def test_beta(self):
rs = np.random.RandomState(42)
rng01 = utils.RandomUniform(0, 1, random_state=rs)
x = np.array([[0.0],
[0.0],
[0.0],
[0.0],
[0.0],
[0.15601864],
[0.37454012],
[0.59865848],
[0.73199394],
[0.95071431]])
x2 = beta.random((10, 1), density=0.5, rng=rng01, sort=True,
normalise=False)
assert(np.linalg.norm(x - x2) < utils.TOLERANCE)
rs = np.random.RandomState(1337)
rng11 = utils.RandomUniform(-1, 1, random_state=rs)
x = np.array([[0.0],
[-0.24365074],
[0.02503597],
[-0.0553771],
[-0.3239276],
[-0.46459304],
[0.64803846],
[-0.30201006],
[0.0],
[-0.32403887]])
x2 = beta.random((10, 1), density=0.75, rng=rng11, sort=False,
normalise=True)
assert(np.linalg.norm(x - x2) < utils.TOLERANCE)
assert(abs(np.linalg.norm(x2) - 1) < utils.TOLERANCE)
def test_functions(self):
rs = np.random.RandomState(1337)
rng01 = utils.RandomUniform(0, 1, random_state=rs)
rng11 = utils.RandomUniform(-1, 1, random_state=rs)
cnst0 = utils.ConstantValue(0, random_state=rs)
x = beta.random((10, 1), density=0.75, rng=rng11, sort=False,
normalise=False)
# L1
grad = np.array([[0.57911668],
[-1.0],
[1.0],
[-1.0],
[-1.0],
[-1.0],
[1.0],
[-1.0],
[0.58823715],
[-1.0]])
assert(np.linalg.norm(0.1 * grad - functions.L1(0.1, rng=rng11).grad(x)) < utils.TOLERANCE)
grad = np.array([[0.0],
[-0.7159978],
[0.0735713],
[-0.1627325],
[-0.9519013],
[-1.0],
[1.0],
[-0.8874939],
[0.0],
[-0.9522283]])
assert(np.linalg.norm(0.1 * grad - functions.SmoothedL1(0.1, mu=5e-1).grad(x)) < utils.TOLERANCE)
grad = np.array([[0.0],
[-1.0],
[1.0],
[-1.0],
[-1.0],
[-1.0],
[1.0],
[-1.0],
[0.0],
[-1.0]])
assert(np.linalg.norm(0.25 * grad - functions.SmoothedL1(0.25, mu=5e-8).grad(x)) < utils.TOLERANCE)
x = beta.random((10, 1), density=0.5, rng=rng11, sort=False,
normalise=False)
# L2
grad = np.array([[0.0],
[-0.31136769],
[-0.18828614],
[0.58389796],
[0.0],
[0.0],
[-0.70064494],
[0.0],
[0.0],
[0.18909872]])
assert(np.linalg.norm(0.1 * grad - functions.L2(0.1, rng=rng01).grad(x)) < utils.TOLERANCE)
assert(abs(np.linalg.norm(functions.L2(0.5, rng=rng01).grad(x)) < 0.5) < utils.TOLERANCE)
assert(abs(np.linalg.norm(functions.L2(1.0, rng=rng01).grad(x)) < 1.0) < utils.TOLERANCE)
assert(abs(np.linalg.norm(functions.L2(1.5, rng=rng01).grad(x)) < 1.5) < utils.TOLERANCE)
# L2 Squared
assert(np.linalg.norm(0.5 * x - functions.L2Squared(0.5).grad(x)) < utils.TOLERANCE)
# Total Variation
x = beta.random((10, 10), density=0.5, rng=rng11, sort=True,
normalise=False)
