def testRandom(self): m = Matrix(5) m.random(3) q, r = m.QRSimple() one = Matrix(5) one.one() self.assertTrue(m.isAlmostEqual(q*r)) self.assertTrue(one.isAlmostEqual(q*q.transpose()))
def testRandom(self): m = Matrix(self.size) m.random(3) q, r = m.QRHouseholder() one = Matrix(self.size) one.one() self.assertTrue(m.isAlmostEqual(q*r)) self.assertTrue(one.isAlmostEqual(q*q.transpose()))
def test(self, m, size):
one = Matrix(size)
one.one()
e_lu = (m * m.invertLU() - one).frobeniusNorm()
e_qr_simple = (m * m.invertQRSimple() - one).frobeniusNorm()
e_qr_house = (m * m.invertQRHouseholder() - one).frobeniusNorm()
self.putMany([size, e_lu, e_qr_simple, e_qr_house])
def testRandom(self):
l = Matrix(self.size)
u = Matrix(self.size)
l.randomLowerTriangular(5)
u.randomUpperTriangular(5)
m = l * u
one = Matrix(self.size)
one.one()
self.assertTrue(one.isAlmostEqual(m * m.invertLU()))
def testUpperTriangularInversion(self):
a = Matrix(15)
a.randomUpperTriangular(87)
b = a.invertUpperTriangular()
c = Matrix(15)
c.one()
print (c - a * b).frobeniusNorm()
self.assertTrue(c.isAlmostEqual(a * b))
self.assertTrue(c.isAlmostEqual(b * a))
def test(self, m, size):
one = Matrix(size)
one.one()
m.random(int(time()))
q, r = m.QRSimple()
a_simple = (q*q.transpose() - one).frobeniusNorm()
b_simple = (m - q*r).frobeniusNorm()
q, r = m.QRHouseholder()
a_house = (q*q.transpose() - one).frobeniusNorm()
b_house = (m - q*r).frobeniusNorm()
self.putMany([size, a_simple, b_simple, a_house, b_house])
def testManipulators(self): a = Matrix(44) a.zero() a.one() a.hilbert()
def testUnit(self): one = Matrix(self.size) one.one() self.assertTrue(one.isAlmostEqual(one.invertLU()))
def testRandom(self): m = Matrix(self.size) m.random(3); one = Matrix(self.size) one.one() self.assertTrue(one.isAlmostEqual(m * m.invertQRHouseholder()))