forked from jalawson/ulinalg
/
ulinalg_tests.py
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/
ulinalg_tests.py
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# test cases for the microulinalg package
import sys
import umatrix
import ulinalg
# ulinalg tries to determine the machine epsilon
# operations resulting in irrational numbers seem to require a tolerance of at least 2*eps
eps = umatrix.flt_eps
def matrix_compare(X, Y, tol=0):
# checks for equal elements and identical shapes
return all([not(abs(X[i,j] - Y[i,j]) > tol) for j in range(X.size(2)) for i in range(X.size(1))])
def construct():
result = {}
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x10 = umatrix.matrix([[0,1,2,3],[4,5,6,7],[8,9,10,11],[12,13,14,15]])
result['square test 1'] = x10.is_square
result['square test 2'] = not x11.is_square
result['transpose column vector'] = matrix_compare(umatrix.matrix([1,2,3,4], cstride=1, rstride=1).T, umatrix.matrix([[1,2,3,4]]))
result['transpose test square'] = matrix_compare(x10.transpose(), umatrix.matrix([[0, 4, 8, 12],[1, 5, 9, 13],[2, 6, 10, 14],[3, 7, 11, 15]]))
result['transpose property'] = matrix_compare(x10.T, umatrix.matrix([[0, 4, 8, 12],[1, 5, 9, 13],[2, 6, 10, 14],[3, 7, 11, 15]]))
# check for shape change view
x12 = x11
result['shape'] = x11.shape == (4, 3)
x11.shape=(3, 4)
result['shape change'] = matrix_compare(x11, umatrix.matrix([[0,1,2,4],[5,6,8,9],[10,12,13,14]])) and (x11 == x12)
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
# check for shape change copy
x12 = x11.reshape((3,4))
result['shape copy'] = matrix_compare(x12, umatrix.matrix([[0,1,2,4],[5,6,8,9],[10,12,13,14]])) and (x12.shape != x11.shape)
return result
def equality():
result = {}
x10 = umatrix.matrix([[0.03,1.2,2.45],[4.5,5.45,6.98],[8,9.0001,10.2],[12.123,13.45,14.0]])
x11 = umatrix.matrix([[0.03,1.2,2.45],[4.5,5.45,6.98],[8,9.0001,10.2],[12.123,13.45,14.0]])
x12 = umatrix.matrix([[0.03,1.2,2.451],[4.5,5.45,6.98],[9,9.0002,10.2],[12.123,13.45+eps,14.0]])
x13 = umatrix.matrix([[0.03,1.2,2.451],[4.5,5.45,6.98],[9,9.0003,10.2],[12.123,13.450001,14.0]])
result['x == y and x.__eq__(y)'] = (x10 == x11) and (x10.__eq__(x11))
result['umatrix.matrix_isclose(x, y) True'] = matrix_compare(x10, x11)
result['umatrix.matrix_isclose(x, y) False'] = matrix_compare(x10, x12) == False
result['umatrix.matrix_isclose(x, y, tol) False tol'] = matrix_compare(x12, x13, tol=eps/2) == False
result['umatrix.matrix_isclose(x, y, tol) True tol'] = matrix_compare(x12, x13, tol=0.001)
try:
result['umatrix.matrix_equal(x, y)'] = umatrix.matrix_equal(x10, x12) == False
except Exception as e:
result['umatrix.matrix_equal(x, y)'] = (False, e)
result['umatrix.matrix_equiv(x, y) same shape'] = umatrix.matrix_equiv(x10, x11)
result['umatrix.matrix_equiv(x, y.reshape) shape'] = umatrix.matrix_equiv(x10, x11.reshape((3,4)))
return result
def element_wise():
result = {}
X = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10]])
try:
result['matrix - matrix'] = matrix_compare(X-X, umatrix.matrix([[0,0,0],[0,0,0],[0,0,0]]))
except Exception as e:
result['matrix + list row default'] = (False, e)
try:
result['matrix - matrix view'] = matrix_compare(X-X.T, umatrix.matrix([[0,-3,-6],[3,0,-3],[6,3,0]]))
except Exception as e:
result['matrix + list row default'] = (False, e)
try:
result['matrix view - matrix'] = matrix_compare(X.T-X, umatrix.matrix([[0,-3,-6],[3,0,-3],[6,3,0]]).T)
except Exception as e:
result['matrix + list row default'] = (False, e)
return result
def list_ops():
result = {}
X = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
Ylist = [1,2,3]
Zlist = [1,2,3,4]
Ymatrix = umatrix.matrix([[1,2,3]])
Zmatrix = umatrix.matrix([[1,2,3,4]])
try:
result['matrix + list row defualt'] = matrix_compare(X+Ylist, umatrix.matrix([[1,3,5],[5,7,9],[9,11,13],[13,15,17]]))
except Exception as e:
result['matrix + list row default'] = (False, e)
try:
result['matrix + list row default broadcast error'] = matrix_compare(X+Zlist, umatrix.matrix([[1,3,5],[5,7,9],[9,11,13],[13,15,17]]))
except Exception as e:
result['matrix + list row default broadcast error'] = True
try:
result['matrix col + list'] = matrix_compare(X[:,1]+Zlist, umatrix.matrix([[2,7,12,17]]).T)
except Exception as e:
result['matrix col + list'] = (False, e)
try:
result['matrix col + list broadcast error'] = matrix_compare(X[:,1]+Ylist, umatrix.matrix([[2,7,12,17]]).T)
except Exception as e:
result['matrix col + list broadcast error'] = True
try:
result['matrix + row matrix'] = matrix_compare(X+Ymatrix, umatrix.matrix([[1,3,5],[5,7,9],[9,11,13],[13,15,17]]))
except Exception as e:
result['matrix + row matrix'] = (False, e)
try:
result['matrix + col matrix'] = matrix_compare(X+Zmatrix.T, umatrix.matrix([[1,2,3],[6,7,8],[11,12,13],[16,17,18]]))
except Exception as e:
result['matrix + col matrix'] = (False, e)
try:
result['matrix + col broadcast error'] = matrix_compare(X+Ymatrix.T, umatrix.matrix([[1,3,5],[5,7,9],[9,11,13],[13,15,17]]))
except Exception as e:
result['matrix + col broadcast error'] = True
return result
def scaler():
result = {}
x10 = umatrix.matrix([[0,1,2,3],[4,5,6,7],[8,9,10,11],[12,13,14,15]])
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
try:
result['scaler * matrix'] = matrix_compare(2*x10, umatrix.matrix([[0, 2, 4, 6],[8, 10, 12, 14],[16, 18, 20, 22],[24, 26, 28, 30]]))
except TypeError:
result['scaler * matrix'] = (False, 'TypeError')
try:
result['scaler + matrix'] = matrix_compare(2.1+x10, umatrix.matrix([[2.1 , 3.1 , 4.1 , 5.1 ],[6.1 , 7.1 , 8.1 , 9.1 ],[10.1, 11.1, 12.1, 13.1],[14.1, 15.1, 16.1, 17.1]]))
except TypeError:
result['scaler + matrix'] = (False, 'TypeError')
try:
result['scaler - matrix'] = matrix_compare(1-x10, umatrix.matrix([[1, 0, -1 , -2],[-3, -4, -5, -6],[-7, -8, -9, -10],[-11, -12, -13, -14]]))
except TypeError:
