def test_lu_matmul(self):
L, U, P = ra.lu(self.exMatrix)
PM = P @ self.exMatrix
LU = L @ U
PiLU = ra.inv(P) @ L @ U
myEqual = lambda x,y: all(x.value.flat == y.value.flat)
self.assertTrue(myEqual(PM, LU))
self.assertTrue(myEqual(self.exMatrix, PiLU))
def setUp(self):
self.exMatrix = ra.RationalMatrix((10*np.random.rand(5,5)).astype(int))
self.exMatrix2 = ra.RationalMatrix((10*np.random.rand(5,5)).astype(int))
self.matAdd1 = self.exMatrix + self.exMatrix2
self.matAdd2 = self.exMatrix2 + self.exMatrix
self.intAdd1 = 5 + self.exMatrix
self.intAdd2 = self.exMatrix + 5
self.fracAdd1 = Fr(1,3) + self.exMatrix
self.fracAdd2 = self.exMatrix + Fr(1,3)
self.floatAdd1 = 0.5 + self.exMatrix
self.floatAdd2 = self.exMatrix + 0.5
def setUp(self):
self.exMatrix = ra.RationalMatrix((10*np.random.rand(5,5)).astype(int))
self.intMultiply1 = 5 * self.exMatrix
self.intMultiply2 = self.exMatrix * 5
self.fracMultiply1 = Fr(1,3) * self.exMatrix
self.fracMultiply2 = self.exMatrix * Fr(1,3)
self.floatMultiply1 = 0.5 * self.exMatrix
self.floatMultiply2 = self.exMatrix * 0.5
def setUp(self):
self.exColumnVector = ra.RationalVector((10*np.random.rand(5,1)).astype(int))
self.intMultiply1 = 5 * self.exColumnVector
self.intMultiply2 = self.exColumnVector * 5
self.fracMultiply1 = Fr(1,3) * self.exColumnVector
self.fracMultiply2 = self.exColumnVector * Fr(1,3)
self.floatMultiply1 = 0.5 * self.exColumnVector
self.floatMultiply2 = self.exColumnVector * 0.5
def test_inverse(self):
invM = ra.inv(self.exMatrix)
self.assertEqual(invM.value[1,2], Fr(63, 3800))
self.assertEqual(invM.value[1,4], Fr(-99, 3800))
self.assertEqual(invM.value[3,3], Fr(1))
self.assertEqual(invM.value[0,3], Fr(0))
self.assertEqual(type(invM.value[1,4]), Fr)
self.assertEqual(type(invM), ra.RationalMatrix)
self.assertEqual(invM.value.shape, (5, 5))
def setUp(self):
self.exMatrix = ra.RationalMatrix(np.zeros((5,5)).astype(int))
self.exMatrix.value[2,4] = Fr(11,7)
self.exMatrix.value[1,2] = Fr(3,5)
self.exColumnVector = ra.RationalVector(np.zeros((5,1)).astype(int))
self.exColumnVector.value[2] = Fr(3,4)
self.exColumnVector.value[4] = Fr(9,2)
self.exRowVector = ra.RationalVector(np.zeros((1,5)).astype(int))
self.exRowVector.value[0][2] = Fr(5,7)
self.exRowVector.value[0][0] = Fr(9,2)
self.mulMM = self.exMatrix @ self.exMatrix
self.mulMC = self.exMatrix @ self.exColumnVector
self.mulCR = self.exColumnVector @ self.exRowVector
self.mulRM = self.exRowVector @ self.exMatrix
self.mulRC = self.exRowVector @ self.exColumnVector
def test_inverse_matmul(self):
invM = ra.inv(self.exMatrix)
I1 = invM @ self.exMatrix
I2 = self.exMatrix @ invM
myEqual = lambda x,y: all(x.value.flat == y.value.flat)
self.assertTrue(myEqual(I1, I2))
self.assertEqual(I1.value[2,2], Fr(1))
self.assertEqual(I1.value[1,2], Fr(0))
self.assertEqual(type(I1.value[1,4]), Fr)
