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1228 lines (1112 loc) · 48.1 KB
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// Copyright (c) 2019 by the SciSharp Team
// Code generated by CodeMinion: https://github.com/SciSharp/CodeMinion
using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;
using Numpy.Models;
using Microsoft.VisualStudio.TestTools.UnitTesting;
using Assert = NUnit.Framework.Assert;
using LA = Numpy.np.linalg;
namespace Numpy.UnitTest
{
[TestClass]
public class NumPy_linalg_fftTest : BaseTestCase
{
[TestMethod]
public void choleskyTest()
{
// >>> A = np.array([[1,-2j],[2j,5]])
// >>> A
// array([[ 1.+0.j, 0.-2.j],
// [ 0.+2.j, 5.+0.j]])
// >>> L = np.linalg.cholesky(A)
// >>> L
// array([[ 1.+0.j, 0.+0.j],
// [ 0.+2.j, 1.+0.j]])
// >>> np.dot(L, L.T.conj()) # verify that L * L.H = A
// array([[ 1.+0.j, 0.-2.j],
// [ 0.+2.j, 5.+0.j]])
// >>> A = [[1,-2j],[2j,5]] # what happens if A is only array_like?
// >>> np.linalg.cholesky(A) # an ndarray object is returned
// array([[ 1.+0.j, 0.+0.j],
// [ 0.+2.j, 1.+0.j]])
// >>> # But a matrix object is returned if A is a matrix object
// >>> LA.cholesky(np.matrix(A))
// matrix([[ 1.+0.j, 0.+0.j],
// [ 0.+2.j, 1.+0.j]])
//
#if TODO
var given= A = np.array({{1,-2j},{2j,5}});
given= A;
var expected=
"array([[ 1.+0.j, 0.-2.j],\n" +
" [ 0.+2.j, 5.+0.j]])";
Assert.AreEqual(expected, given.repr);
given= L = np.linalg.cholesky(A);
given= L;
expected=
"array([[ 1.+0.j, 0.+0.j],\n" +
" [ 0.+2.j, 1.+0.j]])";
Assert.AreEqual(expected, given.repr);
given= np.dot(L, L.T.conj()) # verify that L * L.H = A;
expected=
"array([[ 1.+0.j, 0.-2.j],\n" +
" [ 0.+2.j, 5.+0.j]])";
Assert.AreEqual(expected, given.repr);
given= A = [[1,-2j],[2j,5]] # what happens if A is only array_like?;
given= np.linalg.cholesky(A) # an ndarray object is returned;
expected=
"array([[ 1.+0.j, 0.+0.j],\n" +
" [ 0.+2.j, 1.+0.j]])";
Assert.AreEqual(expected, given.repr);
given= # But a matrix object is returned if A is a matrix object;
given= LA.cholesky(np.matrix(A));
expected=
"matrix([[ 1.+0.j, 0.+0.j],\n" +
" [ 0.+2.j, 1.+0.j]])";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void detTest()
{
// The determinant of a 2-D array [[a, b], [c, d]] is ad - bc:
// >>> a = np.array([[1, 2], [3, 4]])
// >>> np.linalg.det(a)
// -2.0
//
var a = np.array(new int[,] { { 1, 2 }, { 3, 4 } });
var given = np.linalg.det(a);
var expected =
"-2.0";
Assert.AreEqual(expected, given.repr.Substring(0, 4));
// Computing determinants for a stack of matrices:
// >>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ])
// >>> a.shape
// (3, 2, 2)
// >>> np.linalg.det(a)
// array([-2., -3., -8.])
//
a = np.array(new int[,,] { { { 1, 2 }, { 3, 4 } }, { { 1, 2 }, { 2, 1 } }, { { 1, 3 }, { 3, 1 } } });
var shape = a.shape;
expected =
"(3, 2, 2)";
Assert.AreEqual(expected, shape.ToString());
given = np.linalg.det(a);
expected =
"array([-2., -3., -8.])";
Assert.AreEqual(expected, given.repr);
}
[TestMethod]
public void eigTest()
{
// >>> from numpy import linalg as LA
//
#if TODO
var given= from numpy import linalg as LA;
#endif
// (Almost) trivial example with real e-values and e-vectors.
// >>> w, v = LA.eig(np.diag((1, 2, 3)))
// >>> w; v
// array([ 1., 2., 3.])
// array([[ 1., 0., 0.],
// [ 0., 1., 0.],
// [ 0., 0., 1.]])
