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
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 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
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
