, _, _ = quadprog.solve_qp(qp_G, qp_a, qp_C, qp_b, meq)
print(iterations, f)
return x
def solve(trainSamples, gridType, level, lmbd, solver="cvxopt"):
numDims = trainSamples.shape[1]
gridConfig = RegularGridConfiguration()
gridConfig.dim_ = numDims
gridConfig.level_ = level
gridConfig.maxDegree_ = 7
gridConfig.type_ = Grid.stringToGridType(gridType)
grid = Grid.createGrid(gridConfig)
gridStorage = grid.getStorage()
grid.getGenerator().regular(level)
print(("gridStorage:", gridStorage.getSize()))
print(("numDims:", numDims))
print(("trainSamples.shape[0]:", trainSamples.shape[0]))
A_op, A = computeMassMatrix(grid)
C_op, C = computeRegularizationMatrix(grid)
trainSamples_matrix = DataMatrix(trainSamples)
if grid.getType() in multipleEvalNaiveGridTypes:
else:
sle = DensitySystemMatrix(A_op, B_op, C_op, lmbd, trainSamples.shape[0])
b = DataVector(gridStorage.getSize())
sle.generateb(b)
b = b.array()
M = A + lmbd * C
P = np.dot(M.T, M)
ew, v = np.linalg.eig(C)
print("Eigenvalues:", ew)
if (any(ew <= 0.0)):
print("Negative Eigenvalue found !!!")
q = np.dot(b, M).reshape((b.shape[0],))
G = computeInterpolationMatrix(grid)
print(G)
h = np.zeros((grid.getSize(),)).T
alpha = [18.903209 , -9.10141713, -9.01883182, 0.10914204, -1.17484387, -0.27891415, 0.15920611, -9.38665655, -9.00823174, -0.03247397, -2.24949755, -1.57653802, -0.09309876, 5.13592933, 4.54897953, 4.66893825, 4.31965063]
if solver == "quadprog":
x = quadprog_solve_qp(P, q, G, h)
else:
x = cvxopt_solve_qp(P, q, G, h)
print("residual")
print(np.dot(M, -x) - b)
print(np.dot(G, -x))
print(x)
return grid, -x
if __name__ == "__main__":
parser = ArgumentParser(description='Get a program and run it with input')
parser.add_argument('--version', action='version', version='%(prog)s 1.0')
parser.add_argument('--numDims', default=2, type=int, help="dimensionality")
parser.add_argument('--gridType', default="linear", type=str, help="define which sparse grid should be used (poly, polyClenshawcCurtis, polyBoundary, modPoly, modPolyClenshawCurtis, ...)")
parser.add_argument('--level', default=3, type=int, help="level of regular sparse grid")
parser.add_argument('--lmbd', default=0.0, type=float, help="regularization parameter")
parser.add_argument('--solver', default="cvxopt", type=str, help="define which solver should be used for quadratic programming")
parser.add_argument('--makePositive', default=False, action='store_true', help='make density positive')
args = parser.parse_args()
mean = 0.5
var = 0.1
np.random.seed(1234567)
if args.numDims == 1:
U = Normal(mean, var, 0, 1)
trainSamples = np.array([U.rvs(1000)]).T
testSamples = np.array([U.rvs(1000)]).T
else :
U = J([Normal(mean, var, 0, 1) for _ in range(args.numDims)])
trainSamples = U.rvs(1000)
testSamples = U.rvs(1000)
print("SGDE...", end=' ')
dist_sgde = SGDEdist.byLearnerSGDEConfig(trainSamples,
config={"grid_level": args.level,
"grid_type": args.gridType,
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"solver_threshold": 1e-15,
"solver_verbose": True,
"regularization_type": "Laplace",
"crossValidation_lambda": args.lmbd,
"crossValidation_enable": False,
"crossValidation_silent": True,
"sgde_makePositive": args.makePositive,
"sgde_makePositive_candidateSearchAlgorithm": "intersections",
"sgde_makePositive_interpolationAlgorithm": "interpolateBoundaries1d",
"sgde_makePositive_generateConsistentGrid": False,
"sgde_makePositive_verbose": False,
"sgde_unitIntegrand": False}, bounds=U.getBounds())
print("is positive? %s (min=%f)" % ("Yes" if np.all(nodalValues >= 0) else "Nope",
np.min(nodalValues)))
print("-" * 80)
print("SGDE pos...")
grid, alpha = solve(trainSamples, args.gridType, args.level, args.lmbd,
solver=args.solver)
print(("alpha:", alpha))
print("is positive? %s (min=%f)" % ("Yes" if np.all(nodalValues >= 0) else "Nope",
np.min(nodalValues)))
if args.makePositive:
alpha_vec = DataVector(alpha)
MakePositiveInterpolationAlgorithm_InterpolateBoundaries1d,
alpha = alpha_vec.array()
dist_sgde_pos = SGDEdist(grid, alpha,
trainData=trainSamples,
bounds=U.getBounds())
print("cross entropy: %f, %f" % (dist_sgde.crossEntropy(testSamples),
dist_sgde_pos.crossEntropy(testSamples)))
if args.numDims == 1:
fig = plt.figure()
plotSG1d(dist_sgde.grid, dist_sgde.alpha, label=
r"SGDE",
show_grid_points=True)
plotSG1d(dist_sgde_pos.grid, dist_sgde_pos.alpha, label=
r"SGDE pos",
show_grid_points=True)
elif args.numDims == 2:
fig = plt.figure()
plt.title("analytic")
fig = plt.figure()
plotSG2d(dist_sgde.grid, dist_sgde.alpha, addContour=
True,
show_negative=True, show_grid_points=True)
plt.title(r"SGDE (\#gp=%i, vol=%g)" % (dist_sgde.grid.getSize(),
dist_sgde.vol))
fig = plt.figure()
plotSG2d(dist_sgde_pos.grid, dist_sgde_pos.alpha, addContour=
True,
show_negative=True, show_grid_points=True)
plt.title(r"SGDE pos (\#gp=%i, vol=%g)" % (dist_sgde_pos.grid.getSize(),
dist_sgde_pos.vol))
if args.numDims < 3:
plt.show()
1.8.13