# Generate the linear operator for total variation.
A = functions.TotalVariation.A_from_shape((10, 10))
A_ = np.array([[-1.0, 1.0, 0.0],
[0.0, -1.0, 1.0],
[0.0, 0.0, -1.0]])
assert(np.linalg.norm(A[0].todense()[:3, :3] - A_) < utils.TOLERANCE)
A_ = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0],
[-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0,-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0]])
assert(np.linalg.norm(A[1].todense()[:10, 5:15] - A_) < utils.TOLERANCE)
grad = np.array([[-1.37690875], [-0.50249731], [-1.13463951],
[-0.92581747], [-1.12545778], [-0.72495808],
[-1.09539063], [-1.12191557], [-1.14278035],
[-0.38378842], [-0.54044045], [0.1998922],
[0.10727523], [0.42029647], [-0.12845922],
[-0.09340557], [0.0055352], [0.0456007],
[0.8779322], [1.40188876], [-0.57962065],
[0.35934782], [-0.42347626], [0.29359706],
[2.07205284], [0.65534416], [1.01918068],
[-0.45464203], [0.38998718], [-0.19745865],
[-0.62748016], [0.63761495], [-0.68385703],
[1.89910956], [-0.28092104], [-0.17162572],
[0.48321381], [0.79706197], [0.61187108],
[-1.42531316], [0.7902697], [0.60837155],
[1.20533504], [0.09427085], [-0.70922127],
[0.09077005], [0.14231686], [-0.32261771],
[-1.0636391], [0.3522861], [0.46381846],
[-0.32764258], [-0.9267115], [0.68692098],
[-0.28524282], [-1.65222339], [0.3472565],
[-0.82272974], [0.60190561], [0.43221722],
[0.92882439], [0.21409408], [-0.29173676],
[0.43373039], [-0.52463849], [1.59982977],
[-1.20161831], [-1.40845266], [0.34302998],
[0.90820945], [0.79001083], [0.06567102],
[-0.31555666], [-1.34826493], [-1.31252716],
[-1.1824102], [-0.31668549], [-0.1015793],
[-0.19644832], [0.97835737], [-1.23182642],
[-0.63448914], [-1.29006382], [-0.00488059],
[-0.34004922], [0.4112866], [-0.36592392],
[0.06443214], [-1.17634974], [0.58974244],
[-0.55508336], [1.0], [0.99971041],
[0.99956841], [0.86125816], [0.99525803],
[0.96641958], [0.99990113], [0.80759139], [2.0]])
assert(np.linalg.norm(functions.TotalVariation(0.1, A, rng=rng01).grad(x) - 0.1 * grad) < utils.TOLERANCE)
tvgrad = functions.TotalVariation(0.1, A, rng=cnst0).grad(x)
tvmugrad = functions.SmoothedTotalVariation(0.1, A, mu=5e-8).grad(x)
assert(np.linalg.norm(tvgrad - tvmugrad) < utils.TOLERANCE)
# Group Lasso
x = beta.random((10, 1), density=0.5, rng=rng11, sort=False,
normalise=False)
# Create linear operator.
A = functions.GroupLasso.A_from_groups(10, [range(5), range(5, 10)])
glgrad = functions.GroupLasso(1.0, A, rng=rng11).grad(x)
assert(abs(np.linalg.norm(glgrad[:5]) - 1.0) < utils.TOLERANCE)
assert(abs(np.linalg.norm(glgrad[5:]) - 1.0) < utils.TOLERANCE)
glmugrad = functions.SmoothedGroupLasso(1.0, A, mu=5e-8).grad(x)
assert(np.linalg.norm(glgrad - glmugrad) < utils.TOLERANCE)
def test_functions(self):
rs = np.random.RandomState(1337)
rng01 = utils.RandomUniform(0, 1, random_state=rs)
rng11 = utils.RandomUniform(-1, 1, random_state=rs)
cnst0 = utils.ConstantValue(0, random_state=rs)
x = beta.random((10, 1),
density=0.75,
rng=rng11,
sort=False,
normalise=False)
# L1
grad = np.array([[0.57911668], [-1.0], [1.0], [-1.0], [-1.0], [-1.0],
[1.0], [-1.0], [0.58823715], [-1.0]])
assert (
np.linalg.norm(0.1 * grad - functions.L1(0.1, rng=rng11).grad(x)) <
utils.TOLERANCE)
grad = np.array([[0.0], [-0.7159978], [0.0735713], [-0.1627325],
[-0.9519013], [-1.0], [1.0], [-0.8874939], [0.0],
[-0.9522283]])
assert (np.linalg.norm(0.1 * grad -
functions.SmoothedL1(0.1, mu=5e-1).grad(x)) <
utils.TOLERANCE)
grad = np.array([[0.0], [-1.0], [1.0], [-1.0], [-1.0], [-1.0], [1.0],
[-1.0], [0.0], [-1.0]])
assert (np.linalg.norm(0.25 * grad -
functions.SmoothedL1(0.25, mu=5e-8).grad(x)) <
utils.TOLERANCE)
x = beta.random((10, 1),
density=0.5,
rng=rng11,
sort=False,
normalise=False)
# L2
grad = np.array([[0.0], [-0.31136769], [-0.18828614], [0.58389796],
[0.0], [0.0], [-0.70064494], [0.0], [0.0],
[0.18909872]])
assert (
np.linalg.norm(0.1 * grad - functions.L2(0.1, rng=rng01).grad(x)) <
utils.TOLERANCE)
assert (
abs(np.linalg.norm(functions.L2(0.5, rng=rng01).grad(x)) < 0.5) <
utils.TOLERANCE)
assert (
abs(np.linalg.norm(functions.L2(1.0, rng=rng01).grad(x)) < 1.0) <
utils.TOLERANCE)
assert (
abs(np.linalg.norm(functions.L2(1.5, rng=rng01).grad(x)) < 1.5) <
utils.TOLERANCE)
# L2 Squared
assert (np.linalg.norm(0.5 * x - functions.L2Squared(0.5).grad(x)) <
utils.TOLERANCE)
# Total Variation
x = beta.random((10, 10),
density=0.5,
rng=rng11,
sort=True,
normalise=False)
