Python pysgpp.DataVector类代码示例

    def computeMoments(self, ts=None):
        names = ['time',
                 'iteration',
                 'grid_size',
                 'mean',
                 'meanDiscretizationError',
                 'var',
                 'varDiscretizationError']
        # parameters
        ts = self.__samples.keys()
        nrows = len(ts)
        ncols = len(names)
        data = DataMatrix(nrows, ncols)
        v = DataVector(ncols)

        row = 0
        for t in ts:
            v.setAll(0.0)
            v[0] = t
            v[1] = 0
            v[2] = len(self.__samples[t].values())
            v[3], v[4] = self.mean(ts=[t])
            v[5], v[6] = self.var(ts=[t])

            # write results to matrix
            data.setRow(row, v)
            row += 1

        return {'data': data,
                'names': names}

    def testOperationTest_test(self):
        from pysgpp import Grid, DataVector, DataMatrix

        factory = Grid.createLinearBoundaryGrid(1)
        gen = factory.createGridGenerator()
        gen.regular(1)
        
        alpha = DataVector(factory.getStorage().size())        
        
        data = DataMatrix(1,1)
        data.setAll(0.25)
        classes = DataVector(1)
        classes.setAll(1.0)

        testOP = factory.createOperationTest()

        alpha[0] = 0.0
        alpha[1] = 0.0
        alpha[2] = 1.0
        
        c = testOP.test(alpha, data, classes)
        self.failUnless(c > 0.0)
        
        alpha[0] = 0.0
        alpha[1] = 0.0
        alpha[2] = -1.0
        c = testOP.test(alpha, data, classes)
        self.failUnless(c == 0.0)

    def mean(self, grid, alpha, U, T):
        r"""
        Extraction of the expectation the given sparse grid function
        interpolating the product of function value and pdf.

        \int\limits_{[0, 1]^d} f_N(x) * pdf(x) dx
        """
        # extract correct pdf for moment estimation
        vol, W = self._extractPDFforMomentEstimation(U, T)
        D = T.getTransformations()
        # compute the integral of the product
        gs = grid.getStorage()
        acc = DataVector(gs.size())
        acc.setAll(1.)
        tmp = DataVector(gs.size())
        err = 0
        # run over all dimensions
        for i, dims in enumerate(W.getTupleIndices()):
            dist = W[i]
            trans = D[i]

            # get the objects needed for integration the current dimensions
            gpsi, basisi = project(grid, dims)

            if isinstance(dist, SGDEdist):
                # if the distribution is given as a sparse grid function we
                # need to compute the bilinear form of the grids
                # accumulate objects needed for computing the bilinear form
                gpsj, basisj = project(dist.grid, range(len(dims)))

                # compute the bilinear form
                bf = BilinearGaussQuadratureStrategy()
                A, erri = bf.computeBilinearFormByList(gpsi, basisi,
                                                       gpsj, basisj)
                # weight it with the coefficient of the density function
                self.mult(A, dist.alpha, tmp)
            else:
                # the distribution is given analytically, handle them
                # analytically in the integration of the basis functions
                if isinstance(dist, Dist) and len(dims) > 1:
                    raise AttributeError('analytic quadrature not supported for multivariate distributions')
                if isinstance(dist, Dist):
                    dist = [dist]
                    trans = [trans]

                lf = LinearGaussQuadratureStrategy(dist, trans)
                tmp, erri = lf.computeLinearFormByList(gpsi, basisi)

            # print error stats
            # print "%s: %g -> %g" % (str(dims), err, err + D[i].vol() * erri)
            # import ipdb; ipdb.set_trace()

            # accumulate the error
            err += D[i].vol() * erri

            # accumulate the result
            acc.componentwise_mult(tmp)

        moment = alpha.dotProduct(acc)
        return vol * moment, err

def generateLaplaceMatrix(factory, level, verbose=False):
    from pysgpp import DataVector
    storage = factory.getStorage()
    
    gen = factory.createGridGenerator()
    gen.regular(level)
    
    laplace = factory.createOperationLaplace()
    
    # create vector
    alpha = DataVector(storage.size())
    erg = DataVector(storage.size())

    # create stiffness matrix
    m = DataVector(storage.size(), storage.size())
    m.setAll(0)
    for i in xrange(storage.size()):
        # apply unit vectors
        alpha.setAll(0)
        alpha[i] = 1
        laplace.mult(alpha, erg)
        if verbose:
            print erg, erg.sum()
        m.setColumn(i, erg)

    return m

    def estimate(self, vol, grid, alpha, f, U, T):
        r"""
        Extraction of the expectation the given sparse grid function
        interpolating the product of function value and pdf.