//
#if TODO
given= w, v = LA.eig(np.diag((1, 2, 3)));
given= w; v;
var expected=
"array([ 1., 2., 3.])\n" +
"array([[ 1., 0., 0.],\n" +
" [ 0., 1., 0.],\n" +
" [ 0., 0., 1.]])";
Assert.AreEqual(expected, given.repr);
#endif
// Real matrix possessing complex e-values and e-vectors; note that the
// e-values are complex conjugates of each other.
// >>> w, v = LA.eig(np.array([[1, -1], [1, 1]]))
// >>> w; v
// array([ 1. + 1.j, 1. - 1.j])
// array([[ 0.70710678+0.j , 0.70710678+0.j ],
// [ 0.00000000-0.70710678j, 0.00000000+0.70710678j]])
//
#if TODO
given= w, v = LA.eig(np.array({{1, -1}, {1, 1}}));
given= w; v;
expected=
"array([ 1. + 1.j, 1. - 1.j])\n" +
"array([[ 0.70710678+0.j , 0.70710678+0.j ],\n" +
" [ 0.00000000-0.70710678j, 0.00000000+0.70710678j]])";
Assert.AreEqual(expected, given.repr);
#endif
// Complex-valued matrix with real e-values (but complex-valued e-vectors);
// note that a.conj().T = a, i.e., a is Hermitian.
// >>> a = np.array([[1, 1j], [-1j, 1]])
// >>> w, v = LA.eig(a)
// >>> w; v
// array([ 2.00000000e+00+0.j, 5.98651912e-36+0.j]) # i.e., {2, 0}
// array([[ 0.00000000+0.70710678j, 0.70710678+0.j ],
// [ 0.70710678+0.j , 0.00000000+0.70710678j]])
//
#if TODO
given= a = np.array({{1, 1j}, {-1j, 1}});
given= w, v = LA.eig(a);
given= w; v;
expected=
"array([ 2.00000000e+00+0.j, 5.98651912e-36+0.j]) # i.e., {2, 0}\n" +
"array([[ 0.00000000+0.70710678j, 0.70710678+0.j ],\n" +
" [ 0.70710678+0.j , 0.00000000+0.70710678j]])";
Assert.AreEqual(expected, given.repr);
#endif
// Be careful about round-off error!
// >>> a = np.array([[1 + 1e-9, 0], [0, 1 - 1e-9]])
// >>> # Theor. e-values are 1 +/- 1e-9
// >>> w, v = LA.eig(a)
// >>> w; v
// array([ 1., 1.])
// array([[ 1., 0.],
// [ 0., 1.]])
//
#if TODO
given= a = np.array({{1 + 1e-9, 0}, {0, 1 - 1e-9}});
given= # Theor. e-values are 1 +/- 1e-9;
given= w, v = LA.eig(a);
given= w; v;
expected=
"array([ 1., 1.])\n" +
"array([[ 1., 0.],\n" +
" [ 0., 1.]])";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void eighTest()
{
// >>> from numpy import linalg as LA
// >>> a = np.array([[1, -2j], [2j, 5]])
// >>> a
// array([[ 1.+0.j, 0.-2.j],
// [ 0.+2.j, 5.+0.j]])
// >>> w, v = LA.eigh(a)
// >>> w; v
// array([ 0.17157288, 5.82842712])
// array([[-0.92387953+0.j , -0.38268343+0.j ],
// [ 0.00000000+0.38268343j, 0.00000000-0.92387953j]])
//
#if TODO
var given= from numpy import linalg as LA;
given= a = np.array({{1, -2j}, {2j, 5}});
given= a;
var expected=
"array([[ 1.+0.j, 0.-2.j],\n" +
" [ 0.+2.j, 5.+0.j]])";
Assert.AreEqual(expected, given.repr);
given= w, v = LA.eigh(a);
given= w; v;
expected=
"array([ 0.17157288, 5.82842712])\n" +
"array([[-0.92387953+0.j , -0.38268343+0.j ],\n" +
" [ 0.00000000+0.38268343j, 0.00000000-0.92387953j]])";
Assert.AreEqual(expected, given.repr);
#endif
// >>> np.dot(a, v[:, 0]) - w[0] * v[:, 0] # verify 1st e-val/vec pair
// array([2.77555756e-17 + 0.j, 0. + 1.38777878e-16j])
// >>> np.dot(a, v[:, 1]) - w[1] * v[:, 1] # verify 2nd e-val/vec pair
// array([ 0.+0.j, 0.+0.j])
//
#if TODO
given= np.dot(a, v{:, 0}) - w{0} * v{:, 0} # verify 1st e-val/vec pair;
expected=
"array([2.77555756e-17 + 0.j, 0. + 1.38777878e-16j])";
Assert.AreEqual(expected, given.repr);
given= np.dot(a, v{:, 1}) - w{1} * v{:, 1} # verify 2nd e-val/vec pair;
expected=
"array([ 0.+0.j, 0.+0.j])";
Assert.AreEqual(expected, given.repr);
#endif
// >>> A = np.matrix(a) # what happens if input is a matrix object