# Generate the linear operator for total variation.
A = functions.TotalVariation.A_from_shape((10, 10))
A_ = np.array([[-1.0, 1.0, 0.0], [0.0, -1.0, 1.0], [0.0, 0.0, -1.0]])
assert (np.linalg.norm(A[0].todense()[:3, :3] - A_) < utils.TOLERANCE)
A_ = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0],
[-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0]])
assert (np.linalg.norm(A[1].todense()[:10, 5:15] - A_) <
utils.TOLERANCE)
grad = np.array(
[[-1.37690875], [-0.50249731], [-1.13463951], [-0.92581747],
[-1.12545778], [-0.72495808], [-1.09539063], [-1.12191557],
[-1.14278035], [-0.38378842], [-0.54044045], [0.1998922],
[0.10727523], [0.42029647], [-0.12845922], [-0.09340557],
[0.0055352], [0.0456007], [0.8779322], [1.40188876],
[-0.57962065], [0.35934782], [-0.42347626], [0.29359706],
[2.07205284], [0.65534416], [1.01918068], [-0.45464203],
[0.38998718], [-0.19745865], [-0.62748016], [0.63761495],
[-0.68385703], [1.89910956], [-0.28092104], [-0.17162572],
[0.48321381], [0.79706197], [0.61187108], [-1.42531316],
[0.7902697], [0.60837155], [1.20533504], [0.09427085],
[-0.70922127], [0.09077005], [0.14231686], [-0.32261771],
[-1.0636391], [0.3522861], [0.46381846], [-0.32764258],
[-0.9267115], [0.68692098], [-0.28524282], [-1.65222339],
[0.3472565], [-0.82272974], [0.60190561], [0.43221722],
[0.92882439], [0.21409408], [-0.29173676], [0.43373039],
[-0.52463849], [1.59982977], [-1.20161831], [-1.40845266],
[0.34302998], [0.90820945], [0.79001083], [0.06567102],
[-0.31555666], [-1.34826493], [-1.31252716], [-1.1824102],
[-0.31668549], [-0.1015793], [-0.19644832], [0.97835737],
[-1.23182642], [-0.63448914], [-1.29006382], [-0.00488059],
[-0.34004922], [0.4112866], [-0.36592392], [0.06443214],
[-1.17634974], [0.58974244], [-0.55508336], [1.0], [0.99971041],
[0.99956841], [0.86125816], [0.99525803], [0.96641958],
[0.99990113], [0.80759139], [2.0]])
assert (np.linalg.norm(
functions.TotalVariation(0.1, A, rng=rng01).grad(x) - 0.1 * grad) <
utils.TOLERANCE)
tvgrad = functions.TotalVariation(0.1, A, rng=cnst0).grad(x)
tvmugrad = functions.SmoothedTotalVariation(0.1, A, mu=5e-8).grad(x)
assert (np.linalg.norm(tvgrad - tvmugrad) < utils.TOLERANCE)
# Group Lasso
x = beta.random((10, 1),
density=0.5,
rng=rng11,
sort=False,
normalise=False)
# Create linear operator.
A = functions.GroupLasso.A_from_groups(10, [range(5), range(5, 10)])
glgrad = functions.GroupLasso(1.0, A, rng=rng11).grad(x)
assert (abs(np.linalg.norm(glgrad[:5]) - 1.0) < utils.TOLERANCE)
assert (abs(np.linalg.norm(glgrad[5:]) - 1.0) < utils.TOLERANCE)
glmugrad = functions.SmoothedGroupLasso(1.0, A, mu=5e-8).grad(x)
assert (np.linalg.norm(glgrad - glmugrad) < utils.TOLERANCE)
