def testFullRank(self):
dimension = 10
nData = 500
design = numpy.random.randn(dimension, nData).transpose()
data = numpy.random.randn(nData)
fisher = numpy.dot(design.transpose(), design)
rhs = numpy.dot(design.transpose(), data)
solution, residues, rank, sv = numpy.linalg.lstsq(design, data)
cov = numpy.linalg.inv(fisher)
s_svd = LeastSquares.fromDesignMatrix(design, data,
LeastSquares.DIRECT_SVD)
s_design_eigen = LeastSquares.fromDesignMatrix(
design, data, LeastSquares.NORMAL_EIGENSYSTEM)
s_design_cholesky = LeastSquares.fromDesignMatrix(
design, data, LeastSquares.NORMAL_CHOLESKY)
s_normal_eigen = LeastSquares.fromNormalEquations(
fisher, rhs, LeastSquares.NORMAL_EIGENSYSTEM)
s_normal_cholesky = LeastSquares.fromNormalEquations(
fisher, rhs, LeastSquares.NORMAL_CHOLESKY)
self.check(s_svd, solution, rank, fisher, cov, sv)
self.check(s_design_eigen, solution, rank, fisher, cov, sv)
self.check(s_design_cholesky, solution, rank, fisher, cov, sv)
self.check(s_normal_eigen, solution, rank, fisher, cov, sv)
self.check(s_normal_cholesky, solution, rank, fisher, cov, sv)
# test updating solver in-place with the same kind of inputs
design = numpy.random.randn(dimension, nData).transpose()
data = numpy.random.randn(nData)
fisher = numpy.dot(design.transpose(), design)
rhs = numpy.dot(design.transpose(), data)
solution, residues, rank, sv = numpy.linalg.lstsq(design, data)
cov = numpy.linalg.inv(fisher)
s_svd.setDesignMatrix(design, data)
s_design_eigen.setDesignMatrix(design, data)
s_design_cholesky.setDesignMatrix(design, data)
s_normal_eigen.setNormalEquations(fisher, rhs)
s_normal_cholesky.setNormalEquations(fisher, rhs)
self.check(s_svd, solution, rank, fisher, cov, sv)
self.check(s_design_eigen, solution, rank, fisher, cov, sv)
self.check(s_design_cholesky, solution, rank, fisher, cov, sv)
self.check(s_normal_eigen, solution, rank, fisher, cov, sv)
self.check(s_normal_cholesky, solution, rank, fisher, cov, sv)
# test updating solver in-place with the opposite kind of inputs
design = numpy.random.randn(dimension, nData).transpose()
data = numpy.random.randn(nData)
fisher = numpy.dot(design.transpose(), design)
rhs = numpy.dot(design.transpose(), data)
solution, residues, rank, sv = numpy.linalg.lstsq(design, data)
cov = numpy.linalg.inv(fisher)
s_normal_eigen.setDesignMatrix(design, data)
s_normal_cholesky.setDesignMatrix(design, data)
s_design_eigen.setNormalEquations(fisher, rhs)
s_design_cholesky.setNormalEquations(fisher, rhs)
self.check(s_design_eigen, solution, rank, fisher, cov, sv)
self.check(s_design_cholesky, solution, rank, fisher, cov, sv)
self.check(s_normal_eigen, solution, rank, fisher, cov, sv)
self.check(s_normal_cholesky, solution, rank, fisher, cov, sv)
def testFullRank(self):
dimension = 10
nData = 500
design = np.random.randn(dimension, nData).transpose()
data = np.random.randn(nData)
fisher = np.dot(design.transpose(), design)
rhs = np.dot(design.transpose(), data)
solution, residues, rank, sv = np.linalg.lstsq(design, data, rcond=None)
cov = np.linalg.inv(fisher)
s_svd = LeastSquares.fromDesignMatrix(
design, data, LeastSquares.DIRECT_SVD)
s_design_eigen = LeastSquares.fromDesignMatrix(
design, data, LeastSquares.NORMAL_EIGENSYSTEM)
s_design_cholesky = LeastSquares.fromDesignMatrix(
design, data, LeastSquares.NORMAL_CHOLESKY)
s_normal_eigen = LeastSquares.fromNormalEquations(
fisher, rhs, LeastSquares.NORMAL_EIGENSYSTEM)
s_normal_cholesky = LeastSquares.fromNormalEquations(
fisher, rhs, LeastSquares.NORMAL_CHOLESKY)
self.check(s_svd, solution, rank, fisher, cov, sv)
self.check(s_design_eigen, solution, rank, fisher, cov, sv)
self.check(s_design_cholesky, solution, rank, fisher, cov, sv)
self.check(s_normal_eigen, solution, rank, fisher, cov, sv)
self.check(s_normal_cholesky, solution, rank, fisher, cov, sv)
# test updating solver in-place with the same kind of inputs
design = np.random.randn(dimension, nData).transpose()
data = np.random.randn(nData)
fisher = np.dot(design.transpose(), design)
rhs = np.dot(design.transpose(), data)
solution, residues, rank, sv = np.linalg.lstsq(design, data, rcond=None)
cov = np.linalg.inv(fisher)
s_svd.setDesignMatrix(design, data)
s_design_eigen.setDesignMatrix(design, data)
s_design_cholesky.setDesignMatrix(design, data)
s_normal_eigen.setNormalEquations(fisher, rhs)
s_normal_cholesky.setNormalEquations(fisher, rhs)
self.check(s_svd, solution, rank, fisher, cov, sv)
self.check(s_design_eigen, solution, rank, fisher, cov, sv)
self.check(s_design_cholesky, solution, rank, fisher, cov, sv)
self.check(s_normal_eigen, solution, rank, fisher, cov, sv)
self.check(s_normal_cholesky, solution, rank, fisher, cov, sv)
# test updating solver in-place with the opposite kind of inputs
design = np.random.randn(dimension, nData).transpose()
data = np.random.randn(nData)
fisher = np.dot(design.transpose(), design)
rhs = np.dot(design.transpose(), data)
solution, residues, rank, sv = np.linalg.lstsq(design, data, rcond=None)
cov = np.linalg.inv(fisher)
s_normal_eigen.setDesignMatrix(design, data)
s_normal_cholesky.setDesignMatrix(design, data)
s_design_eigen.setNormalEquations(fisher, rhs)
s_design_cholesky.setNormalEquations(fisher, rhs)
self.check(s_design_eigen, solution, rank, fisher, cov, sv)
self.check(s_design_cholesky, solution, rank, fisher, cov, sv)
self.check(s_normal_eigen, solution, rank, fisher, cov, sv)
self.check(s_normal_cholesky, solution, rank, fisher, cov, sv)
def testSingular(self):
dimension = 10
nData = 100
svIn = (numpy.random.randn(dimension) + 1.0)**2 + 1.0
svIn = numpy.sort(svIn)[::-1]