// >>> A
// matrix([[ 1.+0.j, 0.-2.j],
// [ 0.+2.j, 5.+0.j]])
// >>> w, v = LA.eigh(A)
// >>> w; v
// array([ 0.17157288, 5.82842712])
// matrix([[-0.92387953+0.j , -0.38268343+0.j ],
// [ 0.00000000+0.38268343j, 0.00000000-0.92387953j]])
//
#if TODO
given= A = np.matrix(a) # what happens if input is a matrix object;
given= A;
expected=
"matrix([[ 1.+0.j, 0.-2.j],\n" +
" [ 0.+2.j, 5.+0.j]])";
Assert.AreEqual(expected, given.repr);
given= w, v = LA.eigh(A);
given= w; v;
expected=
"array([ 0.17157288, 5.82842712])\n" +
"matrix([[-0.92387953+0.j , -0.38268343+0.j ],\n" +
" [ 0.00000000+0.38268343j, 0.00000000-0.92387953j]])";
Assert.AreEqual(expected, given.repr);
#endif
// >>> # demonstrate the treatment of the imaginary part of the diagonal
// >>> a = np.array([[5+2j, 9-2j], [0+2j, 2-1j]])
// >>> a
// array([[ 5.+2.j, 9.-2.j],
// [ 0.+2.j, 2.-1.j]])
// >>> # with UPLO='L' this is numerically equivalent to using LA.eig() with:
// >>> b = np.array([[5.+0.j, 0.-2.j], [0.+2.j, 2.-0.j]])
// >>> b
// array([[ 5.+0.j, 0.-2.j],
// [ 0.+2.j, 2.+0.j]])
// >>> wa, va = LA.eigh(a)
// >>> wb, vb = LA.eig(b)
// >>> wa; wb
// array([ 1., 6.])
// array([ 6.+0.j, 1.+0.j])
// >>> va; vb
// array([[-0.44721360-0.j , -0.89442719+0.j ],
// [ 0.00000000+0.89442719j, 0.00000000-0.4472136j ]])
// array([[ 0.89442719+0.j , 0.00000000-0.4472136j],
// [ 0.00000000-0.4472136j, 0.89442719+0.j ]])
//
#if TODO
given= # demonstrate the treatment of the imaginary part of the diagonal;
given= a = np.array({{5+2j, 9-2j}, {0+2j, 2-1j}});
given= a;
expected=
"array([[ 5.+2.j, 9.-2.j],\n" +
" [ 0.+2.j, 2.-1.j]])";
Assert.AreEqual(expected, given.repr);
given= # with UPLO='L' this is numerically equivalent to using LA.eig() with:;
given= b = np.array({{5.+0.j, 0.-2.j}, {0.+2.j, 2.-0.j}});
given= b;
expected=
"array([[ 5.+0.j, 0.-2.j],\n" +
" [ 0.+2.j, 2.+0.j]])";
Assert.AreEqual(expected, given.repr);
given= wa, va = LA.eigh(a);
given= wb, vb = LA.eig(b);
given= wa; wb;
expected=
"array([ 1., 6.])\n" +
"array([ 6.+0.j, 1.+0.j])";
Assert.AreEqual(expected, given.repr);
given= va; vb;
expected=
"array([[-0.44721360-0.j , -0.89442719+0.j ],\n" +
" [ 0.00000000+0.89442719j, 0.00000000-0.4472136j ]])\n" +
"array([[ 0.89442719+0.j , 0.00000000-0.4472136j],\n" +
" [ 0.00000000-0.4472136j, 0.89442719+0.j ]])";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void eigvalsTest()
{
// Illustration, using the fact that the eigenvalues of a diagonal matrix
// are its diagonal elements, that multiplying a matrix on the left
// by an orthogonal matrix, Q, and on the right by Q.T (the transpose
// of Q), preserves the eigenvalues of the “middle” matrix. In other words,
// if Q is orthogonal, then Q * A * Q.T has the same eigenvalues as
// A:
// >>> from numpy import linalg as LA
// >>> x = np.random.random()
// >>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]])
// >>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :])
// (1.0, 1.0, 0.0)
//
#if TODO
var given= from numpy import linalg as LA;
given= x = np.random.random();
given= Q = np.array({{np.cos(x), -np.sin(x)}, {np.sin(x), np.cos(x)}});
given= LA.norm(Q{0, :}), LA.norm(Q{1, :}), np.dot(Q{0, :},Q{1, :});
var expected=
"(1.0, 1.0, 0.0)";
Assert.AreEqual(expected, given.repr);
#endif
// Now multiply a diagonal matrix by Q on one side and by Q.T on the other:
// >>> D = np.diag((-1,1))
// >>> LA.eigvals(D)
// array([-1., 1.])
