def test_det():
order = 2
shape = NumCpp.Shape(order)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols]).astype(float)
cArray.setArray(data)
assert round(NumCpp.det(cArray)) == round(np.linalg.det(data).item())
order = 3
shape = NumCpp.Shape(order)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols]).astype(float)
cArray.setArray(data)
assert round(NumCpp.det(cArray)) == round(np.linalg.det(data).item())
order = np.random.randint(4, 8, [1, ]).item()
shape = NumCpp.Shape(order)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols]).astype(float)
cArray.setArray(data)
assert round(NumCpp.det(cArray)) == round(np.linalg.det(data).item())
def test_randFloat():
shapeInput = np.random.randint(1, 100, [
2,
])
inShape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
values = np.random.randint(1, 100, [
2,
])
values.sort()
assert NumCpp.randFloat(inShape, values[0].item(),
values[1].item() + 1) is not None
assert NumCpp.randFloat(values[0].item(), values[1].item() + 1) is not None
def test_cholesky():
shapeInput = np.random.randint(5, 50, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
a = np.random.randint(1, 100, [shape.rows, shape.cols]).flatten()
aL = np.tril(a)
b = aL.dot(aL.transpose())
cArray.setArray(b)
assert np.array_equal(np.round(NumCpp.cholesky(cArray).getNumpyArray()),
np.round(aL))
def test_bernoulli():
shapeInput = np.random.randint(1, 100, [
2,
])
inShape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
p = np.random.rand()
randArray = NumCpp.bernoulli(inShape, p).getNumpyArray()
assert np.array_equiv(randArray.shape, shapeInput)
randValue = NumCpp.bernoulli(p)
assert isinstance(randValue, bool)
def test_factorial():
n = np.random.randint(0, 170)
assert (roundScaler(NumCpp.factorial_Scaler(n), NUM_DECIMALS_ROUND) ==
roundScaler(sp.factorial(n).item(), NUM_DECIMALS_ROUND))
shapeInput = np.random.randint(20, 100, [2, ])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArrayUInt32(shape)
data = np.random.randint(0, 170, [shape.rows, shape.cols], dtype=np.uint32)
cArray.setArray(data)
assert np.array_equal(roundArray(NumCpp.factorial_Array(cArray), NUM_DECIMALS_ROUND),
roundArray(sp.factorial(data), NUM_DECIMALS_ROUND))
def test_laplace():
if NumCpp.NO_USE_BOOST:
return
shapeInput = np.random.randint(1, 100, [
2,
])
inShape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
loc = np.random.rand() * 10
scale = np.random.rand() * 100
assert NumCpp.laplace(inShape, loc, scale) is not None
assert NumCpp.laplace(loc, scale) is not None
def test_gaussianFilter():
for mode in modes.keys():
shape = np.random.randint(100, 200, [2, ]).tolist()
cShape = NumCpp.Shape(shape[0], shape[1])
cArray = NumCpp.NdArray(cShape)
data = np.random.randint(100, 1000, shape).astype(np.double)
cArray.setArray(data)
constantValue = np.random.randint(0, 5, [1, ]).item() # only actaully needed for constant boundary condition
sigma = np.random.rand(1).item() * 2
dataOutC = NumCpp.gaussianFilter(cArray, sigma, modes[mode], constantValue).getNumpyArray()
dataOutPy = filters.gaussian_filter(data, sigma, mode=mode, cval=constantValue)
assert np.array_equal(np.round(dataOutC, 2), np.round(dataOutPy, 2))
def test_nonCentralChiSquared():
if NumCpp.NO_USE_BOOST:
return
shapeInput = np.random.randint(1, 100, [
2,
])
inShape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
k = np.random.rand() * 10
ll = np.random.rand() * 100
assert NumCpp.nonCentralChiSquared(inShape, k, ll) is not None
assert NumCpp.nonCentralChiSquared(k, ll) is not None
def test_choice():
shapeInput = np.random.randint(1, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols)
