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Renamed TestFunctions to ExampleFunctions in order to not confuse pytest.

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pbrod 9 years ago
parent ca48f7147c
commit dd9cfb63ad
1 changed files with 53 additions and 38 deletions
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wafo/padua.py
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@ -85,8 +85,11 @@ Contents.m : Contents file for Matlab
from __future__ import division from __future__ import division
import numpy as np import numpy as np
from numpy.fft import fft from numpy.fft import fft
from wafo.dctpack import dct
# from scipy.fftpack.realtransforms import dct
class TestFunctions(object):
class _ExampleFunctions(object):
''' '''
Computes test function in the points (x, y) Computes test function in the points (x, y)
@ -159,7 +162,8 @@ class TestFunctions(object):
def exp_fun1(x, y): def exp_fun1(x, y):
''' The value of the definite integral on the square [-1,1] x [-1,1], ''' The value of the definite integral on the square [-1,1] x [-1,1],
obtained using a Padua Points cubature formula of degree 2000, obtained using a Padua Points cubature formula of degree 2000,
is 2.1234596326670683e+001 with an estimated absolute error of 7.11e-015. is 2.1234596326670683e+001 with an estimated absolute error of
7.11e-015.
''' '''
return np.exp((x - 0.5)**2 + (y - 0.5)**2) return np.exp((x - 0.5)**2 + (y - 0.5)**2)
@ -167,7 +171,8 @@ class TestFunctions(object):
def exp_fun100(x, y): def exp_fun100(x, y):
'''The value of the definite integral on the square [-1,1] x [-1,1], '''The value of the definite integral on the square [-1,1] x [-1,1],
obtained using a Padua Points cubature formula of degree 2000, obtained using a Padua Points cubature formula of degree 2000,
is 3.1415926535849605e-002 with an estimated absolute error of 3.47e-017. is 3.1415926535849605e-002 with an estimated absolute error of
3.47e-017.
''' '''
return np.exp(-100 * ((x - 0.5)**2 + (y - 0.5)**2)) return np.exp(-100 * ((x - 0.5)**2 + (y - 0.5)**2))
@ -175,7 +180,8 @@ class TestFunctions(object):
def cos30(x, y): def cos30(x, y):
''' The value of the definite integral on the square [-1,1] x [-1,1], ''' The value of the definite integral on the square [-1,1] x [-1,1],
obtained using a Padua Points cubature formula of degree 500, obtained using a Padua Points cubature formula of degree 500,
is 4.3386955120336568e-003 with an estimated absolute error of 2.95e-017. is 4.3386955120336568e-003 with an estimated absolute error of
2.95e-017.
''' '''
return np.cos(30 * (x + y)) return np.cos(30 * (x + y))
@ -194,7 +200,8 @@ class TestFunctions(object):
is up to machine precision is 5.524391382167263 (see ref. 6). is up to machine precision is 5.524391382167263 (see ref. 6).
2. The value of the definite integral on the square [-1,1] x [-1,1], 2. The value of the definite integral on the square [-1,1] x [-1,1],
obtained using a Padua Points cubature formula of degree 500, obtained using a Padua Points cubature formula of degree 500,
is 5.5243913821672628e+000 with an estimated absolute error of 0.00e+000. is 5.5243913821672628e+000 with an estimated absolute error of
0.00e+000.
2D modification of an example by L.N.Trefethen (see ref. 7), 2D modification of an example by L.N.Trefethen (see ref. 7),
f(x)=exp(x). f(x)=exp(x).
''' '''
@ -209,7 +216,8 @@ class TestFunctions(object):
up to machine precision, is 0.597388947274307 (see ref. 6). up to machine precision, is 0.597388947274307 (see ref. 6).
The value of the definite integral on the square [-1,1] x [-1,1], The value of the definite integral on the square [-1,1] x [-1,1],
obtained using a Padua Points cubature formula of degree 500, obtained using a Padua Points cubature formula of degree 500,
is 5.9738894727430725e-001 with an estimated absolute error of 0.00e+000. is 5.9738894727430725e-001 with an estimated absolute error of
0.00e+000.
2D modification of an example by L.N.Trefethen (see ref. 7), 2D modification of an example by L.N.Trefethen (see ref. 7),
f(x)=1/(1+16*x^2). f(x)=1/(1+16*x^2).
@ -223,7 +231,8 @@ class TestFunctions(object):
up to machine precision, is 2.508723139534059 (see ref. 6). up to machine precision, is 2.508723139534059 (see ref. 6).