result['scaler - matrix'] = (False, 'TypeError')
result['matrix + scaler'] = matrix_compare(x10+2.1, umatrix.matrix([[2.1 , 3.1 , 4.1 , 5.1 ],[6.1 , 7.1 , 8.1 , 9.1 ],[10.1, 11.1, 12.1, 13.1],[14.1, 15.1, 16.1, 17.1]]))
result['matrix - scaler'] = matrix_compare(x10-1.4, umatrix.matrix([[-1.4, -0.3999999999999999, 0.6000000000000001 , 1.6],[2.6, 3.6, 4.6, 5.6],[6.6, 7.6, 8.6, 9.6],[10.6, 11.6, 12.6, 13.6]]), tol=eps)
result['matrix * scaler'] = matrix_compare(x10*3, umatrix.matrix([[0, 3, 6, 9],[12, 15, 18, 21],[24, 27, 30, 33],[36, 39, 42, 45]]))
result['matrix / scaler'] = matrix_compare(x10/3, umatrix.matrix([[0.0, 0.3333333333333333, 0.6666666666666667, 1.0],
[1.3333333333333333 , 1.6666666666666667 , 2.0, 2.3333333333333333 ],
[2.66666666666666667 , 3.0, 3.3333333333333333 , 3.6666666666666667 ],
[4.0, 4.3333333333333333 , 4.6666666666666667 , 5.0]]), tol=2*eps)
result['matrix // scaler'] = matrix_compare(x10//3, umatrix.matrix([[0, 0, 0, 1],[1, 1, 2, 2],[2, 3, 3, 3],[4, 4, 4, 5]]))
result['negate matrix'] = matrix_compare(-x10, umatrix.matrix([[0, -1, -2, -3],[-4, -5, -6, -7],[-8, -9, -10, -11],[-12, -13, -14, -15]]))
try:
result['matrix ** scaler'] = matrix_compare(x10**2, umatrix.matrix([[ 0, 1, 4, 9],[16 , 25, 36, 49],[64, 81, 100, 121],[144, 169, 196, 225]]))
except:
result['matrix ** scaler'] = (False, 'NotImplemented')
return result
def assignment():
result = {}
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x11[1,1] = 20
result['matrix element <- value'] = matrix_compare(x11, umatrix.matrix([[0,1,2],[4,20,6],[8,9,10],[12,13,14]]))
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x11[1,1] = [21, 23]
result['matrix element <- list'] = matrix_compare(x11, umatrix.matrix([[0,1,2],[4,21,6],[8,9,10],[12,13,14]]))
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x11[1,:] = 21
result['matrix row <- value'] = matrix_compare(x11, umatrix.matrix([[0,1,2],[21,21,21],[8,9,10],[12,13,14]]))
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x11[1,:] = [20, 21, 22]
result['matrix row <- list'] = matrix_compare(x11, umatrix.matrix([[0,1,2],[20,21,22],[8,9,10],[12,13,14]]))
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x11[:,1] = 20
result['matrix col <- value'] = matrix_compare(x11, umatrix.matrix([[0,20,2],[4,20,6],[8,20,10],[12,20,14]]))
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x11[:,1] = [20, 21, 22, 23]
result['matrix col <- list'] = matrix_compare(x11, umatrix.matrix([[0,20,2],[4,21,6],[8,22,10],[12,23,14]]))
x10 = umatrix.matrix([[0,1,2,3],[4,5,6,7],[8,9,10,11],[12,13,14,15]])
x10[1:3,1:3] = 20
result['submatrix <- value'] = matrix_compare(x10, umatrix.matrix([[0,1,2,3],[4,20,20,7],[8,20,20,11],[12,13,14,15]]))
x10 = umatrix.matrix([[0,1,2,3],[4,5,6,7],[8,9,10,11],[12,13,14,15]])
x10[1:3,1:3] = [20,21,22,23]
result['submatrix <- list'] = matrix_compare(x10, umatrix.matrix([[0,1,2,3],[4,20,21,7],[8,22,23,11],[12,13,14,15]]))
