def test_pls():
d = load_linnerud()
X = d.data
Y = d.target
# 1) Canonical (symmetric) PLS (PLS 2 blocks canonical mode A)
# ===========================================================
# Compare 2 algo.: nipals vs. svd
# ------------------------------
pls_bynipals = pls_.PLSCanonical(n_components=X.shape[1])
pls_bynipals.fit(X, Y)
pls_bysvd = pls_.PLSCanonical(algorithm="svd", n_components=X.shape[1])
pls_bysvd.fit(X, Y)
# check equalities of loading (up to the sign of the second column)
assert_array_almost_equal(
pls_bynipals.x_loadings_,
pls_bysvd.x_loadings_,
decimal=5,
err_msg="nipals and svd implementations lead to different x loadings")
assert_array_almost_equal(
pls_bynipals.y_loadings_,
pls_bysvd.y_loadings_,
decimal=5,
err_msg="nipals and svd implementations lead to different y loadings")
# Check PLS properties (with n_components=X.shape[1])
# ---------------------------------------------------
plsca = pls_.PLSCanonical(n_components=X.shape[1])
plsca.fit(X, Y)
T = plsca.x_scores_
P = plsca.x_loadings_
Wx = plsca.x_weights_
U = plsca.y_scores_
Q = plsca.y_loadings_
Wy = plsca.y_weights_
def check_ortho(M, err_msg):
K = np.dot(M.T, M)
assert_array_almost_equal(K, np.diag(np.diag(K)), err_msg=err_msg)
# Orthogonality of weights
# ~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(Wx, "x weights are not orthogonal")
check_ortho(Wy, "y weights are not orthogonal")
# Orthogonality of latent scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(T, "x scores are not orthogonal")
check_ortho(U, "y scores are not orthogonal")
# Check X = TP' and Y = UQ' (with (p == q) components)
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# center scale X, Y
Xc, Yc, x_mean, y_mean, x_std, y_std =\
pls_._center_scale_xy(X.copy(), Y.copy(), scale=True)
assert_array_almost_equal(Xc, np.dot(T, P.T), err_msg="X != TP'")
assert_array_almost_equal(Yc, np.dot(U, Q.T), err_msg="Y != UQ'")
# Check that rotations on training data lead to scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Xr = plsca.transform(X)
assert_array_almost_equal(Xr,
plsca.x_scores_,
err_msg="rotation on X failed")
Xr, Yr = plsca.transform(X, Y)
assert_array_almost_equal(Xr,
plsca.x_scores_,
err_msg="rotation on X failed")
assert_array_almost_equal(Yr,
plsca.y_scores_,
err_msg="rotation on Y failed")
# "Non regression test" on canonical PLS
# --------------------------------------
# The results were checked against the R-package plspm
pls_ca = pls_.PLSCanonical(n_components=X.shape[1])
pls_ca.fit(X, Y)
x_weights = np.array([[-0.61330704, 0.25616119, -0.74715187],
[-0.74697144, 0.11930791, 0.65406368],
[-0.25668686, -0.95924297, -0.11817271]])
# x_weights_sign_flip holds columns of 1 or -1, depending on sign flip
# between R and python
x_weights_sign_flip = pls_ca.x_weights_ / x_weights
x_rotations = np.array([[-0.61330704, 0.41591889, -0.62297525],
[-0.74697144, 0.31388326, 0.77368233],
[-0.25668686, -0.89237972, -0.24121788]])
x_rotations_sign_flip = pls_ca.x_rotations_ / x_rotations
y_weights = np.array([[+0.58989127, 0.7890047, 0.1717553],
[+0.77134053, -0.61351791, 0.16920272],
[-0.23887670, -0.03267062, 0.97050016]])
y_weights_sign_flip = pls_ca.y_weights_ / y_weights
