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https://github.com/SheffieldML/GPy.git
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lots of F-ordering nonsense. Seems to work though
This commit is contained in:
James Hensman
parent
80a734e153
commit
3375606039
4 changed files with 109 additions and 88 deletions
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@ -17,7 +17,8 @@ import os
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from config import *
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if np.all(np.float64((scipy.__version__).split('.')[:2]) >= np.array([0, 12])):
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import scipy.linalg.lapack as lapack
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#import scipy.linalg.lapack.clapack as lapack
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from scipy.linalg import lapack
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else:
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from scipy.linalg.lapack import flapack as lapack
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@ -41,42 +42,103 @@ else:
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_blas_available = False
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warnings.warn("warning: caught this exception:" + str(e))
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def dtrtri(L, lower=0):
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def force_F_ordered_symmetric(A):
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"""
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Wrapper for lapack dtrtrs function
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return a F ordered version of A, assuming A is symmetric
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"""
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if A.flags['F_CONTIGUOUS']:
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return A
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if A.flags['C_CONTIGUOUS']:
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return A.T
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else:
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return np.asfortranarray(A)
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def force_F_ordered(A):
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"""
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return a F ordered version of A, assuming A is triangular
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"""
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if A.flags['F_CONTIGUOUS']:
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return A
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print "why are your arrays not F order?"
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return np.asfortranarray(A)
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def jitchol(A, maxtries=5):
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A = force_F_ordered_symmetric(A)
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L, info = lapack.dpotrf(A, lower=1)
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if info == 0:
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return L
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else:
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if maxtries==0:
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raise linalg.LinAlgError, "not positive definite, even with jitter."
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diagA = np.diag(A)
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if np.any(diagA <= 0.):
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raise linalg.LinAlgError, "not pd: non-positive diagonal elements"
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jitter = diagA.mean() * 1e-6
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return jitchol(A+np.eye(A.shape[0])*jitter, maxtries-1)
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#def jitchol(A, maxtries=5):
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# A = np.ascontiguousarray(A)
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# L, info = lapack.dpotrf(A, lower=1)
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# if info == 0:
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# return L
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# else:
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# diagA = np.diag(A)
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# if np.any(diagA <= 0.):
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# raise linalg.LinAlgError, "not pd: non-positive diagonal elements"
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# jitter = diagA.mean() * 1e-6
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# while maxtries > 0 and np.isfinite(jitter):
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# print 'Warning: adding jitter of {:.10e}'.format(jitter)
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# try:
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# return linalg.cholesky(A + np.eye(A.shape[0]).T * jitter, lower=True)
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# except:
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# jitter *= 10
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# finally:
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# maxtries -= 1
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# raise linalg.LinAlgError, "not positive definite, even with jitter."
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#
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def dtrtri(L, lower=1):
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"""
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Wrapper for lapack dtrtri function
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Inverse of L
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:param L: Triangular Matrix L
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:param lower: is matrix lower (true) or upper (false)
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:returns: Li, info
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"""
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L = force_F_ordered(L)
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return lapack.dtrtri(L, lower=lower)
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def dtrtrs(A, B, lower=0, trans=0, unitdiag=0):
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def dtrtrs(A, B, lower=1, trans=0, unitdiag=0):
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"""
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Wrapper for lapack dtrtrs function
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:param A: Matrix A
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:param A: Matrix A(triangular)
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:param B: Matrix B
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:param lower: is matrix lower (true) or upper (false)
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:returns:
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"""
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A = force_F_ordered(A)
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#Note: B does not seem to need to be F ordered!
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return lapack.dtrtrs(A, B, lower=lower, trans=trans, unitdiag=unitdiag)
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def dpotrs(A, B, lower=0):
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def dpotrs(A, B, lower=1):
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"""
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Wrapper for lapack dpotrs function
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:param A: Matrix A
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:param B: Matrix B
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:param lower: is matrix lower (true) or upper (false)
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:returns:
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"""
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A = force_F_ordered(A)
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return lapack.dpotrs(A, B, lower=lower)
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def dpotri(A, lower=0):
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def dpotri(A, lower=1):
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"""
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Wrapper for lapack dpotri function
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@ -85,7 +147,12 @@ def dpotri(A, lower=0):
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:returns: A inverse
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"""
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return lapack.dpotri(A, lower=lower)
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assert lower==1, "scipy linalg behaviour is very weird. please use lower, fortran ordered arrays"
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A = force_F_ordered(A)
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R, info = lapack.dpotri(A, lower=0)
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symmetrify(R)
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return R, info
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def pddet(A):
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"""
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@ -133,60 +200,8 @@ def _mdot_r(a, b):
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b = b[0]
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return np.dot(a, b)
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def jitchol(A, maxtries=5):
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A = np.asfortranarray(A)
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L, info = lapack.dpotrf(A, lower=1)
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if info == 0:
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return L
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else:
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diagA = np.diag(A)
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if np.any(diagA <= 0.):
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raise linalg.LinAlgError, "not pd: non-positive diagonal elements"
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jitter = diagA.mean() * 1e-6
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while maxtries > 0 and np.isfinite(jitter):
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print 'Warning: adding jitter of {:.10e}'.format(jitter)
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try:
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return linalg.cholesky(A + np.eye(A.shape[0]).T * jitter, lower=True)
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except:
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jitter *= 10
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finally:
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maxtries -= 1
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raise linalg.LinAlgError, "not positive definite, even with jitter."
