test_QR.py

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import numpy as np
 
import eigenpy
 
rows = 20
cols = 100
rng = np.random.default_rng()
 
A = rng.random((rows, cols))
 
# Test HouseholderQR decomposition
householder_qr = eigenpy.HouseholderQR()
householder_qr = eigenpy.HouseholderQR(rows, cols)
householder_qr = eigenpy.HouseholderQR(A)
 
householder_qr_eye = eigenpy.HouseholderQR(np.eye(rows, rows))
X = rng.random((rows, 20))
assert householder_qr_eye.absDeterminant() == 1.0
assert householder_qr_eye.logAbsDeterminant() == 0.0
 
Y = householder_qr_eye.solve(X)
assert (X == Y).all()
 
# Test FullPivHouseholderQR decomposition
fullpiv_householder_qr = eigenpy.FullPivHouseholderQR()
fullpiv_householder_qr = eigenpy.FullPivHouseholderQR(rows, cols)
fullpiv_householder_qr = eigenpy.FullPivHouseholderQR(A)
 
fullpiv_householder_qr = eigenpy.FullPivHouseholderQR(np.eye(rows, rows))
X = rng.random((rows, 20))
assert fullpiv_householder_qr.absDeterminant() == 1.0
assert fullpiv_householder_qr.logAbsDeterminant() == 0.0
 
Y = fullpiv_householder_qr.solve(X)
assert (X == Y).all()
assert fullpiv_householder_qr.rank() == rows
 
fullpiv_householder_qr.setThreshold(1e-8)
assert fullpiv_householder_qr.threshold() == 1e-8
assert eigenpy.is_approx(np.eye(rows, rows), fullpiv_householder_qr.inverse())
 
# Test ColPivHouseholderQR decomposition
colpiv_householder_qr = eigenpy.ColPivHouseholderQR()
colpiv_householder_qr = eigenpy.ColPivHouseholderQR(rows, cols)
colpiv_householder_qr = eigenpy.ColPivHouseholderQR(A)
 
colpiv_householder_qr = eigenpy.ColPivHouseholderQR(np.eye(rows, rows))
X = rng.random((rows, 20))
assert colpiv_householder_qr.absDeterminant() == 1.0
assert colpiv_householder_qr.logAbsDeterminant() == 0.0
 
Y = colpiv_householder_qr.solve(X)
assert (X == Y).all()
assert colpiv_householder_qr.rank() == rows
 
colpiv_householder_qr.setThreshold(1e-8)
assert colpiv_householder_qr.threshold() == 1e-8
assert eigenpy.is_approx(np.eye(rows, rows), colpiv_householder_qr.inverse())
 
# Test CompleteOrthogonalDecomposition
cod = eigenpy.CompleteOrthogonalDecomposition()
cod = eigenpy.CompleteOrthogonalDecomposition(rows, cols)
cod = eigenpy.CompleteOrthogonalDecomposition(A)
 
cod = eigenpy.CompleteOrthogonalDecomposition(np.eye(rows, rows))
X = rng.random((rows, 20))
assert cod.absDeterminant() == 1.0
assert cod.logAbsDeterminant() == 0.0
 
Y = cod.solve(X)
assert (X == Y).all()
assert cod.rank() == rows
 
cod.setThreshold(1e-8)
assert cod.threshold() == 1e-8
assert eigenpy.is_approx(np.eye(rows, rows), cod.pseudoInverse())