def test_cross_entropy_derivative_cputensor(): be = CPU(rng_seed=0) outputs = CPUTensor([0.5, 0.9, 0.1, 0.0001]) targets = CPUTensor([0.5, 0.99, 0.01, 0.2]) temp = [be.zeros(outputs.shape), be.zeros(outputs.shape)] expected_result = ((outputs.asnumpyarray() - targets.asnumpyarray()) / (outputs.asnumpyarray() * (1 - outputs.asnumpyarray()))) assert_tensor_near_equal( expected_result, cross_entropy_derivative(be, outputs, targets, temp))
def test_cross_entropy_derivative_cputensor(): be = CPU(rng_seed=0) outputs = CPUTensor([0.5, 0.9, 0.1, 0.0001]) targets = CPUTensor([0.5, 0.99, 0.01, 0.2]) temp = [be.zeros(outputs.shape), be.zeros(outputs.shape)] expected_result = ((outputs.asnumpyarray() - targets.asnumpyarray()) / (outputs.asnumpyarray() * (1 - outputs.asnumpyarray()))) assert_tensor_near_equal(expected_result, cross_entropy_derivative(be, outputs, targets, temp))
def compare_cpu_tensors(inputs, outputs, deriv=False): rlin = RectLeaky() be = CPU() temp = be.zeros(inputs.shape) if deriv is True: rlin.apply_derivative(be, CPUTensor(inputs), temp) else: rlin.apply_function(be, CPUTensor(inputs), temp) be.subtract(temp, CPUTensor(outputs), temp) assert_tensor_equal(temp, be.zeros(inputs.shape))
def test_cross_entropy_cputensor(): be = CPU(rng_seed=0) outputs = CPUTensor([0.5, 0.9, 0.1, 0.0001]) targets = CPUTensor([0.5, 0.99, 0.01, 0.2]) temp = [be.zeros(outputs.shape), be.zeros(outputs.shape)] expected_result = np.sum((- targets.asnumpyarray()) * np.log(outputs.asnumpyarray()) - (1 - targets.asnumpyarray()) * np.log(1 - outputs.asnumpyarray()), keepdims=True) assert_tensor_near_equal(expected_result, cross_entropy(be, outputs, targets, temp))
def test_cross_entropy_cputensor(): be = CPU(rng_seed=0) outputs = CPUTensor([0.5, 0.9, 0.1, 0.0001]) targets = CPUTensor([0.5, 0.99, 0.01, 0.2]) temp = [be.zeros(outputs.shape), be.zeros(outputs.shape)] expected_result = np.sum( (-targets.asnumpyarray()) * np.log(outputs.asnumpyarray()) - (1 - targets.asnumpyarray()) * np.log(1 - outputs.asnumpyarray()), keepdims=True) assert_tensor_near_equal(expected_result, cross_entropy(be, outputs, targets, temp))
def test_cross_entropy_limits(): be = CPU(rng_seed=0) outputs = CPUTensor([0.5, 1.0, 0.0, 0.0001]) targets = CPUTensor([0.5, 0.0, 1.0, 0.2]) eps = 2**-23 temp = [be.zeros(outputs.shape), be.zeros(outputs.shape)] expected_result = np.sum( (-targets.asnumpyarray()) * np.log(outputs.asnumpyarray() + eps) - (1 - targets.asnumpyarray()) * np.log(1 - outputs.asnumpyarray() + eps), keepdims=True) assert_tensor_near_equal(expected_result, cross_entropy(be, outputs, targets, temp, eps))
def test_softmax_cputensor(): sftmx = Softmax() inputs = np.array([0, 1, -2]).reshape((3, 1)) be = CPU(rng_seed=0) temp = be.zeros((3, 1)) outputs = np.exp(inputs-1) / np.sum(np.exp(inputs-1)) sftmx.apply_function(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_logistic_cputensor(): lgstc = Logistic() inputs = np.array([0, 1, -2]).reshape((3, 1)) be = CPU(rng_seed=0) temp = be.zeros((3, 1)) outputs = 1.0 / (1.0 + np.exp(-inputs)) lgstc.apply_function(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_softmax_cputensor(): sftmx = Softmax() inputs = np.array([0, 1, -2]).reshape((3, 1)) be = CPU(rng_seed=0) temp = be.zeros((3, 1)) outputs = np.exp(inputs - 1) / np.sum(np.exp(inputs - 1)) sftmx.apply_function(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_tanh_cputensor(): tntest = Tanh() be = CPU(rng_seed=0) CPUTensor([0, 1, -2]) inputs = np.array([0, 1, -2]) temp = be.zeros(inputs.shape) outputs = np.array([true_tanh(0), true_tanh(1), true_tanh(-2)]) tntest.apply_function(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_logistic_derivative_cputensor(): lgstc = Logistic() inputs = np.array([0, 1, -2]).reshape((3, 1)) be = CPU(rng_seed=0) outputs = 1.0 / (1.0 + np.exp(-inputs)) outputs = outputs * (1.0 - outputs) temp = be.zeros(inputs.shape) lgstc.apply_derivative(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_tanh_derivative_cputensor(): tntest = Tanh() inputs = np.array([0, 1, -2]) be = CPU(rng_seed=0) outputs = np.array( [1 - true_tanh(0)**2, 1 - true_tanh(1)**2, 1 - true_tanh(-2)**2]) temp = be.zeros(inputs.shape) tntest.apply_derivative(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_tanh_cputensor(): tntest = Tanh() be = CPU(rng_seed=0) CPUTensor([0, 1, -2]) inputs = np.array([0, 1, -2]) temp = be.zeros(inputs.shape) outputs = np.array([true_tanh(0), true_tanh(1), true_tanh(-2)]) tntest.apply_function(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_tanh_derivative_cputensor(): tntest = Tanh() inputs = np.array([0, 1, -2]) be = CPU(rng_seed=0) outputs = np.array([1 - true_tanh(0) ** 2, 1 - true_tanh(1) ** 2, 1 - true_tanh(-2) ** 2]) temp = be.zeros(inputs.shape) tntest.apply_derivative(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_softmax_derivative_cputensor(): sftmx = Softmax() inputs = np.array([0, 1, -2]).reshape((3, 1)) be = CPU(rng_seed=0) outputs = np.exp(inputs) / np.sum(np.exp(inputs)) errmat = np.ones(inputs.shape) a = np.einsum('ij,ji->i', errmat.T, outputs) outputs = outputs * (errmat - a[np.newaxis, :]) temp = be.zeros(inputs.shape) sftmx.apply_derivative(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
def test_softmax_derivative_cputensor(): sftmx = Softmax() inputs = np.array([0, 1, -2]).reshape((3, 1)) be = CPU(rng_seed=0) outputs = np.exp(inputs) / np.sum(np.exp(inputs)) errmat = np.ones(inputs.shape) a = np.einsum('ij,ji->i', errmat.T, outputs) outputs = outputs * (errmat - a[np.newaxis, :]) temp = be.zeros(inputs.shape) sftmx.apply_derivative(be, CPUTensor(inputs), temp) assert_tensor_near_equal(CPUTensor(outputs), temp)
class TestCPU(object): def __init__(self): # this code gets called prior to each test self.be = CPU() def test_empty_creation(self): tns = self.be.empty((4, 3)) assert tns.shape == (4, 3) def test_array_creation(self): tns = self.be.array([[1, 2], [3, 4]]) assert tns.shape == (2, 2) assert_tensor_equal(tns, CPUTensor([[1, 2], [3, 4]])) def test_zeros_creation(self): tns = self.be.zeros([3, 1]) assert tns.shape == (3, 1) assert_tensor_equal(tns, CPUTensor([[0], [0], [0]])) def test_ones_creation(self): tns = self.be.ones([1, 4]) assert tns.shape == (1, 4) assert_tensor_equal(tns, CPUTensor([[1, 1, 1, 1]])) def test_all_equal(self): left = self.be.ones([2, 2]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 1], [1, 1]])) def test_some_equal(self): left = self.be.ones([2, 2]) right = self.be.array([[0, 1], [0, 1]]) out = self.be.empty([2, 2]) self.be.equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 1], [0, 1]])) def test_none_equal(self): left = self.be.ones([2, 2]) right = self.be.zeros([2, 2]) out = self.be.empty([2, 2]) self.be.equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 0], [0, 0]])) def test_all_not_equal(self): left = self.be.ones([2, 2]) right = self.be.zeros([2, 2]) out = self.be.empty([2, 2]) self.be.not_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 1], [1, 1]])) def test_some_not_equal(self): left = self.be.ones([2, 