// >>> A = np.dot(Q, D)
// >>> A = np.dot(A, Q.T)
// >>> LA.eigvals(A)
// array([ 1., -1.])
//
#if TODO
given= D = np.diag((-1,1));
given= LA.eigvals(D);
expected=
"array([-1., 1.])";
Assert.AreEqual(expected, given.repr);
given= A = np.dot(Q, D);
given= A = np.dot(A, Q.T);
given= LA.eigvals(A);
expected=
"array([ 1., -1.])";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void eigvalshTest()
{
// >>> from numpy import linalg as LA
// >>> a = np.array([[1, -2j], [2j, 5]])
// >>> LA.eigvalsh(a)
// array([ 0.17157288, 5.82842712])
//
#if TODO
var given= from numpy import linalg as LA;
given= a = np.array({{1, -2j}, {2j, 5}});
given= LA.eigvalsh(a);
var expected=
"array([ 0.17157288, 5.82842712])";
Assert.AreEqual(expected, given.repr);
#endif
// >>> # demonstrate the treatment of the imaginary part of the diagonal
// >>> a = np.array([[5+2j, 9-2j], [0+2j, 2-1j]])
// >>> a
// array([[ 5.+2.j, 9.-2.j],
// [ 0.+2.j, 2.-1.j]])
// >>> # with UPLO='L' this is numerically equivalent to using LA.eigvals()
// >>> # with:
// >>> b = np.array([[5.+0.j, 0.-2.j], [0.+2.j, 2.-0.j]])
// >>> b
// array([[ 5.+0.j, 0.-2.j],
// [ 0.+2.j, 2.+0.j]])
// >>> wa = LA.eigvalsh(a)
// >>> wb = LA.eigvals(b)
// >>> wa; wb
// array([ 1., 6.])
// array([ 6.+0.j, 1.+0.j])
//
#if TODO
given= # demonstrate the treatment of the imaginary part of the diagonal;
given= a = np.array({{5+2j, 9-2j}, {0+2j, 2-1j}});
given= a;
expected=
"array([[ 5.+2.j, 9.-2.j],\n" +
" [ 0.+2.j, 2.-1.j]])";
Assert.AreEqual(expected, given.repr);
given= # with UPLO='L' this is numerically equivalent to using LA.eigvals();
given= # with:;
given= b = np.array({{5.+0.j, 0.-2.j}, {0.+2.j, 2.-0.j}});
given= b;
expected=
"array([[ 5.+0.j, 0.-2.j],\n" +
" [ 0.+2.j, 2.+0.j]])";
Assert.AreEqual(expected, given.repr);
given= wa = LA.eigvalsh(a);
given= wb = LA.eigvals(b);
given= wa; wb;
expected=
"array([ 1., 6.])\n" +
"array([ 6.+0.j, 1.+0.j])";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void invTest()
{
// >>> from numpy.linalg import inv
// >>> a = np.array([[1., 2.], [3., 4.]])