        \int\limits_{[0, 1]^d} f(x) * pdf(x) dx
        """
        # first: discretize f
        fgrid, falpha, discError = discretize(grid, alpha, f, self.__epsilon,
                                              self.__refnums, self.__pointsNum,
                                              self.level, self.__deg, True)
        # extract correct pdf for moment estimation
        vol, W, pdfError = self.__extractDiscretePDFforMomentEstimation(U, T)
        D = T.getTransformations()

        # compute the integral of the product
        gs = fgrid.getStorage()
        acc = DataVector(gs.size())
        acc.setAll(1.)
        tmp = DataVector(gs.size())
        for i, dims in enumerate(W.getTupleIndices()):
            sgdeDist = W[i]
            # accumulate objects needed for computing the bilinear form
            gpsi, basisi = project(fgrid, dims)
            gpsj, basisj = project(sgdeDist.grid, range(len(dims)))
            A = self.__computeMassMatrix(gpsi, basisi, gpsj, basisj, W, D)
            # A = ScipyQuadratureStrategy(W, D).computeBilinearForm(fgrid)
            self.mult(A, sgdeDist.alpha, tmp)
            acc.componentwise_mult(tmp)

        moment = falpha.dotProduct(acc)
        return vol * moment, discError[1] + pdfError

    def gradient_fun(self, params):
        '''
        Compute the gradient vector in the current state
        '''
        #import ipdb; ipdb.set_trace() #
        gradient_array = np.empty((self.batch_size, self.grid.getSize()))
        for sample_idx in xrange(self.batch_size):
            x = self._lastseen[sample_idx, :self.dim]
            y = self._lastseen[sample_idx, self.dim]
            params_DV = DataVector(params)
            
            gradient = DataVector(len(params_DV))
            
            single_alpha = DataVector(1)
            single_alpha[0] = 1
            
            data_matrix = DataMatrix(x.reshape(1,-1))
        
            mult_eval = createOperationMultipleEval(self.grid, data_matrix);
            mult_eval.multTranspose(single_alpha, gradient);
         
            residual = gradient.dotProduct(params_DV) - y;
            gradient.mult(residual);
            #import ipdb; ipdb.set_trace() #

            gradient_array[sample_idx, :] =  gradient.array()
        return gradient_array

 def computeTrilinearFormByRow(self,
                               gpsk, basisk,
                               gpi, basisi,
                               gpj, basisj):
     """
     Compute the trilinear form of two grid point with a list
     of grid points
     @param gpk: list of HashGridIndex
     @param basisk: SG++ Basis for grid indices k
     @param gpi: HashGridIndex
     @param basisi: SG++ Basis for grid indices i
     @param gpj: HashGridIndex
     @param basisj: SG++ Basis for grid indices j
     @return DataVector
     """
     b = DataVector(len(gpsk))
     b.setAll(1.0)
     err = 0.
     # run over all entries
     for k, gpk in enumerate(gpsk):
         # run over all dimensions
         for d in xrange(gpi.dim()):
             # compute trilinear form for one entry
             value, erri = self.getTrilinearFormEntry(gpk, basisk,
                                                      gpi, basisi,
                                                      gpj, basisj,
                                                      d)
             b[k] *= value
             err += erri
     return b, err

    def var(self, grid, alpha, U, T, mean):
        r"""
        Estimate the expectation value using Monte-Carlo.

        \frac{1}{N}\sum\limits_{i = 1}^N (f_N(x_i) - E(f))^2

        where x_i \in \Gamma
        """
        # init
        _, W = self._extractPDFforMomentEstimation(U, T)
        moments = np.zeros(self.__npaths)
        vecMean = DataVector(self.__n)
        vecMean.setAll(mean)
        for i in xrange(self.__npaths):
            samples = self.__getSamples(W, T, self.__n)
            res = evalSGFunctionMulti(grid, alpha, samples)
            res.sub(vecMean)
            res.sqr()

            # compute the moment
            moments[i] = res.sum() / (len(res) - 1.)

        # error statistics
        err = np.Inf

        # calculate moment
        return np.sum(moments) / self.__npaths, err

def plotSG3d(grid, alpha, n=50, f=lambda x: x):
    fig = plt.figure()
    ax = fig.gca(projection='3d')
    X = np.linspace(0, 1, n)
    Y = np.linspace(0, 1, n)
    X, Y = np.meshgrid(X, Y)
    Z = np.zeros(n * n).reshape(n, n)
    for i in xrange(len(X)):
        for j, (x, y) in enumerate(zip(X[i], Y[i])):
            Z[i, j] = f(evalSGFunction(grid, alpha, DataVector([x, y])))

    # get grid points
    gs = grid.getStorage()
    gps = np.zeros([gs.size(), 2])
    p = DataVector(2)
    for i in xrange(gs.size()):
        gs.get(i).getCoords(p)
        gps[i, :] = p.array()

    surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,
                           linewidth=0, antialiased=False)
    ax.scatter(gps[:, 0], gps[:, 1], np.zeros(gs.size()))
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)
    # ax.set_zlim(0, 2)