2]) right = self.be.array([[0, 1], [0, 1]]) out = self.be.empty([2, 2]) self.be.not_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 0], [1, 0]])) def test_none_not_equal(self): left = self.be.ones([2, 2]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.not_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 0], [0, 0]])) def test_greater(self): left = self.be.array([[-1, 0], [1, 92]]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.greater(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 0], [0, 1]])) def test_greater_equal(self): left = self.be.array([[-1, 0], [1, 92]]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.greater_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 0], [1, 1]])) def test_less(self): left = self.be.array([[-1, 0], [1, 92]]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.less(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 1], [0, 0]])) def test_less_equal(self): left = self.be.array([[-1, 0], [1, 92]]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.less_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 1], [1, 0]])) def test_argmin_noaxis(self): be = CPU() tsr = be.array([[-1, 0], [1, 92]]) out = be.empty([1, 1]) be.argmin(tsr, None, out) assert_tensor_equal(out, CPUTensor([[0]])) def test_argmin_axis0(self): be = CPU() tsr = be.array([[-1, 0], [1, 92]]) out = be.empty((1, 2)) be.argmin(tsr, 0, out) assert_tensor_equal(out, CPUTensor([[0, 0]])) def test_argmin_axis1(self): be = CPU() tsr = be.array([[-1, 10], [11, 9]]) out = be.empty((2, 1)) be.argmin(tsr, 1, out) assert_tensor_equal(out, CPUTensor([0, 1])) def test_argmax_noaxis(self): be = CPU() tsr = be.array([[-1, 0], [1, 92]]) out = be.empty([1, 1]) be.argmax(tsr, None, out) assert_tensor_equal(out, CPUTensor(3)) def test_argmax_axis0(self): be = CPU() tsr = be.array([[-1, 0], [1, 92]]) out = be.empty((2, )) be.argmax(tsr, 0, out) assert_tensor_equal(out, CPUTensor([1, 1])) def test_argmax_axis1(self): be = CPU() tsr = be.array([[-1, 10], [11, 9]]) out = be.empty((2, )) be.argmax(tsr, 1, out) assert_tensor_equal(out, CPUTensor([1, 0])) def test_2norm(self): tsr = self.be.array([[-1, 0], [1, 3]]) rpow = 1. / 2 # -> sum([[1, 0], [1, 9]], axis=0)**.5 -> sqrt([2, 9]) assert_tensor_equal(self.be.norm(tsr, order=2, axis=0), CPUTensor([[2**rpow, 9**rpow]])) # -> sum([[1, 0], [1, 9]], axis=1)**.5 -> sqrt([1, 10]) assert_tensor_equal(self.be.norm(tsr, order=2, axis=1), CPUTensor([1**rpow, 10**rpow])) def test_1norm(self): tsr = self.be.array([[-1, 0], [1, 3]]) # -> sum([[1, 0], [1, 3]], axis=0)**1 -> [2, 3] assert_tensor_equal(self.be.norm(tsr, order=1, axis=0), CPUTensor([[2, 3]])) # -> sum([[1, 0], [1, 3]], axis=1)**1 -> [1, 4] assert_tensor_equal(self.be.norm(tsr, order=1, axis=1), CPUTensor([1, 4])) def test_0norm(self): tsr = self.be.array([[-1, 0], [1, 3]]) # -> sum(tsr != 0, axis=0) -> [2, 1] assert_tensor_equal(self.be.norm(tsr, order=0, axis=0), CPUTensor([[2, 1]])) # -> sum(tsr != 0, axis=1) -> [1, 2] assert_tensor_equal(self.be.norm(tsr, order=0, axis=1), CPUTensor([1, 2])) def test_infnorm(self): tsr = self.be.array([[-1, 0], [1, 3]]) # -> max(abs(tsr), axis=0) -> [1, 3] assert_tensor_equal(self.be.norm(tsr, order=float('inf'), axis=0), CPUTensor([[1, 3]])) # -> max(abs(tsr), axis=1) -> [1, 3] assert_tensor_equal(self.be.norm(tsr, order=float('inf'), axis=1), CPUTensor([1, 3])) def test_neginfnorm(self): tsr = self.be.array([[-1, 0], [1, 3]]) # -> min(abs(tsr), axis=0) -> [1, 0] assert_tensor_equal(self.be.norm(tsr, order=float('-inf'), axis=0), CPUTensor([[1, 