// >>> ainv = inv(a)
// >>> np.allclose(np.dot(a, ainv), np.eye(2))
// True
// >>> np.allclose(np.dot(ainv, a), np.eye(2))
// True
//
#if TODO
var given= from numpy.linalg import inv;
given= a = np.array({{1., 2.}, {3., 4.}});
given= ainv = inv(a);
given= np.allclose(np.dot(a, ainv), np.eye(2));
var expected=
"True";
Assert.AreEqual(expected, given.repr);
given= np.allclose(np.dot(ainv, a), np.eye(2));
expected=
"True";
Assert.AreEqual(expected, given.repr);
#endif
// If a is a matrix object, then the return value is a matrix as well:
// >>> ainv = inv(np.matrix(a))
// >>> ainv
// matrix([[-2. , 1. ],
// [ 1.5, -0.5]])
//
#if TODO
given= ainv = inv(np.matrix(a));
given= ainv;
expected=
"matrix([[-2. , 1. ],\n" +
" [ 1.5, -0.5]])";
Assert.AreEqual(expected, given.repr);
#endif
// Inverses of several matrices can be computed at once:
// >>> a = np.array([[[1., 2.], [3., 4.]], [[1, 3], [3, 5]]])
// >>> inv(a)
// array([[[-2. , 1. ],
// [ 1.5, -0.5]],
// [[-5. , 2. ],
// [ 3. , -1. ]]])
//
#if TODO
given= a = np.array({{{1., 2.}, {3., 4.}}, {{1, 3}, {3, 5}}});
given= inv(a);
expected=
"array([[[-2. , 1. ],\n" +
" [ 1.5, -0.5]],\n" +
" [[-5. , 2. ],\n" +
" [ 3. , -1. ]]])";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void lstsqTest()
{
// Fit a line, y = mx + c, through some noisy data-points:
// >>> x = np.array([0, 1, 2, 3])
// >>> y = np.array([-1, 0.2, 0.9, 2.1])
//
#if TODO
var given= x = np.array({0, 1, 2, 3});
given= y = np.array({-1, 0.2, 0.9, 2.1});
#endif
// By examining the coefficients, we see that the line should have a
// gradient of roughly 1 and cut the y-axis at, more or less, -1.
// We can rewrite the line equation as y = Ap, where A = [[x 1]]
// and p = [[m], [c]]. Now use lstsq to solve for p:
// >>> A = np.vstack([x, np.ones(len(x))]).T
// >>> A
// array([[ 0., 1.],
// [ 1., 1.],
// [ 2., 1.],
// [ 3., 1.]])
//
#if TODO
given= A = np.vstack({x, np.ones(len(x))}).T;
given= A;
var expected=
"array([[ 0., 1.],\n" +
" [ 1., 1.],\n" +
" [ 2., 1.],\n" +
" [ 3., 1.]])";
Assert.AreEqual(expected, given.repr);
#endif
// >>> m, c = np.linalg.lstsq(A, y, rcond=None)[0]
// >>> print(m, c)
// 1.0 -0.95
//
#if TODO
given= m, c = np.linalg.lstsq(A, y, rcond=None){0};
given= print(m, c);
expected=
"1.0 -0.95";
Assert.AreEqual(expected, given.repr);
#endif
// Plot the data along with the fitted line:
// >>> import matplotlib.pyplot as plt
// >>> plt.plot(x, y, 'o', label='Original data', markersize=10)
// >>> plt.plot(x, m*x + c, 'r', label='Fitted line')
// >>> plt.legend()
// >>> plt.show()
//
#if TODO
given= import matplotlib.pyplot as plt;
given= plt.plot(x, y, 'o', label='Original data', markersize=10);
given= plt.plot(x, m*x + c, 'r', label='Fitted line');
given= plt.legend();
given= plt.show();
#endif
}
[TestMethod]
public void normTest()
{
// >>> from numpy import linalg as LA
// >>> a = np.arange(9) - 4
// >>> a
// array([-4, -3, -2, -1, 0, 1, 2, 3, 4])
// >>> b = a.reshape((3, 3))
// >>> b
// array([[-4, -3, -2],
// [-1, 0, 1],
// [ 2, 3, 4]])
//
var a = np.arange(9) - 4;
NDarray given = a;
var expected =
"array([-4, -3, -2, -1, 0, 1, 2, 3, 4])";
Assert.AreEqual(expected, given.repr);
var b = a.reshape(3, 3);
given = b;
expected =
"array([[-4, -3, -2],\n" +
" [-1, 0, 1],\n" +
" [ 2, 3, 4]])";
Assert.AreEqual(expected, given.repr);
// >>> LA.norm(a)
// 7.745966692414834
// >>> LA.norm(b)
// 7.745966692414834
// >>> LA.norm(b, 'fro')
// 7.745966692414834
// >>> LA.norm(a, np.inf)
// 4.0
// >>> LA.norm(b, np.inf)
// 9.0
// >>> LA.norm(a, -np.inf)
// 0.0
// >>> LA.norm(b, -np.inf)
// 2.0
//
