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#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
def quadM(m, n):
res = ot.Matrix(m, n)
for i in range(m):
for j in range(n):
res[i, j] = (i + 1.0) ** (j + 1.0)
return res
def testQR(m, n, full, keep):
matrix1 = quadM(m, n)
print("M=", matrix1)
if keep:
Q, R = matrix1.computeQR(full)
else:
Q, R = matrix1.computeQRInPlace(full)
print("full=", full, "keep=", keep)
print("Q= ", Q)
print("R=", R)
print("Q*R=", Q * R)
if keep:
print("M2=", matrix1)
# Square case
matrix1 = quadM(3, 3)
matrix1.setName("matrix1")
print("matrix1 = ", repr(matrix1))
result1 = matrix1.computeSingularValues()
print("svd (svd only)= ", repr(result1))
result1, u, v = matrix1.computeSVD(True)
print("svd (svd + U, V full)= ", repr(result1))
result1, u, v = matrix1.computeSVD(False)
print("svd (svd + U, V small)= ", repr(result1), ", U=", repr(u), ", v=", repr(v))
# Rectangular case, m < n
matrix1 = quadM(3, 5)
matrix1.setName("matrix1")
print("matrix1 = ", repr(matrix1))
result1 = matrix1.computeSingularValues()
print("svd (svd only)= ", repr(result1))
result1, u, v = matrix1.computeSVD(True)
print("svd (svd + U, V full)= ", repr(result1))
result1, u, v = matrix1.computeSVD(False)
print("svd (svd + U, V small)= ", repr(result1), ", U=", repr(u), ", v=", repr(v))
# Rectangular case, m > n
matrix1 = quadM(5, 3)
matrix1.setName("matrix1")
print("matrix1 = ", repr(matrix1))
result1 = matrix1.computeSingularValues()
print("svd (svd only)= ", repr(result1))
result1, u, v = matrix1.computeSVD(True)
print("svd (svd + U, V full)= ", repr(result1))
# result1, u, v = matrix1.computeSVD(False)
# print "svd (svd + U, V small)= ", repr(result1), ", U=", repr(u), ",
# v=", repr(v)
for iFull in range(2):
for iKeep in range(2):
testQR(3, 3, iFull == 1, iKeep == 1)
testQR(3, 5, iFull == 1, iKeep == 1)
testQR(5, 3, iFull == 1, iKeep == 1)
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