y_rotations = np.array([[+0.58989127, 0.7168115, 0.30665872],
[+0.77134053, -0.70791757, 0.19786539],
[-0.23887670, -0.00343595, 0.94162826]])
y_rotations_sign_flip = pls_ca.y_rotations_ / y_rotations
# x_weights = X.dot(x_rotation)
# Hence R/python sign flip should be the same in x_weight and x_rotation
assert_array_almost_equal(x_rotations_sign_flip, x_weights_sign_flip)
# This test that R / python give the same result up to column
# sign indeterminacy
assert_array_almost_equal(np.abs(x_rotations_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(y_rotations_sign_flip, y_weights_sign_flip)
assert_array_almost_equal(np.abs(y_rotations_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
# 2) Regression PLS (PLS2): "Non regression test"
# ===============================================
# The results were checked against the R-packages plspm, misOmics and pls
pls_2 = pls_.PLSRegression(n_components=X.shape[1])
pls_2.fit(X, Y)
x_weights = np.array([[-0.61330704, -0.00443647, 0.78983213],
[-0.74697144, -0.32172099, -0.58183269],
[-0.25668686, 0.94682413, -0.19399983]])
x_weights_sign_flip = pls_2.x_weights_ / x_weights
x_loadings = np.array([[-0.61470416, -0.24574278, 0.78983213],
[-0.65625755, -0.14396183, -0.58183269],
[-0.51733059, 1.00609417, -0.19399983]])
x_loadings_sign_flip = pls_2.x_loadings_ / x_loadings
y_weights = np.array([[+0.32456184, 0.29892183, 0.20316322],
[+0.42439636, 0.61970543, 0.19320542],
[-0.13143144, -0.26348971, -0.17092916]])
y_weights_sign_flip = pls_2.y_weights_ / y_weights
y_loadings = np.array([[+0.32456184, 0.29892183, 0.20316322],
[+0.42439636, 0.61970543, 0.19320542],
[-0.13143144, -0.26348971, -0.17092916]])
y_loadings_sign_flip = pls_2.y_loadings_ / y_loadings
# x_loadings[:, i] = Xi.dot(x_weights[:, i]) \forall i
assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(x_loadings_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(y_loadings_sign_flip, y_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(y_loadings_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
# 3) Another non-regression test of Canonical PLS on random dataset
# =================================================================
# The results were checked against the R-package plspm
n = 500
p_noise = 10
q_noise = 5
# 2 latents vars:
rng = check_random_state(11)
l1 = rng.normal(size=n)
l2 = rng.normal(size=n)
latents = np.array([l1, l1, l2, l2]).T
X = latents + rng.normal(size=4 * n).reshape((n, 4))
Y = latents + rng.normal(size=4 * n).reshape((n, 4))
X = np.concatenate((X, rng.normal(size=p_noise * n).reshape(n, p_noise)),
axis=1)
Y = np.concatenate((Y, rng.normal(size=q_noise * n).reshape(n, q_noise)),
axis=1)
pls_ca = pls_.PLSCanonical(n_components=3)
pls_ca.fit(X, Y)
x_weights = np.array([[0.65803719, 0.19197924, 0.21769083],
[0.7009113, 0.13303969, -0.15376699],
[0.13528197, -0.68636408, 0.13856546],
[0.16854574, -0.66788088, -0.12485304],
[-0.03232333, -0.04189855, 0.40690153],
[0.1148816, -0.09643158, 0.1613305],
[0.04792138, -0.02384992, 0.17175319],
[-0.06781, -0.01666137, -0.18556747],
[-0.00266945, -0.00160224, 0.11893098],
[-0.00849528, -0.07706095, 0.1570547],
[-0.00949471, -0.02964127, 0.34657036],
[-0.03572177, 0.0945091, 0.3414855],
[0.05584937, -0.02028961, -0.57682568],