Assert.GreaterOrEqual(7.74596669f, LA.norm(a));
Assert.GreaterOrEqual(7.74596669f, LA.norm(b));
Assert.GreaterOrEqual(7.74596669f, LA.norm(b, "fro"));
Assert.AreEqual(4, LA.norm(a, Constants.inf));
Assert.AreEqual(9, LA.norm(b, Constants.inf));
Assert.AreEqual(0, LA.norm(a, Constants.neg_inf));
Assert.AreEqual(2, LA.norm(b, Constants.neg_inf));
// >>> LA.norm(a, 1)
// 20.0
// >>> LA.norm(b, 1)
// 7.0
// >>> LA.norm(a, -1)
// -4.6566128774142013e-010
// >>> LA.norm(b, -1)
// 6.0
// >>> LA.norm(a, 2)
// 7.745966692414834
// >>> LA.norm(b, 2)
// 7.3484692283495345
//
Assert.AreEqual(20, LA.norm(a, 1));
Assert.AreEqual(7, LA.norm(b, 1));
Assert.GreaterOrEqual(0f, LA.norm(a, -1));
Assert.GreaterOrEqual(6, LA.norm(b, -1));
Assert.GreaterOrEqual(7.74596669f, LA.norm(a, 2));
Assert.GreaterOrEqual(7.34846922f, LA.norm(b, 2));
// >>> LA.norm(a, -2)
// nan
// >>> LA.norm(b, -2)
// 1.8570331885190563e-016
// >>> LA.norm(a, 3)
// 5.8480354764257312
// >>> LA.norm(a, -3)
// nan
//
#if TODO
object given = null;
object expected = null;
given= LA.norm(a, -2);
expected=
"nan";
Assert.AreEqual(expected, given.repr);
given= LA.norm(b, -2);
expected=
"1.8570331885190563e-016";
Assert.AreEqual(expected, given.repr);
given= LA.norm(a, 3);
expected=
"5.8480354764257312";
Assert.AreEqual(expected, given.repr);
given= LA.norm(a, -3);
expected=
"nan";
Assert.AreEqual(expected, given.repr);
#endif
// Using the axis argument to compute vector norms:
// >>> c = np.array([[ 1, 2, 3],
// ... [-1, 1, 4]])
// >>> LA.norm(c, axis=0)
// array([ 1.41421356, 2.23606798, 5. ])
// >>> LA.norm(c, axis=1)
// array([ 3.74165739, 4.24264069])
// >>> LA.norm(c, ord=1, axis=1)
// array([ 6., 6.])
//
#if TODO
object given = null;
object expected = null;
given= c = np.array([[ 1, 2, 3],;
expected=
"... [-1, 1, 4]])";
Assert.AreEqual(expected, given.repr);
given= LA.norm(c, axis=0);
expected=
"array([ 1.41421356, 2.23606798, 5. ])";
Assert.AreEqual(expected, given.repr);
given= LA.norm(c, axis=1);
expected=
"array([ 3.74165739, 4.24264069])";
Assert.AreEqual(expected, given.repr);
given= LA.norm(c, ord=1, axis=1);
expected=
"array([ 6., 6.])";
Assert.AreEqual(expected, given.repr);
#endif
// Using the axis argument to compute matrix norms:
// >>> m = np.arange(8).reshape(2,2,2)
// >>> LA.norm(m, axis=(1,2))
// array([ 3.74165739, 11.22497216])
// >>> LA.norm(m[0, :, :]), LA.norm(m[1, :, :])
// (3.7416573867739413, 11.224972160321824)
//
#if TODO
object given = null;
object expected = null;
given= m = np.arange(8).reshape(2,2,2);
given= LA.norm(m, axis=(1,2));
expected=
"array([ 3.74165739, 11.22497216])";
Assert.AreEqual(expected, given.repr);
given= LA.norm(m[0, :, :]), LA.norm(m[1, :, :]);
expected=
"(3.7416573867739413, 11.224972160321824)";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void pinvTest()
{
// The following example checks that a * a+ * a == a and
// a+ * a * a+ == a+:
// >>> a = np.random.randn(9, 6)
// >>> B = np.linalg.pinv(a)
// >>> np.allclose(a, np.dot(a, np.dot(B, a)))
// True
// >>> np.allclose(B, np.dot(B, np.dot(a, B)))
// True
//
#if TODO
var given= a = np.random.randn(9, 6);
given= B = np.linalg.pinv(a);
given= np.allclose(a, np.dot(a, np.dot(B, a)));
var expected=
"True";
Assert.AreEqual(expected, given.repr);
given= np.allclose(B, np.dot(B, np.dot(a, B)));
expected=
"True";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void solveTest()
{
// Solve the system of equations 3 * x0 + x1 = 9 and x0 + 2 * x1 = 8:
// >>> a = np.array([[3,1], [1,2]])
// >>> b = np.array([9,8])
// >>> x = np.linalg.solve(a, b)
// >>> x
// array([ 2., 3.])
