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Renamed TestFunctions to ExampleFunctions in order to not confuse pytest.

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master
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
import numpy as np
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)
@ -159,7 +162,8 @@ class TestFunctions(object):
def exp_fun1(x, y):
''' The value of the definite integral on the square [-1,1] x [-1,1],
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)
@ -167,7 +171,8 @@ class TestFunctions(object):
def exp_fun100(x, y):
'''The value of the definite integral on the square [-1,1] x [-1,1],
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))
@ -175,7 +180,8 @@ class TestFunctions(object):
def cos30(x, y):
''' The value of the definite integral on the square [-1,1] x [-1,1],
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))
@ -194,7 +200,8 @@ class TestFunctions(object):
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],
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),
f(x)=exp(x).
'''
@ -209,7 +216,8 @@ class TestFunctions(object):
up to machine precision, is 0.597388947274307 (see ref. 6).
The value of the definite integral on the square [-1,1] x [-1,1],
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),
f(x)=1/(1+16*x^2).
@ -223,7 +231,8 @@ class TestFunctions(object):
up to machine precision, is 2.508723139534059 (see ref. 6).
The value of the definite integral on the square [-1,1] x [-1,1],
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),
f(x)=abs(x)^3.
@ -237,7 +246,8 @@ class TestFunctions(object):
up to machine precision, is 2.230985141404135 (see ref. 6).
The value of the definite integral on the square [-1,1] x [-1,1],
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),
f(x)=exp(-x^2).
@ -251,7 +261,8 @@ class TestFunctions(object):
up to machine precision, is 0.853358758654305 (see ref. 6).
The value of the definite integral on the square [-1,1] x [-1,1],
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),
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.abs_cubed, s.gauss, s.exp_inv]
return test_function[id](x, y)
testfunct = TestFunctions()
example_functions = _ExampleFunctions()
def _find_m(n):
@ -348,7 +359,6 @@ def padua_fit(Pad, fun, *args):
'''
N = np.shape(Pad)[1]
# recover the degree n from N = (n+1)(n+2)/2
n = int(round(-3 + np.sqrt(1 + 8 * N)) / 2)
@ -375,6 +385,7 @@ def padua_fit(Pad, fun, *args):
return C0f, error_estimate(C0f)
def paduavals2coefs(f):
useFFTwhenNisMoreThan = 100
m = len(f)
@ -394,12 +405,12 @@ def paduavals2coefs(f):
t1 = np.r_[0:n + 1].reshape(-1, 1)
Tn1 = np.cos(t1 * t1.T * np.pi / n)
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))
else:
# 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[:, 1] = .5 * C[:, 1]
@ -415,14 +426,11 @@ def paduavals2coefs(f):
def padua_fit2(Pad, fun, *args):
N = np.shape(Pad)[1]
# 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)
return paduavals2coefs(C0f)
def _compute_moments(n):
k = np.r_[0:n: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 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
----------
@ -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)
original_shape = X.shape
min, max = np.minimum, np.maximum
min, max = np.minimum, np.maximum # @ReservedAssignment
a, b, c, d = domain
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)
TX2[1:n + 1] = TX2[1:n + 1] * np.sqrt(2)
if use_meshgrid:
return np.dot(TX1.T, np.dot(coefficients, TX2)).T # eval on meshgrid points
val = np.sum(np.dot(TX1.T, coefficients) * TX2.T, axis=1) # scattered points
# eval on meshgrid 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)

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