x10 = umatrix.matrix([[0,1,2,3],[4,5,6,7],[8,9,10,11],[12,13,14,15]])
x10[1:3,1:3] = umatrix.matrix([[20,21],[22,23]])
result['submatrix <- matrix'] = matrix_compare(x10, umatrix.matrix([[0,1,2,3],[4,20,21,7],[8,22,23,11],[12,13,14,15]]))
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
try:
x11[1] = [18,19]
result['matrix non-splice <- matrix/vector'] = not matrix_compare(x11, umatrix.matrix([[0,1,2],[18,19,6],[8,9,10],[12,13,14]]))
except NotImplementedError:
result['matrix non-splice <- matrix/vector'] = True
return result
def slicing():
result = {}
x10 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
result['extract single element'] = x10[1,2] == 6
result['extract a row'] = matrix_compare(x10[1,:], umatrix.matrix([[4, 5, 6]]))
result['extract a col'] = matrix_compare(x10[:,1], umatrix.matrix([1, 5, 9, 13], cstride=1, rstride=1))
result['extract rows'] = matrix_compare(x10[1:4,:], umatrix.matrix([[4, 5, 6],[8, 9, 10],[12, 13, 14]]))
result['extract columns'] = matrix_compare(x10[:,1:3], umatrix.matrix([[1, 2],[5, 6],[9, 10],[13, 14]]))
result['extract sub'] = matrix_compare(x10[1:3,1:3], umatrix.matrix([[5, 6],[9, 10]]))
result['extract row from transpose'] = matrix_compare(x10.T[0], umatrix.matrix([[0, 4, 8, 12]]))
result['extract col from transpose'] = matrix_compare(x10.T[:,1], umatrix.matrix([4, 5, 6], cstride=1, rstride=1))
result['extract sub from transpose'] = matrix_compare(x10.T[1:3,1:3], umatrix.matrix([[5, 9],[6, 10]]))
return result
def products():
result = {}
x11 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
x10 = umatrix.matrix([[0,1,2,3],[4,5,6,7],[8,9,10,11],[12,13,14,15]])
x1 = umatrix.matrix([[0.71,-0.71,0.7],[0.71,0.71,0.5],[0,0,1]])
y_row = umatrix.matrix([[1,0,1]])
y_col = umatrix.matrix([1, 0, 1], cstride=1, rstride=1)
result['matrix * scaler'] = matrix_compare(x10*2, umatrix.matrix([[0, 2, 4, 6],[8, 10, 12, 14],[16, 18, 20, 22],[24, 26, 28, 30]]))
result['matrix * matrix elementwise'] = matrix_compare(x11*x11, umatrix.matrix([[0, 1, 4],[16, 25, 36],[64, 81, 100],[144, 169, 196]]))
result['row dot matrix 1x3 . 3x3'] = matrix_compare(ulinalg.dot(y_row,x1), umatrix.matrix([[ 0.71, -0.71, 1.7 ]]))
try:
result['matrix dot col 3x3 . 3x1'] = matrix_compare(ulinalg.dot(x1,y_col), umatrix.matrix([1.41, 1.21, 1.0], cstride=1, rstride=1))
except ValueError:
result['matrix dot col 3x3 . 3x1'] = False
x = umatrix.matrix([[ 3., -2., -2.]])
y = umatrix.matrix([[-1., 0., 5.]])
x1 = umatrix.matrix([[ 3., -2.]])
y1 = umatrix.matrix([[-1., 0.]])
result['cross product (x,y)'] = matrix_compare(ulinalg.cross(x,y), umatrix.matrix([[-10.0 , -13.0 , -2.0]]))
result['cross product (y,x)'] = matrix_compare(ulinalg.cross(y,x), umatrix.matrix([[10.0 , 13.0 , 2.0]]))
result['cross product 2 (x,y)'] = matrix_compare(ulinalg.cross(x1,y1), umatrix.matrix([[-2.0]]))
x = umatrix.matrix([[ 3., -2., -2.],[-1., 0., 5.]])
y = umatrix.matrix([[-1., 0., 5.]])
