Python moves.xrange函数代码示例

    def extend(self, xi, yi, orders=None):
        """
        Extend the PiecewisePolynomial by a list of points

        Parameters
        ----------
        xi : array_like of length N1
            a sorted list of x-coordinates
        yi : list of lists of length N1
            yi[i] (if axis==0) is the list of derivatives known at xi[i]
        orders : list of integers, or integer
            a list of polynomial orders, or a single universal order
        direction : {None, 1, -1}
            indicates whether the xi are increasing or decreasing
            +1 indicates increasing
            -1 indicates decreasing
            None indicates that it should be deduced from the first two xi

        """
        if self._y_axis == 0:
            # allow yi to be a ragged list
            for i in xrange(len(xi)):
                if orders is None or _isscalar(orders):
                    self.append(xi[i],yi[i],orders)
                else:
                    self.append(xi[i],yi[i],orders[i])
        else:
            preslice = (slice(None,None,None),) * self._y_axis
            for i in xrange(len(xi)):
                if orders is None or _isscalar(orders):
                    self.append(xi[i],yi[preslice + (i,)],orders)
                else:
                    self.append(xi[i],yi[preslice + (i,)],orders[i])

 def __add__(self, other):
     # First check if argument is a scalar
     if isscalarlike(other):
         new = dok_matrix(self.shape, dtype=self.dtype)
         # Add this scalar to every element.
         M, N = self.shape
         for i in xrange(M):
             for j in xrange(N):
                 aij = self.get((i, j), 0) + other
                 if aij != 0:
                     new[i, j] = aij
         # new.dtype.char = self.dtype.char
     elif isinstance(other, dok_matrix):
         if other.shape != self.shape:
             raise ValueError("matrix dimensions are not equal")
         # We could alternatively set the dimensions to the the largest of
         # the two matrices to be summed.  Would this be a good idea?
         new = dok_matrix(self.shape, dtype=self.dtype)
         new.update(self)
         for key in other.keys():
             new[key] += other[key]
     elif isspmatrix(other):
         csc = self.tocsc()
         new = csc + other
     elif isdense(other):
         new = self.todense() + other
     else:
         raise TypeError("data type not understood")
     return new

 def __radd__(self, other):
     # First check if argument is a scalar
     if isscalarlike(other):
         new = dok_matrix(self.shape, dtype=self.dtype)
         # Add this scalar to every element.
         M, N = self.shape
         for i in xrange(M):
             for j in xrange(N):
                 aij = self.get((i, j), 0) + other
                 if aij != 0:
                     new[i, j] = aij
     elif isinstance(other, dok_matrix):
         if other.shape != self.shape:
             raise ValueError("matrix dimensions are not equal")
         new = dok_matrix(self.shape, dtype=self.dtype)
         new.update(self)
         for key in other:
             new[key] += other[key]
     elif isspmatrix(other):
         csc = self.tocsc()
         new = csc + other
     elif isdense(other):
         new = other + self.todense()
     else:
         raise TypeError("data type not understood")
     return new

    def _evaluate_derivatives(self, x, der=None):
        n = self.n
        r = self.r

        if der is None:
            der = self.n
        pi = np.zeros((n, len(x)))
        w = np.zeros((n, len(x)))
        pi[0] = 1
        p = np.zeros((len(x), self.r))
        p += self.c[0,np.newaxis,:]

        for k in xrange(1,n):
            w[k-1] = x - self.xi[k-1]
            pi[k] = w[k-1]*pi[k-1]
            p += pi[k,:,np.newaxis]*self.c[k]

        cn = np.zeros((max(der,n+1), len(x), r), dtype=self.dtype)
        cn[:n+1,:,:] += self.c[:n+1,np.newaxis,:]
        cn[0] = p
        for k in xrange(1,n):
            for i in xrange(1,n-k+1):
                pi[i] = w[k+i-1]*pi[i-1]+pi[i]
                cn[k] = cn[k]+pi[i,:,np.newaxis]*cn[k+i]
            cn[k] *= factorial(k)

        cn[n,:,:] = 0
        return cn[:der]

    def __init__(self, xi, yi, axis=0):
        _Interpolator1DWithDerivatives.__init__(self, xi, yi, axis)

        self.xi = np.asarray(xi)
        self.yi = self._reshape_yi(yi)
        self.n, self.r = self.yi.shape

        c = np.zeros((self.n+1, self.r), dtype=self.dtype)
        c[0] = self.yi[0]
        Vk = np.zeros((self.n, self.r), dtype=self.dtype)
        for k in xrange(1,self.n):
            s = 0
            while s <= k and xi[k-s] == xi[k]:
                s += 1
            s -= 1
            Vk[0] = self.yi[k]/float(factorial(s))
            for i in xrange(k-s):
                if xi[i] == xi[k]:
                    raise ValueError("Elements if `xi` can't be equal.")
                if s == 0:
                    Vk[i+1] = (c[i]-Vk[i])/(xi[i]-xi[k])
                else:
                    Vk[i+1] = (Vk[i+1]-Vk[i])/(xi[i]-xi[k])
            c[k] = Vk[k-s]
        self.c = c

def lagrange(x, w):
    """
    Return a Lagrange interpolating polynomial.

    Given two 1-D arrays `x` and `w,` returns the Lagrange interpolating
    polynomial through the points ``(x, w)``.

    Warning: This implementation is numerically unstable. Do not expect to
    be able to use more than about 20 points even if they are chosen optimally.

    Parameters
    ----------
    x : array_like
        `x` represents the x-coordinates of a set of datapoints.
    w : array_like
        `w` represents the y-coordinates of a set of datapoints, i.e. f(`x`).