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def jitchol_old(A, maxtries=5):
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"""
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:param A: An almost pd square matrix
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:rval L: the Cholesky decomposition of A
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.. note:
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Adds jitter to K, to enforce positive-definiteness
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if stuff breaks, please check:
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np.allclose(sp.linalg.cholesky(XXT, lower = True), np.triu(sp.linalg.cho_factor(XXT)[0]).T)
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"""
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try:
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return linalg.cholesky(A, lower=True)
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except linalg.LinAlgError:
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diagA = np.diag(A)
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if np.any(diagA < 0.):
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raise linalg.LinAlgError, "not pd: negative diagonal elements"
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jitter = diagA.mean() * 1e-6
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for i in range(1, maxtries + 1):
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print '\rWarning: adding jitter of {:.10e} '.format(jitter),
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try:
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return linalg.cholesky(A + np.eye(A.shape[0]).T * jitter, lower=True)
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except:
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jitter *= 10
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raise linalg.LinAlgError, "not positive definite, even with jitter."
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def pdinv(A, *args):
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"""
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:param A: A DxD pd numpy array
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:rval Ai: the inverse of A
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@ -201,7 +216,7 @@ def pdinv(A, *args):
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"""
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L = jitchol(A, *args)
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logdet = 2.*np.sum(np.log(np.diag(L)))
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Li = chol_inv(L)
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Li = dtrtri(L)
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Ai, _ = lapack.dpotri(L)
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# Ai = np.tril(Ai) + np.tril(Ai,-1).T
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symmetrify(Ai)
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@ -209,7 +224,7 @@ def pdinv(A, *args):
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return Ai, L, Li, logdet
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def chol_inv(L):
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def dtrtri(L):
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"""
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Inverts a Cholesky lower triangular matrix
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@ -218,7 +233,8 @@ def chol_inv(L):
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"""
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return lapack.dtrtri(L, lower=True)[0]
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L = force_F_ordered(L)
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return lapack.dtrtri(L, lower=1)[0]
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def multiple_pdinv(A):
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@ -234,7 +250,7 @@ def multiple_pdinv(A):
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N = A.shape[-1]
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chols = [jitchol(A[:, :, i]) for i in range(N)]
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halflogdets = [np.sum(np.log(np.diag(L[0]))) for L in chols]
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invs = [lapack.dpotri(L[0], True)[0] for L in chols]
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invs = [dpotri(L[0], True)[0] for L in chols]
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invs = [np.triu(I) + np.triu(I, 1).T for I in invs]
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return np.dstack(invs), np.array(halflogdets)
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@ -425,7 +441,8 @@ def tdot_blas(mat, out=None):
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symmetrify(out, upper=True)
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return out
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return np.ascontiguousarray(out)
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def tdot(*args, **kwargs):
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if _blas_available:
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@ -557,24 +574,24 @@ def cholupdate(L, x):
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def backsub_both_sides(L, X, transpose='left'):
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""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
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if transpose == 'left':
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tmp, _ = lapack.dtrtrs(L, np.asfortranarray(X), lower=1, trans=1)
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return lapack.dtrtrs(L, np.asfortranarray(tmp.T), lower=1, trans=1)[0].T
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tmp, _ = dtrtrs(L, X, lower=1, trans=1)
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return dtrtrs(L, tmp.T, lower=1, trans=1)[0].T
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else:
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tmp, _ = lapack.dtrtrs(L, np.asfortranarray(X), lower=1, trans=0)
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return lapack.dtrtrs(L, np.asfortranarray(tmp.T), lower=1, trans=0)[0].T
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tmp, _ = dtrtrs(L, X, lower=1, trans=0)
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return dtrtrs(L, tmp.T, lower=1, trans=0)[0].T
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def PCA(Y, input_dim):
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"""
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Principal component analysis: maximum likelihood solution by SVD
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Principal component analysis: maximum likelihood solution by SVD
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:param Y: NxD np.array of data
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:param input_dim: int, dimension of projection
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:param Y: NxD np.array of data
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:param input_dim: int, dimension of projection
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:rval X: - Nxinput_dim np.array of dimensionality reduced data
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:rval W: - input_dimxD mapping from X to Y
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:rval X: - Nxinput_dim np.array of dimensionality reduced data
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:rval W: - input_dimxD mapping from X to Y
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"""
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"""
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if not np.allclose(Y.mean(axis=0), 0.0):
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print "Y is not zero mean, centering it locally (GPy.util.linalg.PCA)"
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