The value of the definite integral on the square [-1,1] x [-1,1], The value of the definite integral on the square [-1,1] x [-1,1],
obtained using a Padua Points cubature formula of degree 500, obtained using a Padua Points cubature formula of degree 500,
is 2.5087231395340579e+000 with an estimated absolute error of 0.00e+000. is 2.5087231395340579e+000 with an estimated absolute error of
0.00e+000.
2D modification of an example by L.N.Trefethen (see ref. 7), 2D modification of an example by L.N.Trefethen (see ref. 7),
f(x)=abs(x)^3. f(x)=abs(x)^3.
@ -237,7 +246,8 @@ class TestFunctions(object):
up to machine precision, is 2.230985141404135 (see ref. 6). up to machine precision, is 2.230985141404135 (see ref. 6).
The value of the definite integral on the square [-1,1] x [-1,1], The value of the definite integral on the square [-1,1] x [-1,1],
obtained using a Padua Points cubature formula of degree 500, obtained using a Padua Points cubature formula of degree 500,
is 2.2309851414041333e+000 with an estimated absolute error of 2.66e-015. is 2.2309851414041333e+000 with an estimated absolute error of
2.66e-015.
2D modification of an example by L.N.Trefethen (see ref. 7), 2D modification of an example by L.N.Trefethen (see ref. 7),
f(x)=exp(-x^2). f(x)=exp(-x^2).
@ -251,7 +261,8 @@ class TestFunctions(object):
up to machine precision, is 0.853358758654305 (see ref. 6). up to machine precision, is 0.853358758654305 (see ref. 6).
The value of the definite integral on the square [-1,1] x [-1,1], The value of the definite integral on the square [-1,1] x [-1,1],
obtained using a Padua Points cubature formula of degree 2000, obtained using a Padua Points cubature formula of degree 2000,
is 8.5335875865430544e-001 with an estimated absolute error of 3.11e-015. is 8.5335875865430544e-001 with an estimated absolute error of
3.11e-015.
2D modification of an example by L.N.Trefethen (see ref. 7), 2D modification of an example by L.N.Trefethen (see ref. 7),
f(x)=exp(-1/x^2). f(x)=exp(-1/x^2).
@ -269,7 +280,7 @@ class TestFunctions(object):
s.exp_fun100, s.cos30, s.constant, s.exp_xy, s.runge, s.exp_fun100, s.cos30, s.constant, s.exp_xy, s.runge,
s.abs_cubed, s.gauss, s.exp_inv] s.abs_cubed, s.gauss, s.exp_inv]
return test_function[id](x, y) return test_function[id](x, y)
testfunct = TestFunctions() example_functions = _ExampleFunctions()
def _find_m(n): def _find_m(n):
@ -348,7 +359,6 @@ def padua_fit(Pad, fun, *args):
''' '''
N = np.shape(Pad)[1] N = np.shape(Pad)[1]
# recover the degree n from N = (n+1)(n+2)/2 # recover the degree n from N = (n+1)(n+2)/2
n = int(round(-3 + np.sqrt(1 + 8 * N)) / 2) n = int(round(-3 + np.sqrt(1 + 8 * N)) / 2)
@ -375,54 +385,52 @@ def padua_fit(Pad, fun, *args):
return C0f, error_estimate(C0f) return C0f, error_estimate(C0f)
def paduavals2coefs(f): def paduavals2coefs(f):
useFFTwhenNisMoreThan=100 useFFTwhenNisMoreThan = 100
m = len(f) m = len(f)
n = int(round(-1.5 + np.sqrt(.25+2*m))) n = int(round(-1.5 + np.sqrt(.25 + 2 * m)))
x = padua_points(n) x = padua_points(n)
idx = _find_m(n) idx = _find_m(n)
w = 0*x[0] + 1./(n*(n+1)) w = 0 * x[0] + 1. / (n * (n + 1))
idx1 = np.all(np.abs(x) == 1, axis=0) idx1 = np.all(np.abs(x) == 1, axis=0)
w[idx1] = .5*w[idx1] w[idx1] = .5 * w[idx1]
idx2 = np.all(np.abs(x) != 1, axis=0) idx2 = np.all(np.abs(x) != 1, axis=0)