[0.05744254, -0.01482333, -0.17431274]])
x_weights_sign_flip = pls_ca.x_weights_ / x_weights
x_loadings = np.array([[0.65649254, 0.1847647, 0.15270699],
[0.67554234, 0.15237508, -0.09182247],
[0.19219925, -0.67750975, 0.08673128],
[0.2133631, -0.67034809, -0.08835483],
[-0.03178912, -0.06668336, 0.43395268],
[0.15684588, -0.13350241, 0.20578984],
[0.03337736, -0.03807306, 0.09871553],
[-0.06199844, 0.01559854, -0.1881785],
[0.00406146, -0.00587025, 0.16413253],
[-0.00374239, -0.05848466, 0.19140336],
[0.00139214, -0.01033161, 0.32239136],
[-0.05292828, 0.0953533, 0.31916881],
[0.04031924, -0.01961045, -0.65174036],
[0.06172484, -0.06597366, -0.1244497]])
x_loadings_sign_flip = pls_ca.x_loadings_ / x_loadings
y_weights = np.array([[0.66101097, 0.18672553, 0.22826092],
[0.69347861, 0.18463471, -0.23995597],
[0.14462724, -0.66504085, 0.17082434],
[0.22247955, -0.6932605, -0.09832993],
[0.07035859, 0.00714283, 0.67810124],
[0.07765351, -0.0105204, -0.44108074],
[-0.00917056, 0.04322147, 0.10062478],
[-0.01909512, 0.06182718, 0.28830475],
[0.01756709, 0.04797666, 0.32225745]])
y_weights_sign_flip = pls_ca.y_weights_ / y_weights
y_loadings = np.array([[0.68568625, 0.1674376, 0.0969508],
[0.68782064, 0.20375837, -0.1164448],
[0.11712173, -0.68046903, 0.12001505],
[0.17860457, -0.6798319, -0.05089681],
[0.06265739, -0.0277703, 0.74729584],
[0.0914178, 0.00403751, -0.5135078],
[-0.02196918, -0.01377169, 0.09564505],
[-0.03288952, 0.09039729, 0.31858973],
[0.04287624, 0.05254676, 0.27836841]])
y_loadings_sign_flip = pls_ca.y_loadings_ / y_loadings
assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_loadings_sign_flip), 1, 4)
assert_array_almost_equal(y_loadings_sign_flip, y_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_loadings_sign_flip), 1, 4)
# Orthogonality of weights
# ~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(pls_ca.x_weights_, "x weights are not orthogonal")
check_ortho(pls_ca.y_weights_, "y weights are not orthogonal")
# Orthogonality of latent scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(pls_ca.x_scores_, "x scores are not orthogonal")
check_ortho(pls_ca.y_scores_, "y scores are not orthogonal")
def train(self, data):
# # Scale (in place)
X, Y, self.x_mean_, self.y_mean_, self.x_std_, self.y_std_ = (
_center_scale_xy(data[0], data[1]))
return super(CCA, self).train([X, Y])
def test_pls():
d = load_linnerud()
X = d.data
Y = d.target
# 1) Canonical (symmetric) PLS (PLS 2 blocks canonical mode A)
# ===========================================================
# Compare 2 algo.: nipals vs. svd
# ------------------------------
pls_bynipals = pls_.PLSCanonical(n_components=X.shape[1])
pls_bynipals.fit(X, Y)
pls_bysvd = pls_.PLSCanonical(algorithm="svd", n_components=X.shape[1])
pls_bysvd.fit(X, Y)
# check equalities of loading (up to the sign of the second column)
assert_array_almost_equal(
pls_bynipals.x_loadings_,
pls_bysvd.x_loadings_, decimal=5,
err_msg="nipals and svd implementations lead to different x loadings")
assert_array_almost_equal(
pls_bynipals.y_loadings_,
pls_bysvd.y_loadings_, decimal=5,
err_msg="nipals and svd implementations lead to different y loadings")