    """
    M = len(x)
    p = poly1d(0.0)
    for j in xrange(M):
        pt = poly1d(w[j])
        for k in xrange(M):
            if k == j: continue
            fac = x[j]-x[k]
            pt *= poly1d([1.0,-x[k]])/fac
        p += pt
    return p

 def test_cascade(self):
     for J in xrange(1, 7):
         for i in xrange(1, 5):
             lpcoef = wavelets.daub(i)
             k = len(lpcoef)
             x, phi, psi = wavelets.cascade(lpcoef, J)
             assert_(len(x) == len(phi) == len(psi))
             assert_equal(len(x), (k - 1) * 2 ** J)

 def test_improvement(self):
     import time
     start = time.time()
     for i in xrange(100):
         quad(self.lib.sin, 0, 100)
     fast = time.time() - start
     start = time.time()
     for i in xrange(100):
         quad(math.sin, 0, 100)
     slow = time.time() - start
     assert_(fast < 0.5*slow, (fast, slow))

    def test_nd_simplex(self):
        # simple smoke test: triangulate a n-dimensional simplex
        for nd in xrange(2, 8):
            points = np.zeros((nd+1, nd))
            for j in xrange(nd):
                points[j,j] = 1.0
            points[-1,:] = 1.0

            tri = qhull.Delaunay(points)

            tri.vertices.sort()

            assert_equal(tri.vertices, np.arange(nd+1, dtype=np.int)[None,:])
            assert_equal(tri.neighbors, -1 + np.zeros((nd+1), dtype=np.int)[None,:])

 def setUp(self):
     self.tck = splrep([0,1,2,3,4,5], [0,10,-1,3,7,2], s=0)
     self.test_xs = np.linspace(-1,6,100)
     self.spline_ys = splev(self.test_xs, self.tck)
     self.spline_yps = splev(self.test_xs, self.tck, der=1)
     self.xi = np.unique(self.tck[0])
     self.yi = [[splev(x, self.tck, der=j) for j in xrange(3)] for x in self.xi]

 def test_exponential(self):
     degree = 5
     p = approximate_taylor_polynomial(np.exp, 0, degree, 1, 15)
     for i in xrange(degree+1):
         assert_almost_equal(p(0),1)
         p = p.deriv()
     assert_almost_equal(p(0),0)

    def __getitem__(self, index):
        """Return the element(s) index=(i, j), where j may be a slice.
        This always returns a copy for consistency, since slices into
        Python lists return copies.
        """
        i, j = self._unpack_index(index)

        if isscalarlike(i) and isscalarlike(j):
            return self._get1(int(i), int(j))

        i, j = self._index_to_arrays(i, j)
        if i.size == 0:
            return lil_matrix((0,0), dtype=self.dtype)
        return self.__class__([[self._get1(int(i[ii, jj]), int(j[ii, jj])) for jj in
                                xrange(i.shape[1])] for ii in 
                               xrange(i.shape[0])])

    def test_concurrent_ok(self):
        f = lambda t, y: 1.0

        for k in xrange(3):
            for sol in ('vode', 'zvode', 'lsoda', 'dopri5', 'dop853'):
                r = ode(f).set_integrator(sol)
                r.set_initial_value(0, 0)

                r2 = ode(f).set_integrator(sol)
                r2.set_initial_value(0, 0)

                r.integrate(r.t + 0.1)
                r2.integrate(r2.t + 0.1)
                r2.integrate(r2.t + 0.1)

                assert_allclose(r.y, 0.1)
                assert_allclose(r2.y, 0.2)

            for sol in ('dopri5', 'dop853'):
                r = ode(f).set_integrator(sol)
                r.set_initial_value(0, 0)

                r2 = ode(f).set_integrator(sol)
                r2.set_initial_value(0, 0)

                r.integrate(r.t + 0.1)
                r.integrate(r.t + 0.1)
                r2.integrate(r2.t + 0.1)
                r.integrate(r.t + 0.1)
                r2.integrate(r2.t + 0.1)

                assert_allclose(r.y, 0.3)
                assert_allclose(r2.y, 0.2)

    def derivatives(self, x, der):
        """
        Evaluate a derivative of the piecewise polynomial

        Parameters
        ----------
        x : scalar or array_like of length N

        der : integer
            how many derivatives (including the function value as
            0th derivative) to extract

        Returns
        -------
        y : array_like of shape der by R or der by N or der by N by R

        """
        if _isscalar(x):
            pos = np.clip(np.searchsorted(self.xi, x) - 1, 0, self.n - 2)
            y = self.polynomials[pos].derivatives(x, der=der)
        else:
            x = np.asarray(x)
            m = len(x)
            pos = np.clip(np.searchsorted(self.xi, x) - 1, 0, self.n - 2)
            if self.vector_valued:
                y = np.zeros((der, m, self.r))
            else:
                y = np.zeros((der, m))
            for i in xrange(self.n - 1):
                c = pos == i
                y[:, c] = self.polynomials[i].derivatives(x[c], der=der)
        return y

    def __call__(self, x):
        """Evaluate the piecewise polynomial

        Parameters
        ----------
        x : scalar or array-like of length N

        Returns
        -------
        y : scalar or array-like of length R or length N or N by R
        """
        if _isscalar(x):
            pos = np.clip(np.searchsorted(self.xi, x) - 1, 0, self.n - 2)
            y = self.polynomials[pos](x)
        else:
            x = np.asarray(x)
            m = len(x)
            pos = np.clip(np.searchsorted(self.xi, x) - 1, 0, self.n - 2)
            if self.vector_valued:
                y = np.zeros((m, self.r))
            else:
                y = np.zeros(m)
            for i in xrange(self.n - 1):
                c = pos == i
                y[c] = self.polynomials[i](x[c])
        return y