w[idx2] = 2*w[idx2] w[idx2] = 2 * w[idx2]
G = np.zeros(idx.max()+1) G = np.zeros(idx.max() + 1)
G[idx] = 4*w*f G[idx] = 4 * w * f
if ( n < useFFTwhenNisMoreThan ): if (n < useFFTwhenNisMoreThan):
t1 = np.r_[0:n+1].reshape(-1, 1) t1 = np.r_[0:n + 1].reshape(-1, 1)
Tn1 = np.cos(t1*t1.T*np.pi/n) Tn1 = np.cos(t1 * t1.T * np.pi / n)
t2 = np.r_[0:n+2].reshape(-1, 1) t2 = np.r_[0:n + 2].reshape(-1, 1)
Tn2 = np.cos(t2*t2.T*np.pi/(n+1)); Tn2 = np.cos(t2 * t2.T * np.pi / (n + 1))
C = np.dot(Tn2, np.dot(G,Tn1)) C = np.dot(Tn2, np.dot(G, Tn1))
else: else:
# dct = @(c) chebtech2.coeffs2vals(c); # dct = @(c) chebtech2.coeffs2vals(c);
C = np.rot90(dct(dct(G.T).T), axis=1) C = np.rot90(dct(dct(G.T).T)) #, axis=1)
C[0] = .5*C[0] C[0] = .5 * C[0]
C[:,1] = .5*C[:, 1] C[:, 1] = .5 * C[:, 1]
C[0,-1] = .5*C[0, -1] C[0, -1] = .5 * C[0, -1]
del C[-1] del C[-1]
# Take upper-left triangular part: # Take upper-left triangular part:
return np.fliplr(np.triu(np.fliplr(C))) return np.fliplr(np.triu(np.fliplr(C)))
#C = triu(C(:,end:-1:1)); # C = triu(C(:,end:-1:1));
#C = C(:,end:-1:1); # C = C(:,end:-1:1);
def padua_fit2(Pad, fun, *args): def padua_fit2(Pad, fun, *args):
N = np.shape(Pad)[1] N = np.shape(Pad)[1]
# recover the degree n from N = (n+1)(n+2)/2 # recover the degree n from N = (n+1)(n+2)/2
n = int(round(-3 + np.sqrt(1 + 8 * N)) / 2) _n = int(round(-3 + np.sqrt(1 + 8 * N)) / 2)
C0f = fun(Pad[0], Pad[1], *args) C0f = fun(Pad[0], Pad[1], *args)
return paduavals2coefs(C0f) return paduavals2coefs(C0f)
def _compute_moments(n): def _compute_moments(n):
k = np.r_[0:n:2] k = np.r_[0:n:2]
mom = 2 * np.sqrt(2) / (1 - k ** 2) mom = 2 * np.sqrt(2) / (1 - k ** 2)
@ -449,7 +457,8 @@ def padua_val(X, Y, coefficients, domain=(-1, 1, -1, 1), use_meshgrid=False):
Evaluate polynomial in padua form at X, Y. Evaluate polynomial in padua form at X, Y.
Evaluate the interpolation polynomial defined through its coefficient Evaluate the interpolation polynomial defined through its coefficient
matrix coefficients at the target points X(:,1),X(:,2) or at the meshgrid(X1,X2) matrix coefficients at the target points X(:,1),X(:,2) or at the
meshgrid(X1,X2)
Parameters Parameters
---------- ----------
@ -469,7 +478,7 @@ def padua_val(X, Y, coefficients, domain=(-1, 1, -1, 1), use_meshgrid=False):
''' '''
X, Y = np.atleast_1d(X, Y) X, Y = np.atleast_1d(X, Y)
original_shape = X.shape original_shape = X.shape
min, max = np.minimum, np.maximum min, max = np.minimum, np.maximum # @ReservedAssignment
a, b, c, d = domain a, b, c, d = domain
n = np.shape(coefficients)[1] n = np.shape(coefficients)[1]
@ -481,6 +490,12 @@ def padua_val(X, Y, coefficients, domain=(-1, 1, -1, 1), use_meshgrid=False):
TX1[1:n + 1] = TX1[1:n + 1] * np.sqrt(2) TX1[1:n + 1] = TX1[1:n + 1] * np.sqrt(2)
TX2[1:n + 1] = TX2[1:n + 1] * np.sqrt(2) TX2[1:n + 1] = TX2[1:n + 1] * np.sqrt(2)
if use_meshgrid: if use_meshgrid:
return np.dot(TX1.T, np.dot(coefficients, TX2)).T # eval on meshgrid points # eval on meshgrid points
val = np.sum(np.dot(TX1.T, coefficients) * TX2.T, axis=1) # scattered points return np.dot(TX1.T, np.dot(coefficients, TX2)).T
val = np.sum(
np.dot(
TX1.T,
coefficients) *
TX2.T,
axis=1) # scattered points
return val.reshape(original_shape) return val.reshape(original_shape)

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