//
#if TODO
var given= a = np.array({{3,1}, {1,2}});
given= b = np.array({9,8});
given= x = np.linalg.solve(a, b);
given= x;
var expected=
"array([ 2., 3.])";
Assert.AreEqual(expected, given.repr);
#endif
// Check that the solution is correct:
// >>> np.allclose(np.dot(a, x), b)
// True
//
#if TODO
given= np.allclose(np.dot(a, x), b);
expected=
"True";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void svdTest()
{
// >>> a = np.random.randn(9, 6) + 1j*np.random.randn(9, 6)
// >>> b = np.random.randn(2, 7, 8, 3) + 1j*np.random.randn(2, 7, 8, 3)
//
#if TODO
var given= a = np.random.randn(9, 6) + 1j*np.random.randn(9, 6);
given= b = np.random.randn(2, 7, 8, 3) + 1j*np.random.randn(2, 7, 8, 3);
#endif
// Reconstruction based on full SVD, 2D case:
// >>> u, s, vh = np.linalg.svd(a, full_matrices=True)
// >>> u.shape, s.shape, vh.shape
// ((9, 9), (6,), (6, 6))
// >>> np.allclose(a, np.dot(u[:, :6] * s, vh))
// True
// >>> smat = np.zeros((9, 6), dtype=complex)
// >>> smat[:6, :6] = np.diag(s)
// >>> np.allclose(a, np.dot(u, np.dot(smat, vh)))
// True
//
#if TODO
given= u, s, vh = np.linalg.svd(a, full_matrices=True);
given= u.shape, s.shape, vh.shape;
var expected=
"((9, 9), (6,), (6, 6))";
Assert.AreEqual(expected, given.repr);
given= np.allclose(a, np.dot(u{:, :6} * s, vh));
expected=
"True";
Assert.AreEqual(expected, given.repr);
given= smat = np.zeros((9, 6), dtype=complex);
given= smat{:6, :6} = np.diag(s);
given= np.allclose(a, np.dot(u, np.dot(smat, vh)));
expected=
"True";
Assert.AreEqual(expected, given.repr);
#endif
// Reconstruction based on reduced SVD, 2D case:
// >>> u, s, vh = np.linalg.svd(a, full_matrices=False)
// >>> u.shape, s.shape, vh.shape
// ((9, 6), (6,), (6, 6))
// >>> np.allclose(a, np.dot(u * s, vh))
// True
// >>> smat = np.diag(s)
// >>> np.allclose(a, np.dot(u, np.dot(smat, vh)))
// True
//
#if TODO
given= u, s, vh = np.linalg.svd(a, full_matrices=False);
given= u.shape, s.shape, vh.shape;
expected=
"((9, 6), (6,), (6, 6))";
Assert.AreEqual(expected, given.repr);
given= np.allclose(a, np.dot(u * s, vh));
expected=
"True";
Assert.AreEqual(expected, given.repr);
given= smat = np.diag(s);
given= np.allclose(a, np.dot(u, np.dot(smat, vh)));
expected=
"True";
Assert.AreEqual(expected, given.repr);
#endif
// Reconstruction based on full SVD, 4D case:
// >>> u, s, vh = np.linalg.svd(b, full_matrices=True)
// >>> u.shape, s.shape, vh.shape
// ((2, 7, 8, 8), (2, 7, 3), (2, 7, 3, 3))
// >>> np.allclose(b, np.matmul(u[..., :3] * s[..., None, :], vh))
// True
// >>> np.allclose(b, np.matmul(u[..., :3], s[..., None] * vh))
// True
//
#if TODO
given= u, s, vh = np.linalg.svd(b, full_matrices=True);
given= u.shape, s.shape, vh.shape;
expected=
"((2, 7, 8, 8), (2, 7, 3), (2, 7, 3, 3))";
Assert.AreEqual(expected, given.repr);
given= np.allclose(b, np.matmul(u{..., :3} * s{..., None, :}, vh));
expected=
"True";
Assert.AreEqual(expected, given.repr);
given= np.allclose(b, np.matmul(u{..., :3}, s{..., None} * vh));