self.assertEqual(type(I1), ra.RationalMatrix)
self.assertEqual(I1.value.shape, (5, 5))
def setUp(self):
self.exRowVector = ra.RationalVector((10*np.random.rand(1,5)).astype(int))
self.exRowVector2 = ra.RationalVector((10*np.random.rand(1,5)).astype(int))
self.exColumnVector = ra.RationalVector((10*np.random.rand(5,1)).astype(int))
self.exColumnVector2 = ra.RationalVector((10*np.random.rand(5,1)).astype(int))
self.rowVecAdd1 = self.exRowVector + self.exRowVector2
self.rowVecAdd2 = self.exRowVector2 + self.exRowVector
self.colVecAdd1 = self.exColumnVector + self.exColumnVector2
self.colVecAdd2 = self.exColumnVector2 + self.exColumnVector
self.intRowAdd1 = 5 + self.exRowVector
self.intRowAdd2 = self.exRowVector + 5
self.fracRowAdd1 = Fr(1,3) + self.exRowVector
self.fracRowAdd2 = self.exRowVector + Fr(1,3)
self.floatRowAdd1 = 0.5 + self.exRowVector
self.floatRowAdd2 = self.exRowVector + 0.5
self.intColAdd1 = 5 + self.exColumnVector
self.intColAdd2 = self.exColumnVector + 5
self.fracColAdd1 = Fr(1,3) + self.exColumnVector
self.fracColAdd2 = self.exColumnVector + Fr(1,3)
self.floatColAdd1 = 0.5 + self.exColumnVector
self.floatColAdd2 = self.exColumnVector + 0.5
def test_lu_decomposition(self):
L, U, P = ra.lu(self.exMatrix)
self.assertEqual(L.value[4,2], Fr(3, 71))
self.assertEqual(L.value[2,4], Fr(0))
self.assertEqual(U.value[4,4], Fr(760, 497))
self.assertEqual(U.value[2,4], Fr(1))
self.assertEqual(U.value[2,1], Fr(0))
self.assertEqual(P.value[4,2], Fr(1))
self.assertEqual(P.value[4,3], Fr(0))
self.assertEqual(type(L.value[1,4]), Fr)
self.assertEqual(type(L), ra.RationalMatrix)
self.assertEqual(L.value.shape, (5, 5))
self.assertEqual(type(U.value[1,4]), Fr)
self.assertEqual(type(U), ra.RationalMatrix)
self.assertEqual(U.value.shape, (5, 5))
self.assertEqual(type(P.value[1,4]), Fr)
self.assertEqual(type(P), ra.RationalMatrix)
self.assertEqual(P.value.shape, (5, 5))
def setUp(self):
self.exMatrix = ra.RationalMatrix(np.identity(5).astype(int))
self.exMatrix.value[2,4] = Fr(11,7)
self.exMatrix.value[1,2] = Fr(3,5)
self.exMatrix.value[4,2] = Fr(71,3)
def setUp(self):
self.exMatrixA = ra.RationalMatrix((10*np.random.rand(5,5)).astype(int))
self.exMatrixB = ra.RationalMatrix((10*np.random.rand(5,5)).astype(int))
self.exMatrixC = ra.RationalMatrix((10*np.random.rand(5,5)).astype(int))
self.exMatrixD = ra.RationalMatrix((10*np.random.rand(5,5)).astype(int))
def setUp(self):
self.exMatrix = ra.RationalMatrix(np.zeros((5,5)).astype(int))
self.exColumnVector = ra.RationalVector(np.zeros((5,1)).astype(int))
self.exRowVector = ra.RationalVector(np.zeros((1,5)).astype(int))
def setUp(self):
self.exMatrix = ra.RationalMatrix((10*np.random.rand(5,5)).astype(int))
self.exRowVector = ra.RationalVector((10*np.random.rand(1,5)).astype(int))
self.exColumnVector = ra.RationalVector((10*np.random.rand(5,1)).astype(int))