# Check PLS properties (with n_components=X.shape[1])
# ---------------------------------------------------
plsca = pls_.PLSCanonical(n_components=X.shape[1])
plsca.fit(X, Y)
T = plsca.x_scores_
P = plsca.x_loadings_
Wx = plsca.x_weights_
U = plsca.y_scores_
Q = plsca.y_loadings_
Wy = plsca.y_weights_
def check_ortho(M, err_msg):
K = np.dot(M.T, M)
assert_array_almost_equal(K, np.diag(np.diag(K)), err_msg=err_msg)
# Orthogonality of weights
# ~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(Wx, "x weights are not orthogonal")
check_ortho(Wy, "y weights are not orthogonal")
# Orthogonality of latent scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(T, "x scores are not orthogonal")
check_ortho(U, "y scores are not orthogonal")
# Check X = TP' and Y = UQ' (with (p == q) components)
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# center scale X, Y
Xc, Yc, x_mean, y_mean, x_std, y_std =\
pls_._center_scale_xy(X.copy(), Y.copy(), scale=True)
assert_array_almost_equal(Xc, np.dot(T, P.T), err_msg="X != TP'")
assert_array_almost_equal(Yc, np.dot(U, Q.T), err_msg="Y != UQ'")
# Check that rotations on training data lead to scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Xr = plsca.transform(X)
assert_array_almost_equal(Xr, plsca.x_scores_,
err_msg="rotation on X failed")
Xr, Yr = plsca.transform(X, Y)
assert_array_almost_equal(Xr, plsca.x_scores_,
err_msg="rotation on X failed")
assert_array_almost_equal(Yr, plsca.y_scores_,
err_msg="rotation on Y failed")
# "Non regression test" on canonical PLS
# --------------------------------------
# The results were checked against the R-package plspm
pls_ca = pls_.PLSCanonical(n_components=X.shape[1])
pls_ca.fit(X, Y)
x_weights = np.array(
[[-0.61330704, 0.25616119, -0.74715187],
[-0.74697144, 0.11930791, 0.65406368],
[-0.25668686, -0.95924297, -0.11817271]])
# x_weights_sign_flip holds columns of 1 or -1, depending on sign flip
# between R and python
x_weights_sign_flip = pls_ca.x_weights_ / x_weights
x_rotations = np.array(
[[-0.61330704, 0.41591889, -0.62297525],
[-0.74697144, 0.31388326, 0.77368233],
[-0.25668686, -0.89237972, -0.24121788]])
x_rotations_sign_flip = pls_ca.x_rotations_ / x_rotations
y_weights = np.array(
[[+0.58989127, 0.7890047, 0.1717553],
[+0.77134053, -0.61351791, 0.16920272],
[-0.23887670, -0.03267062, 0.97050016]])
y_weights_sign_flip = pls_ca.y_weights_ / y_weights
y_rotations = np.array(
[[+0.58989127, 0.7168115, 0.30665872],
[+0.77134053, -0.70791757, 0.19786539],
[-0.23887670, -0.00343595, 0.94162826]])
y_rotations_sign_flip = pls_ca.y_rotations_ / y_rotations
# x_weights = X.dot(x_rotation)
# Hence R/python sign flip should be the same in x_weight and x_rotation
assert_array_almost_equal(x_rotations_sign_flip, x_weights_sign_flip)
# This test that R / python give the same result up to column
# sign indeterminacy
assert_array_almost_equal(np.abs(x_rotations_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(y_rotations_sign_flip, y_weights_sign_flip)
assert_array_almost_equal(np.abs(y_rotations_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
# 2) Regression PLS (PLS2): "Non regression test"
# ===============================================
# The results were checked against the R-packages plspm, misOmics and pls
pls_2 = pls_.PLSRegression(n_components=X.shape[1])