cArray.setArray(data)
assert NumCpp.choiceSingle(cArray) is not None
shapeInput = np.random.randint(1, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols)
cArray.setArray(data)
num = np.random.randint(1, data.size, [
1,
]).item()
assert NumCpp.choiceMultiple(cArray, num) is not None
def test_pivotLU_decomposition():
sizeInput = np.random.randint(5, 50)
shape = NumCpp.Shape(sizeInput)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols])
cArray.setArray(data)
l, u, p = NumCpp.pivotLU_decomposition(cArray)
lhs = p.dot(data)
rhs = l.dot(u)
assert np.array_equal(np.round(lhs, 10), np.round(rhs, 10))
shapeInput = np.random.randint(5, 50, [2, ])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols])
cArray.setArray(data)
uArray = NumCpp.NdArray()
sArray = NumCpp.NdArray()
vArray = NumCpp.NdArray()
NumCpp.svd(cArray, uArray, sArray, vArray)
data2 = np.dot(uArray.getNumpyArray(), np.dot(sArray.getNumpyArray(), vArray.getNumpyArray()))
assert np.array_equal(np.round(data, 9), np.round(data2, 9))
def test_matrix_power():
order = np.random.randint(5, 50, [1, ]).item()
shape = NumCpp.Shape(order)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols])
cArray.setArray(data)
assert np.array_equal(NumCpp.matrix_power(cArray, 0).getNumpyArray(), np.linalg.matrix_power(data, 0))
order = np.random.randint(5, 50, [1, ]).item()
shape = NumCpp.Shape(order)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols])
cArray.setArray(data)
assert np.array_equal(NumCpp.matrix_power(cArray, 1).getNumpyArray(), np.linalg.matrix_power(data, 1))
order = np.random.randint(5, 50, [1, ]).item()
shape = NumCpp.Shape(order)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols])
cArray.setArray(data)
assert np.array_equal(np.round(NumCpp.matrix_power(cArray, -1).getNumpyArray(), 8),
np.round(np.linalg.matrix_power(data, -1), 8))
order = np.random.randint(5, 50, [1, ]).item()
shape = NumCpp.Shape(order)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 5, [shape.rows, shape.cols]).astype(float)
cArray.setArray(data)
power = np.random.randint(2, 9, [1, ]).item()
assert np.array_equal(NumCpp.matrix_power(cArray, power).getNumpyArray(), np.linalg.matrix_power(data, power))
order = np.random.randint(5, 50, [1, ]).item()
shape = NumCpp.Shape(order)
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 100, [shape.rows, shape.cols])
cArray.setArray(data)
power = np.random.randint(2, 9, [1, ]).item() * -1
assert np.array_equal(np.round(NumCpp.matrix_power(cArray, power).getNumpyArray(), 9),
np.round(np.linalg.matrix_power(data, power), 9))
def test_gamma1pm1():
# There is no scipy equivalent to this function
value = np.random.rand(1).item()
assert NumCpp.gamma1pm1_Scaler(value) is not None
shapeInput = np.random.randint(20, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols)
cArray.setArray(data)
assert NumCpp.gamma1pm1_Array(cArray) is not None
def test_prime():
# There is no scipy equivalent to this function
value = np.random.randint(10000)
assert NumCpp.prime_Scaler(value) is not None
shapeInput = np.random.randint(20, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArrayUInt32(shape)
data = np.random.randint(0, 10000, [shape.rows, shape.cols])
cArray.setArray(data)
assert NumCpp.prime_Array(cArray) is not None
def test_permutation():
assert NumCpp.permutationScaler(np.random.randint(1, 100, [
1,
]).item()) is not None
shapeInput = np.random.randint(1, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.randint(1, 10, [shape.rows, shape.cols])
cArray.setArray(data)
assert NumCpp.permutationArray(cArray) is not None
def test_multi_dot():
shapeInput = np.random.randint(5, 50, [2, ])