svIn[-1] = 0.0
svIn[-2] = svIn[0] * 1E-4
# Just use SVD to get a pair of orthogonal matrices; we'll use our own singular values
# so we can control the stability of the matrix.
u, s, vt = numpy.linalg.svd(numpy.random.randn(dimension, nData),
full_matrices=False)
design = numpy.dot(u * svIn, vt).transpose()
data = numpy.random.randn(nData)
fisher = numpy.dot(design.transpose(), design)
rhs = numpy.dot(design.transpose(), data)
threshold = 10 * sys.float_info.epsilon
solution, residues, rank, sv = numpy.linalg.lstsq(design,
data,
rcond=threshold)
self.assertClose(svIn, sv)
cov = numpy.linalg.pinv(fisher, rcond=threshold)
s_svd = LeastSquares.fromDesignMatrix(design, data,
LeastSquares.DIRECT_SVD)
s_design_eigen = LeastSquares.fromDesignMatrix(
design, data, LeastSquares.NORMAL_EIGENSYSTEM)
s_normal_eigen = LeastSquares.fromNormalEquations(
fisher, rhs, LeastSquares.NORMAL_EIGENSYSTEM)
self.check(s_svd, solution, rank, fisher, cov, sv)
self.check(s_design_eigen, solution, rank, fisher, cov, sv)
self.check(s_normal_eigen, solution, rank, fisher, cov, sv)
s_svd.setThreshold(1E-3)
s_design_eigen.setThreshold(1E-6)
s_normal_eigen.setThreshold(1E-6)
self.assertEqual(s_svd.getRank(), dimension - 2)
self.assertEqual(s_design_eigen.getRank(), dimension - 2)
self.assertEqual(s_normal_eigen.getRank(), dimension - 2)
# Just check that solutions are different from before, but consistent with each other;
# I can't figure out how get numpy.lstsq to deal with the thresholds appropriately to
# test against that.
self.assertNotClose(s_svd.getSolution(), solution)
self.assertNotClose(s_design_eigen.getSolution(), solution)
self.assertNotClose(s_normal_eigen.getSolution(), solution)
self.assertClose(s_svd.getSolution(), s_design_eigen.getSolution())
self.assertClose(s_svd.getSolution(), s_normal_eigen.getSolution())
def testSingular(self):
dimension = 10
nData = 100
svIn = (np.random.randn(dimension) + 1.0)**2 + 1.0
svIn = np.sort(svIn)[::-1]
svIn[-1] = 0.0
svIn[-2] = svIn[0] * 1E-4
# Just use SVD to get a pair of orthogonal matrices; we'll use our own singular values
# so we can control the stability of the matrix.
u, s, vt = np.linalg.svd(np.random.randn(dimension, nData),
full_matrices=False)
design = np.dot(u * svIn, vt).transpose()
data = np.random.randn(nData)
fisher = np.dot(design.transpose(), design)
rhs = np.dot(design.transpose(), data)
threshold = 10 * sys.float_info.epsilon
solution, residues, rank, sv = np.linalg.lstsq(
design, data, rcond=threshold)
self._assertClose(svIn, sv)
cov = np.linalg.pinv(fisher, rcond=threshold)
s_svd = LeastSquares.fromDesignMatrix(
design, data, LeastSquares.DIRECT_SVD)
s_design_eigen = LeastSquares.fromDesignMatrix(
design, data, LeastSquares.NORMAL_EIGENSYSTEM)
s_normal_eigen = LeastSquares.fromNormalEquations(
fisher, rhs, LeastSquares.NORMAL_EIGENSYSTEM)
self.check(s_svd, solution, rank, fisher, cov, sv)
self.check(s_design_eigen, solution, rank, fisher, cov, sv)
self.check(s_normal_eigen, solution, rank, fisher, cov, sv)
s_svd.setThreshold(1E-3)
s_design_eigen.setThreshold(1E-6)
s_normal_eigen.setThreshold(1E-6)
self.assertEqual(s_svd.getRank(), dimension - 2)
self.assertEqual(s_design_eigen.getRank(), dimension - 2)
self.assertEqual(s_normal_eigen.getRank(), dimension - 2)
# Just check that solutions are different from before, but consistent with each other;
# I can't figure out how get np.lstsq to deal with the thresholds appropriately to
# test against that.
self._assertNotClose(s_svd.getSolution(), solution)
self._assertNotClose(s_design_eigen.getSolution(), solution)
self._assertNotClose(s_normal_eigen.getSolution(), solution)
self._assertClose(s_svd.getSolution(), s_design_eigen.getSolution())
self._assertClose(s_svd.getSolution(), s_normal_eigen.getSolution())