pls_2.fit(X, Y)
x_weights = np.array(
[[-0.61330704, -0.00443647, 0.78983213],
[-0.74697144, -0.32172099, -0.58183269],
[-0.25668686, 0.94682413, -0.19399983]])
x_weights_sign_flip = pls_2.x_weights_ / x_weights
x_loadings = np.array(
[[-0.61470416, -0.24574278, 0.78983213],
[-0.65625755, -0.14396183, -0.58183269],
[-0.51733059, 1.00609417, -0.19399983]])
x_loadings_sign_flip = pls_2.x_loadings_ / x_loadings
y_weights = np.array(
[[+0.32456184, 0.29892183, 0.20316322],
[+0.42439636, 0.61970543, 0.19320542],
[-0.13143144, -0.26348971, -0.17092916]])
y_weights_sign_flip = pls_2.y_weights_ / y_weights
y_loadings = np.array(
[[+0.32456184, 0.29892183, 0.20316322],
[+0.42439636, 0.61970543, 0.19320542],
[-0.13143144, -0.26348971, -0.17092916]])
y_loadings_sign_flip = pls_2.y_loadings_ / y_loadings
# x_loadings[:, i] = Xi.dot(x_weights[:, i]) \forall i
assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(x_loadings_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(y_loadings_sign_flip, y_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(y_loadings_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
# 3) Another non-regression test of Canonical PLS on random dataset
# =================================================================
# The results were checked against the R-package plspm
n = 500
p_noise = 10
q_noise = 5
# 2 latents vars:
rng = check_random_state(11)
l1 = rng.normal(size=n)
l2 = rng.normal(size=n)
latents = np.array([l1, l1, l2, l2]).T
X = latents + rng.normal(size=4 * n).reshape((n, 4))
Y = latents + rng.normal(size=4 * n).reshape((n, 4))
X = np.concatenate(
(X, rng.normal(size=p_noise * n).reshape(n, p_noise)), axis=1)
Y = np.concatenate(
(Y, rng.normal(size=q_noise * n).reshape(n, q_noise)), axis=1)
pls_ca = pls_.PLSCanonical(n_components=3)
pls_ca.fit(X, Y)
x_weights = np.array(
[[0.65803719, 0.19197924, 0.21769083],
[0.7009113, 0.13303969, -0.15376699],
[0.13528197, -0.68636408, 0.13856546],
[0.16854574, -0.66788088, -0.12485304],
[-0.03232333, -0.04189855, 0.40690153],
[0.1148816, -0.09643158, 0.1613305],
[0.04792138, -0.02384992, 0.17175319],
[-0.06781, -0.01666137, -0.18556747],
[-0.00266945, -0.00160224, 0.11893098],
[-0.00849528, -0.07706095, 0.1570547],
[-0.00949471, -0.02964127, 0.34657036],
[-0.03572177, 0.0945091, 0.3414855],
[0.05584937, -0.02028961, -0.57682568],
[0.05744254, -0.01482333, -0.17431274]])
x_weights_sign_flip = pls_ca.x_weights_ / x_weights
x_loadings = np.array(
[[0.65649254, 0.1847647, 0.15270699],
[0.67554234, 0.15237508, -0.09182247],
[0.19219925, -0.67750975, 0.08673128],
[0.2133631, -0.67034809, -0.08835483],
[-0.03178912, -0.06668336, 0.43395268],
[0.15684588, -0.13350241, 0.20578984],
[0.03337736, -0.03807306, 0.09871553],
[-0.06199844, 0.01559854, -0.1881785],
[0.00406146, -0.00587025, 0.16413253],
[-0.00374239, -0.05848466, 0.19140336],
[0.00139214, -0.01033161, 0.32239136],
[-0.05292828, 0.0953533, 0.31916881],
[0.04031924, -0.01961045, -0.65174036],
[0.06172484, -0.06597366, -0.1244497]])
x_loadings_sign_flip = pls_ca.x_loadings_ / x_loadings
y_weights = np.array(
[[0.66101097, 0.18672553, 0.22826092],
[0.69347861, 0.18463471, -0.23995597],