shape1 = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
shape2 = NumCpp.Shape(shape1.cols, np.random.randint(5, 50, [1, ]).item())
shape3 = NumCpp.Shape(shape2.cols, np.random.randint(5, 50, [1, ]).item())
shape4 = NumCpp.Shape(shape3.cols, np.random.randint(5, 50, [1, ]).item())
cArray1 = NumCpp.NdArray(shape1)
cArray2 = NumCpp.NdArray(shape2)
cArray3 = NumCpp.NdArray(shape3)
cArray4 = NumCpp.NdArray(shape4)
data1 = np.random.randint(1, 10, [shape1.rows, shape1.cols])
data2 = np.random.randint(1, 10, [shape2.rows, shape2.cols])
data3 = np.random.randint(1, 10, [shape3.rows, shape3.cols])
data4 = np.random.randint(1, 10, [shape4.rows, shape4.cols])
cArray1.setArray(data1)
cArray2.setArray(data2)
cArray3.setArray(data3)
cArray4.setArray(data4)
assert np.array_equal(np.round(NumCpp.multi_dot(cArray1, cArray2, cArray3, cArray4), 9),
np.round(np.linalg.multi_dot([data1, data2, data3, data4]), 9))
shapeInput = np.random.randint(5, 50, [2, ])
shape1 = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
shape2 = NumCpp.Shape(shape1.cols, np.random.randint(5, 50, [1, ]).item())
shape3 = NumCpp.Shape(shape2.cols, np.random.randint(5, 50, [1, ]).item())
shape4 = NumCpp.Shape(shape3.cols, np.random.randint(5, 50, [1, ]).item())
cArray1 = NumCpp.NdArrayComplexDouble(shape1)
cArray2 = NumCpp.NdArrayComplexDouble(shape2)
cArray3 = NumCpp.NdArrayComplexDouble(shape3)
cArray4 = NumCpp.NdArrayComplexDouble(shape4)
real1 = np.random.randint(1, 100, [shape1.rows, shape1.cols])
imag1 = np.random.randint(1, 100, [shape1.rows, shape1.cols])
data1 = real1 + 1j * imag1
real2 = np.random.randint(1, 100, [shape2.rows, shape2.cols])
imag2 = np.random.randint(1, 100, [shape2.rows, shape2.cols])
data2 = real2 + 1j * imag2
real3 = np.random.randint(1, 100, [shape3.rows, shape3.cols])
imag3 = np.random.randint(1, 100, [shape3.rows, shape3.cols])
data3 = real3 + 1j * imag3
real4 = np.random.randint(1, 100, [shape4.rows, shape4.cols])
imag4 = np.random.randint(1, 100, [shape4.rows, shape4.cols])
data4 = real4 + 1j * imag4
cArray1.setArray(data1)
cArray2.setArray(data2)
cArray3.setArray(data3)
cArray4.setArray(data4)
assert np.array_equal(np.round(NumCpp.multi_dot(cArray1, cArray2, cArray3, cArray4), 9),
np.round(np.linalg.multi_dot([data1, data2, data3, data4]), 9))
def test_complementaryMedianFilter():
for mode in modes.keys():
shape = np.random.randint(100, 200, [2, ]).tolist()
cShape = NumCpp.Shape(shape[0], shape[1])
cArray = NumCpp.NdArray(cShape)
data = np.random.randint(100, 1000, shape)
cArray.setArray(data)
kernalSize = 0
while kernalSize % 2 == 0:
kernalSize = np.random.randint(5, 15)
constantValue = np.random.randint(0, 5, [1, ]).item() # only actaully needed for constant boundary condition
dataOutC = NumCpp.complementaryMedianFilter(cArray, kernalSize, modes[mode], constantValue).getNumpyArray()
dataOutPy = data - filters.median_filter(data, size=kernalSize, mode=mode, cval=constantValue)
assert np.array_equal(dataOutC, dataOutPy)
def test_uniform_filter():
for mode in modes.keys():
shape = np.random.randint(100, 200, [2, ]).tolist()
cShape = NumCpp.Shape(shape[0], shape[1])
cArray = NumCpp.NdArray(cShape)
data = np.random.randint(100, 1000, shape).astype(np.double)
cArray.setArray(data)
kernalSize = 0
while kernalSize % 2 == 0:
kernalSize = np.random.randint(5, 15)
constantValue = np.random.randint(0, 5, [1, ]).item() # only actaully needed for constant boundary condition
dataOutC = NumCpp.uniformFilter(cArray, kernalSize, modes[mode], constantValue).getNumpyArray()
dataOutPy = filters.uniform_filter(data, size=kernalSize, mode=mode, cval=constantValue)