0]])) # -> min(abs(tsr), axis=1) -> [0, 1] assert_tensor_equal(self.be.norm(tsr, order=float('-inf'), axis=1), CPUTensor([0, 1])) def test_lrgnorm(self): tsr = self.be.array([[-1, 0], [1, 3]]) rpow = 1. / 5 # -> sum([[1, 0], [1, 243]], axis=0)**rpow -> rpow([2, 243]) assert_tensor_equal(self.be.norm(tsr, order=5, axis=0), CPUTensor([[2**rpow, 243**rpow]])) # -> sum([[1, 0], [1, 243]], axis=1)**rpow -> rpow([1, 244]) # 244**.2 == ~3.002465 hence the near_equal test assert_tensor_near_equal(self.be.norm(tsr, order=5, axis=1), CPUTensor([1**rpow, 244**rpow]), 1e-6) def test_negnorm(self): tsr = self.be.array([[-1, -2], [1, 3]]) rpow = -1. / 3 # -> sum([[1, .125], [1, .037037]], axis=0)**rpow -> rpow([2, .162037]) assert_tensor_equal(self.be.norm(tsr, order=-3, axis=0), CPUTensor([[2**rpow, .162037037037**rpow]])) # -> sum([[1, .125], [1, .037037]], axis=1)**rpow -> # rpow([1.125, 1.037037]) assert_tensor_near_equal(self.be.norm(tsr, order=-3, axis=1), CPUTensor([1.125**rpow, 1.037037**rpow]), 1e-6)
class TestCPU(object): def __init__(self): # this code gets called prior to each test self.be = CPU() def test_empty_creation(self): tns = self.be.empty((4, 3)) assert tns.shape == (4, 3) def test_array_creation(self): tns = self.be.array([[1, 2], [3, 4]]) assert tns.shape == (2, 2) assert_tensor_equal(tns, CPUTensor([[1, 2], [3, 4]])) def test_zeros_creation(self): tns = self.be.zeros([3, 1]) assert tns.shape == (3, 1) assert_tensor_equal(tns, CPUTensor([[0], [0], [0]])) def test_ones_creation(self): tns = self.be.ones([1, 4]) assert tns.shape == (1, 4) assert_tensor_equal(tns, CPUTensor([[1, 1, 1, 1]])) def test_all_equal(self): left = self.be.ones([2, 2]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 1], [1, 1]])) def test_some_equal(self): left = self.be.ones([2, 2]) right = self.be.array([[0, 1], [0, 1]]) out = self.be.empty([2, 2]) self.be.equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 1], [0, 1]])) def test_none_equal(self): left = self.be.ones([2, 2]) right = self.be.zeros([2, 2]) out = self.be.empty([2, 2]) self.be.equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 0], [0, 0]])) def test_all_not_equal(self): left = self.be.ones([2, 2]) right = self.be.zeros([2, 2]) out = self.be.empty([2, 2]) self.be.not_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 1], [1, 1]])) def test_some_not_equal(self): left = self.be.ones([2, 2]) right = self.be.array([[0, 1], [0, 1]]) out = self.be.empty([2, 2]) self.be.not_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 0], [1, 0]])) def test_none_not_equal(self): left = self.be.ones([2, 2]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.not_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 0], [0, 0]])) def test_greater(self): left = self.be.array([[-1, 0], [1, 92]]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.greater(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 0], [0, 1]])) def test_greater_equal(self): left = self.be.array([[-1, 0], [1, 92]]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.greater_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[0, 0], [1, 1]])) def test_less(self): left = self.be.array([[-1, 0], [1, 92]]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.less(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 1], [0, 0]])) def test_less_equal(self): left = self.be.array([[-1, 0], [1, 92]]) right = self.be.ones([2, 2]) out = self.be.empty([2, 2]) self.be.less_equal(left, right, out) assert out.shape == (2, 2) assert_tensor_equal(out, CPUTensor([[1, 1], [1, 0]])) def test_argmin_noaxis(self): be = CPU() tsr = be.array([[-1, 0], [1, 92]]) out = be.empty([1, 1]) be.argmin(tsr, None, out) assert_tensor_equal(out, CPUTensor([[0]])) def test_argmin_axis0(self): be = CPU() tsr = be.array([[-1, 0], [1, 92]]) out = be.empty((1, 2)) be.argmin(tsr, 0, out) assert_tensor_equal(out, CPUTensor([[0, 0]])) def test_argmin_axis1(self): be = CPU() tsr = be.array([[-1, 10], [11, 9]]) out = be.empty((2, 1)) be.argmin(tsr, 1, out) assert_tensor_equal(out, CPUTensor([0, 1])) def test_argmax_noaxis(self): be = CPU() tsr = be.array([[-1, 0], [1, 92]]) out = be.empty([1, 1]) be.argmax(tsr, None, out) assert_tensor_equal(out, CPUTensor(3)) def test_argmax_axis0(self): be = CPU() tsr = be.array([[-1, 0], [1, 92]]) out = be.empty((2, )) be.argmax(tsr, 0, out) assert_tensor_equal(out, CPUTensor([1, 1])) def test_argmax_axis1(self): be = CPU() tsr = be.array([[-1, 10], [11, 9]]) out = be.empty((2, )) be.argmax(tsr, 1, out) assert_tensor_equal(out, CPUTensor([1, 0])) def test_2norm(self): tsr = self.be.array([[-1, 0], [1, 3]]) rpow = 1. / 2 # -> sum([[1, 0], [1, 9]], axis=0)**.5 -> sqrt([2, 9]) assert_tensor_equal(self.be.norm(tsr, order=2, axis=0), CPUTensor([[2**rpow, 9**rpow]])) # -> sum([[1, 0], [1, 9]], axis=1)**.5 -> sqrt([1, 10]) assert_tensor_equal(self.be.norm(tsr, order=2, axis=1), CPUTensor([1**rpow, 10**rpow])) def test_1norm(self): tsr = self.be.array([[-1, 0], [1, 3]]) # -> sum([[1, 0], [1, 3]], axis=0)**1 -> [2, 3] assert_tensor_equal(self.be.norm(tsr, order=1, axis=0), CPUTensor([[2, 3]])) # -> sum([[1, 0], [1, 3]], axis=1)**1 -> [1, 4] assert_tensor_equal(self.be.norm(tsr, order=1, axis=1), CPUTensor([1, 4])) def test_0norm(self): tsr = self.be.array([[-1, 0], [1, 3]]) # -> sum(tsr != 0, axis=0) -> [2, 1] assert_tensor_equal(self.be.norm(tsr, order=0, axis=0), CPUTensor([[2, 1]])) # -> sum(tsr != 0, axis=1) -> [1, 2] assert_tensor_equal(self.be.norm(tsr, order=0, axis=1), CPUTensor([1, 2])) def test_infnorm(self): tsr = self.be.array([[-1, 0], [1, 3]]) # -> max(abs(tsr), axis=0) -> [1, 3] assert_tensor_equal(self.be.norm(tsr, order=float('inf'), axis=0), CPUTensor([[1, 3]])) # -> max(abs(tsr), axis=1) -> [1, 3] assert_tensor_equal(self.be.norm(tsr, order=float('inf'), axis=1), CPUTensor([1, 3])) def test_neginfnorm(self): tsr = self.be.array([[-1, 0], [1, 3]]) # -> min(abs(tsr), axis=0) -> [1, 0] assert_tensor_equal(self.be.norm(tsr, order=float('-inf'), axis=0), CPUTensor([[1, 0]])) # -> min(abs(tsr), axis=1) -> [0, 1] assert_tensor_equal(self.be.norm(tsr, order=float('-inf'), axis=1), CPUTensor([0, 1])) def test_lrgnorm(self): tsr = self.be.array([[-1, 0], [1, 3]]) rpow = 1. / 5 # -> sum([[1, 0], [1, 243]], axis=0)**rpow -> rpow([2, 243]) assert_tensor_equal(self.be.norm(tsr, order=5, axis=0), CPUTensor([[2**rpow, 243**rpow]])) # -> sum([[1, 0], [1, 243]], axis=1)**rpow -> rpow([1, 244]) # 244**.2 == ~3.002465 hence the near_equal test assert_tensor_near_equal(self.be.norm(tsr, order=5, axis=1), CPUTensor([1**rpow, 244**rpow]), 1e-6) def test_negnorm(self): tsr = self.be.array([[-1, -2], [1, 3]]) rpow = -1. / 3 # -> sum([[1, .125], [1, .037037]], axis=0)**rpow -> rpow([2, .162037]) assert_tensor_equal(self.be.norm(tsr, order=-3, axis=0), CPUTensor([[2**rpow, .162037037037**rpow]])) # -> sum([[1, .125], [1, .037037]], axis=1)**rpow -> # rpow([1.125, 1.037037]) assert_tensor_near_equal(self.be.norm(tsr, order=-3, axis=1), CPUTensor([1.125**rpow, 1.037037**rpow]), 1e-6)