def test_svd(self):
#Test that SVD works
#Take a sample matrix:
M = [[1.0, 2.0, 3.0, 4.0], [3.0, 5.0, -1.0, 0.0],
[2.0, -2.0, 1.0, 1.0], [-5.0, -2.0, -1.0, 0.0]]
#And calculate it's bidiagonal transform:
U, s, V = svd.svd(M)
#ENsure that decomposition is correct.
M1 = reduce(mmul, [U, from_diag(s), V])
self.assertTrue(mat_eq(M, M1, 1e-5))
#Ensure that matrices are orthogonal
self.assertOrthogonal(U)
self.assertOrthogonal(V)
def test_svd(self):
#Test that SVD works
#Take a sample matrix:
M = [[1.0, 2.0, 3.0, 4.0],
[3.0, 5.0, -1.0, 0.0],
[2.0, -2.0, 1.0, 1.0],
[-5.0, -2.0, -1.0, 0.0]]
#And calculate it's bidiagonal transform:
U,s,V = svd.svd( M )
#ENsure that decomposition is correct.
M1 = reduce( mmul, [U, from_diag(s), V] )
self.assertTrue( mat_eq( M, M1, 1e-5 ) )
#Ensure that matrices are orthogonal
self.assertOrthogonal( U )
self.assertOrthogonal( V )
def test_svd_singular(self):
#Let's make a singular matrix M:
x = [[1.0, 2.0, 3.0, 4.0], [-5.0, -2.0, -1.0, 0.0]]
M = mmul(transpose(x), x)
#And see, what it's SVD looks like:
U, s, V = svd.svd(M)
#ensure that rank is correct
self.assertTrue(sum(1 if abs(si) > 1e-5 else 0
for si in s) == 2) #rank must be 2
#ENsure that decomposition is correct.
M1 = reduce(mmul, [U, from_diag(s), V])
self.assertTrue(mat_eq(M, M1, 1e-5))
#Ensure that matrices are orthogonal
self.assertOrthogonal(U)
self.assertOrthogonal(V)
def test_svd_singular(self):
#Let's make a singular matrix M:
x = [[1.0, 2.0, 3.0, 4.0],
[-5.0, -2.0, -1.0, 0.0]]
M = mmul(transpose(x), x)
#And see, what it's SVD looks like:
U,s,V = svd.svd(M)
#ensure that rank is correct
self.assertTrue( sum( 1 if abs(si) > 1e-5 else 0
for si in s ) == 2 ) #rank must be 2
#ENsure that decomposition is correct.
M1 = reduce( mmul, [U, from_diag(s), V] )
self.assertTrue( mat_eq( M, M1, 1e-5 ) )
#Ensure that matrices are orthogonal
self.assertOrthogonal( U )
self.assertOrthogonal( V )
"""
eps = gmpy.mpf(2, prec) ** (-prec + 3)
return NumericContext(
one=gmpy.mpf(1,prec),
zero=gmpy.mpf(0, prec),
fabs=abs,
sqrt=gmpy.fsqrt,
from_int = lambda x: gmpy.mpf(x, prec),
eps = eps
)
if __name__=="__main__":
import pyla.core as pylinalg
from pyla import svd
context = GMPYContext(300)
m = pylinalg.to_context_mat(pylinalg.rand_mat(4,4),
context=context)
u,s,v = svd.svd( m, context=context, tol = context.from_int(1e-150) )
print (pylinalg.show_mat(u))
print (pylinalg.show_mat(v))
print (s)
m1 = reduce( pylinalg.mmul, [u, pylinalg.from_diag(s,context=context),
v] )
print ("-------------------------------------")
print (pylinalg.show_mat( pylinalg.mat_diff( m, m1 ) ))