assert np.array_equal(np.round(dataOutC, 8), np.round(dataOutPy, 8))
def test_triangle():
if NumCpp.NO_USE_BOOST:
return
shapeInput = np.random.randint(1, 100, [
2,
])
inShape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
values = np.random.rand(3)
values.sort()
assert NumCpp.triangle(inShape, values[0].item(), values[1].item(),
values[2].item()) is not None
assert NumCpp.triangle(values[0].item(), values[1].item(),
values[2].item()) is not None
def test_zeta():
if NumCpp.NO_USE_BOOST and not NumCpp.STL_SPECIAL_FUNCTIONS:
return
value = np.random.rand(1).item() * 5 + 1
assert (roundScaler(NumCpp.riemann_zeta_Scaler(value), NUM_DECIMALS_ROUND) ==
roundScaler(sp.zeta(value, 1).item(), NUM_DECIMALS_ROUND))
shapeInput = np.random.randint(20, 100, [2, ])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols) * 5 + 1
cArray.setArray(data)
assert np.array_equal(roundArray(NumCpp.riemann_zeta_Array(cArray), NUM_DECIMALS_ROUND),
roundArray(sp.zeta(data, 1), NUM_DECIMALS_ROUND))
def test_gaussianFilter1d():
for mode in modes.keys():
size = np.random.randint(1000, 2000, [1, ]).item()
cShape = NumCpp.Shape(1, size)
cArray = NumCpp.NdArray(cShape)
data = np.random.randint(100, 1000, [size, ]).astype(np.double)
cArray.setArray(data)
kernalSize = 0
while kernalSize % 2 == 0:
kernalSize = np.random.randint(5, 15)
sigma = np.random.rand(1).item() * 2
constantValue = np.random.randint(0, 5, [1, ]).item() # only actaully needed for constant boundary condition
dataOutC = NumCpp.gaussianFilter1d(cArray, sigma, modes[mode], constantValue).getNumpyArray().flatten()
dataOutPy = filters.gaussian_filter(data, sigma, mode=mode, cval=constantValue)
assert np.array_equal(np.round(dataOutC, 7), np.round(dataOutPy, 7))
def test_medianFilter1d():
for mode in modes.keys():
size = np.random.randint(1000, 2000, [1, ]).item()
cShape = NumCpp.Shape(1, size)
cArray = NumCpp.NdArray(cShape)
data = np.random.randint(100, 1000, [size, ])
cArray.setArray(data)
kernalSize = 0
while kernalSize % 2 == 0:
kernalSize = np.random.randint(5, 15)
constantValue = np.random.randint(0, 5, [1, ]).item() # only actaully needed for constant boundary condition
dataOutC = NumCpp.medianFilter1d(cArray, kernalSize, modes[mode], constantValue).getNumpyArray().flatten()
dataOutPy = filters.generic_filter(data, np.median, footprint=np.ones([kernalSize, ]),
mode=mode, cval=constantValue)
assert np.array_equal(dataOutC, dataOutPy)
def test_trigamma():
if NumCpp.NO_USE_BOOST:
return
value = np.random.rand(1).item()
assert (roundScaler(NumCpp.trigamma_Scaler(value), NUM_DECIMALS_ROUND) ==
roundScaler(sp.polygamma(1, value).item(), NUM_DECIMALS_ROUND))
shapeInput = np.random.randint(20, 100, [2, ])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols)
cArray.setArray(data)
assert np.array_equal(roundArray(NumCpp.trigamma_Array(cArray), NUM_DECIMALS_ROUND),
roundArray(sp.polygamma(1, data), NUM_DECIMALS_ROUND))
def test_expint():
if NumCpp.NO_USE_BOOST and not NumCpp.STL_SPECIAL_FUNCTIONS:
return
a = np.random.rand(1).item()
assert (roundScaler(NumCpp.expint_Scaler(a), NUM_DECIMALS_ROUND) ==
roundScaler(sp.expi(a).item(), NUM_DECIMALS_ROUND))
shapeInput = np.random.randint(20, 100, [2, ])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
aArray = NumCpp.NdArray(shape)
a = np.random.rand(shape.rows, shape.cols)
aArray.setArray(a)
assert np.array_equal(roundArray(NumCpp.expint_Array(aArray), NUM_DECIMALS_ROUND),
roundArray(sp.expi(a), NUM_DECIMALS_ROUND))
def test_spherical_hankel_1():
# There is no equivalent scipy functions
order = np.random.randint(0, 10)
value = np.random.rand(1).item()