    fig.colorbar(surf, shrink=0.5, aspect=5)
    return fig, ax, Z

    def currentDiagHess(self, params):
        #return np.ones(params.shape)
#         if hasattr(self, 'H'):
#             return self.H
#         op_l2_dot = createOperationLTwoDotProduct(self.grid)
#         self.H = np.empty((self.grid.getSize(), self.grid.getSize()))
#         u = DataVector(self.grid.getSize())
#         u.setAll(0.0)
#         result = DataVector(self.grid.getSize())
#         for grid_idx in xrange(self.grid.getSize()):
#             u[grid_idx] = 1.0
#             op_l2_dot.mult(u, result)
#             self.H[grid_idx,:] = result.array()
#             u[grid_idx] = 0.0
#         self.H = np.diag(self.H).reshape(1,-1)
#         return self.H
        #import ipdb; ipdb.set_trace()
        size = self._lastseen.shape[0]
        data_matrix = DataMatrix(self._lastseen[:,:self.dim])
        mult_eval = createOperationMultipleEval(self.grid, data_matrix);
        params_DV = DataVector(self.grid.getSize())
        params_DV.setAll(0.)
        results_DV = DataVector(size)
        self.H = np.zeros(self.grid.getSize())
        for i in xrange(self.grid.getSize()):
            params_DV[i] = 1.0
            mult_eval.mult(params_DV, results_DV);
            self.H[i] = results_DV.l2Norm()**2
            params_DV[i] = 0.0
        self.H = self.H.reshape(1,-1)/size
        #import ipdb; ipdb.set_trace() 
        return self.H

 def testOperationB(self):
     from pysgpp import Grid, DataVector, DataMatrix
     factory = Grid.createLinearBoundaryGrid(1)
     gen = factory.createGridGenerator()
     gen.regular(2)
     
     alpha = DataVector(factory.getStorage().size())
     p = DataMatrix(1,1)
     beta = DataVector(1)
     
     
     alpha.setAll(0.0)
     p.set(0,0,0.25)
     beta[0] = 1.0
     
     opb = factory.createOperationB()
     opb.mult(beta, p, alpha)
     
     self.failUnlessAlmostEqual(alpha[0], 0.75)
     self.failUnlessAlmostEqual(alpha[1], 0.25)
     self.failUnlessAlmostEqual(alpha[2], 0.5)
     self.failUnlessAlmostEqual(alpha[3], 1.0)
     self.failUnlessAlmostEqual(alpha[4], 0.0)
     
     alpha.setAll(0.0)
     alpha[2] = 1.0
     
     p.set(0,0, 0.25)
     
     beta[0] = 0.0
     
     opb.multTranspose(alpha, p, beta)
     self.failUnlessAlmostEqual(beta[0], 0.5)

    def serializeToFile(self, memento, filename):
        fstream = self.gzOpen(filename, "w")
        
        try:
            figure = plt.figure()
            grid = memento
            storage = grid.getStorage()
            coord_vector = DataVector(storage.dim())
            points = zeros([storage.size(), storage.dim()])
            for i in xrange(storage.size()):
                point = storage.get(i)
                point.getCoords(coord_vector)
                points[i] = [j for j in coord_vector.array()]
            num_of_sublots = storage.dim()*(storage.dim()-1)/2
            rows = int(ceil(sqrt(num_of_sublots)))
            cols = int(floor(sqrt(num_of_sublots)))
            i = 1
            
            for x1 in xrange(1,storage.dim()):
                for x2 in xrange(2,storage.dim()+1):
                     figure.add_subplot(rows*100 + cols*10 + i)
                     figure.add_subplot(rows, cols, i)
                     plt.xlabel('x%d'%x1, figure=figure)
                     plt.ylabel('x%d'%x2, figure=figure)
                     plt.scatter(points[:,x1-1], points[:,x2-1], figure=figure)

                     i +=1
            plt.savefig(fstream, figure=figure)
            plt.close(figure)
        finally:
            fstream.close()

 def setUp(self):
     self.grid = Grid.createLinearGrid(2)  # a simple 2D grid
     self.grid.createGridGenerator().regular(3)  # max level 3 => 17 points
     self.HashGridStorage = self.grid.getStorage()
     alpha = DataVector(self.grid.getSize())
     alpha.setAll(1.0)
     for i in [9, 10, 11, 12]:
         alpha[i] = 0.0
     coarseningFunctor = SurplusCoarseningFunctor(alpha, 4, 0.5)
     self.grid.createGridGenerator().coarsen(coarseningFunctor, alpha)

    def calc_indicator_value(self, index):

        numData = self.trainData.getNrows()
        numCoeff = self.grid.getSize()
        seq = self.grid.getStorage().seq(index)

        num = 0
        denom = 0

        tmp = DataVector(numCoeff)
        self.multEval.multTranspose(self.errors, tmp) 

        num = tmp.__getitem__(seq)
        num **= 2

        alpha = DataVector(numCoeff)
        col = DataVector(numData)
        alpha.__setitem__(seq, 1.0)
        self.multEval.mult(alpha, col)

        col.sqr()

        denom = col.sum()

        if denom == 0:
            print "Denominator is zero"
            value = 0
        else:
            value = num/denom 

        return value

 def testDotProduct(self):
     from pysgpp import DataVector
     
     x = 0
     
     d = DataVector(3)
     for i in xrange(len(d)):
         d[i] = i + 1
         x += d[i] * d[i]
         
     self.assertEqual(d.dotProduct(d), x)