try:
result['cross product shape mismatch (x,y)'] = matrix_compare(ulinalg.cross(x,y), umatrix.matrix([[-10.0 , -13.0 , -2.0]]))
except ValueError:
result['cross product shape mismatch (x,y)'] = True
return result
def iteration():
result = {}
x10 = umatrix.matrix([[0,1,2],[4,5,6],[8,9,10],[12,13,14]])
Z = [i for i in x10]
result['iteration over matrix'] = Z == [umatrix.matrix([[0, 1, 2]]), umatrix.matrix([[4, 5, 6]]), umatrix.matrix([[8 , 9 , 10]]), umatrix.matrix([[12, 13, 14]])]
Z = [i for i in x10[1,:]]
result['iteration over row slice'] = Z == [4, 5, 6]
Z = [i for i in x10[:,1]]
result['iteration over col slice'] = Z == [1, 5, 9, 13]
Z = [i for i in x10[1:3,1:2]]
result['iteration over submatrix'] = Z == [5, 9]
return result
def det_inv_test():
result = {}
# first test
g = umatrix.matrix([[ 0. , 0. , 0. , 0. , 0. , 1. ],
[ 0.03125, 0.0625 , 0.125 , 0.25 , 0.5 , 1. ],
[ 0. , 0. , 0. , 0. , 1. , 0. ],
[ 0.3125 , 0.5 , 0.75 , 1. , 1. , 0. ],
[ 0. , 0. , 0. , 2. , 0. , 0. ],
[ 2.5 , 3. , 3. , 2. , 0. , 0. ]])
g_inv = umatrix.matrix([[-192. , 192. , -48. , -48. , -4. , 4. ],
[ 240. , -240. , 64. , 56. , 6. , -4. ],
[ -80. , 80. , -24. , -16. , -3. , 1. ],
[ 0. , 0. , 0. , 0. , 0.5, 0. ],
[ 0. , 0. , 1. , 0. , 0. , 0. ],
[ 1. , 0. , 0. , 0. , 0. , 0. ]])
(det,inv) = ulinalg.det_inv(g)
result['determinant 1'] = (abs(det - 0.0078125) < 0.000001)
result['inverse 1'] = umatrix.matrix_equal(inv, g_inv, 0.000001)
# second test
x = umatrix.matrix([[3.,2.,0.,1.],[4.,0.,1.,2.],[3.,0.,2.,1.],[9.,2.,3.,1.]])
(det,inv) = ulinalg.det_inv(x)
det_res = det == 24.0
f = umatrix.matrix([[-0.25 , 0.25 , -0.5 , 0.25 ],
[0.66666666666666667 , -0.49999999999999999, 0.50000000000000001 , -0.16666666666666667],
[0.16666666666666667 , -0.49999999999999999, 1.00000000000000002 , -0.16666666666666667],
[0.41666666666666667 , 0.25 , 0.50000000000000001 , -0.41666666666666667]])
result['inverse 2'] = matrix_compare(inv, f, tol=eps*2)#, tol=0.000000000000001)
f[3,3] = -0.416668
result['determinant 2'] = det_res
result['matrix_equal True'] = umatrix.matrix_equal(inv, f, tol=0.0001)
result['matrix_equal False'] = umatrix.matrix_equal(inv, f) == False
x1 = umatrix.matrix([[0.71,-0.71,0.7],[0.71,0.71,0.5],[0,0,1]])
z = ulinalg.pinv(x1)
result['psuedo inverse'] = matrix_compare(z, umatrix.matrix([[0.7042253521126759 , 0.704225352112676 , -0.8450704225352109 ],
[-0.704225352112676 , 0.704225352112676 , 0.1408450704225352 ],
[1.110223024625157e-16, 5.551115123125783e-17, 0.9999999999999998 ]]), tol=2*eps)
return result
final_results = {}
for t in [construct,
equality,
scaler,
det_inv_test,
products,
assignment,
slicing,
iteration,
list_ops,
element_wise
]:
results = t()
print('---', t.__name__, '-'*(60-len(t.__name__)))
for k,v in results.items():
if type(v) == tuple:
print('Test : {0:44s} ===> {1} : {2}'.format(k, [' Fail','Pass'][v[0]], v[1]))
else:
print('Test : {0:44s} ===> {1}'.format(k, [' Fail','Pass'][v]))
final_results.update(results)
tests_total = len(final_results)
tests_passed = 0
for i in final_results.values():
if type(i) == tuple:
tests_passed += i[0]
else:
tests_passed += i
print('-'*60)
print('Total ==> {0:3d} Passed ==> {1:3d} Failed ==> {2:3d} Tol ==> {3}'.format(tests_total, tests_passed, tests_total-tests_passed, eps))