assert NumCpp.spherical_hankel_2_Scaler(order, value) is not None
shapeInput = np.random.randint(20, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
order = np.random.randint(0, 6)
value = NumCpp.NdArray(shape)
valuePy = np.random.rand(shape.rows, shape.cols) * 10
value.setArray(valuePy)
assert NumCpp.spherical_hankel_2_Array(order, value) is not None
def test_softmax():
shapeInput = np.random.randint(20, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols)
cArray.setArray(data)
assert np.array_equal(
roundArray(NumCpp.softmax(cArray, NumCpp.Axis.NONE),
NUM_DECIMALS_ROUND),
roundArray(sp.softmax(data), NUM_DECIMALS_ROUND))
shapeInput = np.random.randint(20, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols)
cArray.setArray(data)
assert np.array_equal(
roundArray(NumCpp.softmax(cArray, NumCpp.Axis.ROW),
NUM_DECIMALS_ROUND),
roundArray(sp.softmax(data, axis=0), NUM_DECIMALS_ROUND))
shapeInput = np.random.randint(20, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols)
cArray.setArray(data)
assert np.array_equal(
roundArray(NumCpp.softmax(cArray, NumCpp.Axis.COL),
NUM_DECIMALS_ROUND),
roundArray(sp.softmax(data, axis=1), NUM_DECIMALS_ROUND))
def test_laplaceFilter():
for mode in modes.keys():
shape = np.random.randint(100, 200, [
2,
]).tolist()
cShape = NumCpp.Shape(shape[0], shape[1]) # noqa
cArray = NumCpp.NdArray(cShape)
data = np.random.randint(100, 1000, shape).astype(float) # noqa
cArray.setArray(data)
constantValue = np.random.randint(0, 5, [
1,
]).item() # only actaully needed for constant boundary condition
dataOutC = NumCpp.laplaceFilter(cArray, modes[mode],
constantValue).getNumpyArray()
dataOutPy = filters.laplace(data, mode=mode, cval=constantValue)
assert np.array_equal(dataOutC, dataOutPy)
def test_airy_bi_prime():
value = np.random.rand(1).item()
assert (roundScaler(NumCpp.airy_bi_prime_Scaler(value),
NUM_DECIMALS_ROUND) == roundScaler(
sp.airy(value)[3].item(), NUM_DECIMALS_ROUND))
shapeInput = np.random.randint(20, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols)
cArray.setArray(data)
assert np.array_equal(
roundArray(NumCpp.airy_bi_prime_Array(cArray), NUM_DECIMALS_ROUND),
roundArray(sp.airy(data)[3], NUM_DECIMALS_ROUND))
def test_beta():
if NumCpp.NO_USE_BOOST:
return
shapeInput = np.random.randint(1, 100, [
2,
])
inShape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
alpha = np.random.rand()
beta = np.random.rand()
randArray = NumCpp.beta(inShape, alpha, beta).getNumpyArray()
assert np.array_equiv(randArray.shape, shapeInput)
randValue = NumCpp.beta(alpha, beta)
assert isinstance(randValue, float)
def test_digamma():
value = np.random.rand(1).item() * 10
assert (roundScaler(NumCpp.digamma_Scaler(value),
NUM_DECIMALS_ROUND) == roundScaler(
sp.digamma(value), NUM_DECIMALS_ROUND))
shapeInput = np.random.randint(20, 100, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
cArray = NumCpp.NdArray(shape)
data = np.random.rand(shape.rows, shape.cols) * 10
cArray.setArray(data)
assert np.array_equal(
roundArray(NumCpp.digamma_Array(cArray), NUM_DECIMALS_ROUND),
roundArray(sp.digamma(data), NUM_DECIMALS_ROUND))
def test_lstsq():
shapeInput = np.random.randint(5, 50, [
2,
])
shape = NumCpp.Shape(shapeInput[0].item(), shapeInput[1].item())
aArray = NumCpp.NdArray(shape)
bArray = NumCpp.NdArray(1, shape.rows)
aData = np.random.randint(1, 100, [shape.rows, shape.cols])
bData = np.random.randint(1, 100, [
shape.rows,
])
aArray.setArray(aData)
bArray.setArray(bData)
x = NumCpp.lstsq(aArray, bArray, 1e-12).getNumpyArray().flatten()
assert np.array_equal(
np.round(x, 9),
np.round(np.linalg.lstsq(aData, bData, rcond=None)[0], 9))