expected=
"True";
Assert.AreEqual(expected, given.repr);
#endif
// Reconstruction based on reduced SVD, 4D case:
// >>> u, s, vh = np.linalg.svd(b, full_matrices=False)
// >>> u.shape, s.shape, vh.shape
// ((2, 7, 8, 3), (2, 7, 3), (2, 7, 3, 3))
// >>> np.allclose(b, np.matmul(u * s[..., None, :], vh))
// True
// >>> np.allclose(b, np.matmul(u, s[..., None] * vh))
// True
//
#if TODO
given= u, s, vh = np.linalg.svd(b, full_matrices=False);
given= u.shape, s.shape, vh.shape;
expected=
"((2, 7, 8, 3), (2, 7, 3), (2, 7, 3, 3))";
Assert.AreEqual(expected, given.repr);
given= np.allclose(b, np.matmul(u * s{..., None, :}, vh));
expected=
"True";
Assert.AreEqual(expected, given.repr);
given= np.allclose(b, np.matmul(u, s{..., None} * vh));
expected=
"True";
Assert.AreEqual(expected, given.repr);
#endif
}
[TestMethod]
public void fftTest()
{
// >>> np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8))
// array([ -3.44505240e-16 +1.14383329e-17j,
// 8.00000000e+00 -5.71092652e-15j,
// 2.33482938e-16 +1.22460635e-16j,
// 1.64863782e-15 +1.77635684e-15j,
// 9.95839695e-17 +2.33482938e-16j,
// 0.00000000e+00 +1.66837030e-15j,
// 1.14383329e-17 +1.22460635e-16j,
// -1.64863782e-15 +1.77635684e-15j])
//
#if TODO
var given= np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8));
var expected=
"array([ -3.44505240e-16 +1.14383329e-17j,\n" +
" 8.00000000e+00 -5.71092652e-15j,\n" +
" 2.33482938e-16 +1.22460635e-16j,\n" +
" 1.64863782e-15 +1.77635684e-15j,\n" +
" 9.95839695e-17 +2.33482938e-16j,\n" +
" 0.00000000e+00 +1.66837030e-15j,\n" +
" 1.14383329e-17 +1.22460635e-16j,\n" +
" -1.64863782e-15 +1.77635684e-15j])";
Assert.AreEqual(expected, given.repr);
#endif
// In this example, real input has an FFT which is Hermitian, i.e., symmetric
// in the real part and anti-symmetric in the imaginary part, as described in
// the numpy.fft documentation:
// >>> import matplotlib.pyplot as plt
// >>> t = np.arange(256)
// >>> sp = np.fft.fft(np.sin(t))
// >>> freq = np.fft.fftfreq(t.shape[-1])
// >>> plt.plot(freq, sp.real, freq, sp.imag)
// [<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>]
// >>> plt.show()
//
#if TODO
given= import matplotlib.pyplot as plt;
given= t = np.arange(256);
given= sp = np.fft.fft(np.sin(t));
given= freq = np.fft.fftfreq(t.shape{-1});
given= plt.plot(freq, sp.real, freq, sp.imag);
expected=
"[<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>]";
Assert.AreEqual(expected, given.repr);
given= plt.show();
#endif
}
[TestMethod]
public void fft2Test()
{
// >>> a = np.mgrid[:5, :5][0]
// >>> np.fft.fft2(a)
// array([[ 50.0 +0.j , 0.0 +0.j , 0.0 +0.j ,
// 0.0 +0.j , 0.0 +0.j ],
// [-12.5+17.20477401j, 0.0 +0.j , 0.0 +0.j ,
// 0.0 +0.j , 0.0 +0.j ],
// [-12.5 +4.0614962j , 0.0 +0.j , 0.0 +0.j ,
// 0.0 +0.j , 0.0 +0.j ],
// [-12.5 -4.0614962j , 0.0 +0.j , 0.0 +0.j ,
// 0.0 +0.j , 0.0 +0.j ],
// [-12.5-17.20477401j, 0.0 +0.j , 0.0 +0.j ,
// 0.0 +0.j , 0.0 +0.j ]])