[0.14462724, -0.66504085, 0.17082434],
[0.22247955, -0.6932605, -0.09832993],
[0.07035859, 0.00714283, 0.67810124],
[0.07765351, -0.0105204, -0.44108074],
[-0.00917056, 0.04322147, 0.10062478],
[-0.01909512, 0.06182718, 0.28830475],
[0.01756709, 0.04797666, 0.32225745]])
y_weights_sign_flip = pls_ca.y_weights_ / y_weights
y_loadings = np.array(
[[0.68568625, 0.1674376, 0.0969508],
[0.68782064, 0.20375837, -0.1164448],
[0.11712173, -0.68046903, 0.12001505],
[0.17860457, -0.6798319, -0.05089681],
[0.06265739, -0.0277703, 0.74729584],
[0.0914178, 0.00403751, -0.5135078],
[-0.02196918, -0.01377169, 0.09564505],
[-0.03288952, 0.09039729, 0.31858973],
[0.04287624, 0.05254676, 0.27836841]])
y_loadings_sign_flip = pls_ca.y_loadings_ / y_loadings
assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_loadings_sign_flip), 1, 4)
assert_array_almost_equal(y_loadings_sign_flip, y_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_loadings_sign_flip), 1, 4)
# Orthogonality of weights
# ~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(pls_ca.x_weights_, "x weights are not orthogonal")
check_ortho(pls_ca.y_weights_, "y weights are not orthogonal")
# Orthogonality of latent scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(pls_ca.x_scores_, "x scores are not orthogonal")
check_ortho(pls_ca.y_scores_, "y scores are not orthogonal")
def fit(self, X, Y):
# print('Training CCA, regularization = %0.4f, %d components' % (self.reg, self.n_components))
X = X.copy()
Y = Y.copy()
# Subtract mean and divide by std
X, Y, self.x_mean_, self.y_mean_, self.x_std_, self.y_std_ = (
_center_scale_xy(X, Y))
data = [X, Y]
# Get dimensions of data and number of canonical components
kernel = [d.T for d in data]
nDs = len(kernel)
nFs = [k.shape[0] for k in kernel]
numCC = min([k.shape[1] for k in kernel
]) if self.n_components is None else self.n_components
# Get the auto- and cross-covariance matrices
crosscovs = [
np.dot(ki, kj.T) / len(ki.T - 1) for ki in kernel for kj in kernel
]
# Allocate left-hand side (LH) and right-hand side (RH):
LH = np.zeros((sum(nFs), sum(nFs)))
RH = np.zeros((sum(nFs), sum(nFs)))
# Fill the left and right sides of the eigenvalue problem
# Eq. (7) in https://www.frontiersin.org/articles/10.3389/fninf.2016.00049/full
for ii in range(nDs):
RH[sum(nFs[:ii]):sum(nFs[:ii + 1]), sum(nFs[:ii]):sum(nFs[:ii + 1])] = \
(crosscovs[ii * (nDs + 1)] + self.reg[ii] * np.eye(nFs[ii]))
for jj in range(nDs):
if ii != jj:
LH[sum(nFs[:jj]):sum(nFs[:jj + 1]),
sum(nFs[:ii]):sum(nFs[:ii + 1])] = crosscovs[nDs * jj +
ii]
# The matrices are symmetric, i.e. A = A^T, this makes sure that small differences are evened out.
LH = (LH + LH.T) / 2.
RH = (RH + RH.T) / 2.
maxCC = LH.shape[0]
# Solve the generalized eigenvalue problem for the two symmetric matrices
# Returns the eigenvalues and the eigenvectors
r, Vs = eigh(LH, RH, eigvals=(maxCC - numCC, maxCC - 1))
r[np.isnan(r)] = 0
rindex = np.argsort(r)[::-1]
comp = []
Vs = Vs[:, rindex]
for ii in range(nDs):
comp.append(Vs[sum(nFs[:ii]):sum(nFs[:ii + 1]), :numCC])
self.x_weights_ = comp[0]
self.y_weights_ = comp[1]
self.x_loadings_ = np.dot(self.x_weights_.T, crosscovs[0]).T
self.y_loadings_ = np.dot(self.y_weights_.T, crosscovs[-1]).T
return self