def eig_sym(G, compute_z=True, uplo='U'):
"""
compute Eigenvalue Decompositon of a symmetric or Hermitian matrix G
G = V D V^{*}
Parameters
-------------------------------------
G: PitchArray, GPUArray or numpy.ndarray
if G is GPUArray or PitchArray, its gpudata will be destroyed
after calling the function
compute_z: bool
whether return eigenvectors
uplo: str
'U' or 'u' assumes the entries of G are stored
in upper triangular part,
lower off diagonal triangular part is not referenced
'L' or 'l' assumes the entries of G are stored
in lower triangular part,
upper off diagonal triangular part is not referenced
Returns
-------------------------------------
D: PitchArray
a row vector containing all eigenvalues with ascending order
V: PitchArray
if compute_z, jth column of V contains orthonormal
eigenvector associated with jth eigenvalue
Examples
D = eig_sym(G, compute_z = False)
D,V = eig_sym(G, compute_z = True)
"""
if cula._libcula_toolkit != 'premium':
raise ValueError("eigenvalue decomposition is only supported "
"in premium version of CULA")
if G.__class__ is not parray.PitchArray:
if G.__class__ is garray.GPUArray:
h_G = G.get()
del G.gpudata
A = parray.to_gpu(h_G)
elif G.__class__ is np.ndarray:
A = parray.to_gpu(G)
else:
raise TypeError("G must be either parray, or GPUArray or ndarray")
else:
A = G
if len(A.shape) != 2:
raise TypeError("eig only works on 2D matrix")
if A.shape[0] != A.shape[1]:
raise ValueError("G must be square matrix")
if uplo in ['u', 'U']:
uplo = 'L'
elif uplo in ['l', 'L']:
uplo = 'U'
else:
raise ValueError("uplo must be 'U' or 'L'")
real_dtype = np.dtype(np.float32)
if A.dtype == np.complex64:
eig_func = cula.culaDeviceCheev
elif A.dtype == np.float32:
eig_func = cula.culaDeviceSsyev
else:
if A.dtype == np.complex128:
eig_func = cula.culaDeviceZheev
elif A.dtype == np.float64:
eig_func = cula.culaDeviceDsyev
else:
raise ValueError('unsupported type')
real_dtype = np.dtype(np.float64)
D = parray.empty(A.shape[0], real_dtype)
cula.culaInitialize()
handle = cublashandle()
if compute_z:
jobz = 'V'
else:
jobz = 'N'
eig_func(handle.handle, jobz, uplo, A.shape[0], A.gpudata, A.ld, D.gpudata)
#cula.culaShutdown()
if compute_z:
return D, A.conj().T()
else:
return D
def eig_sym(G, compute_z = True, uplo = 'U'):
"""
compute Eigenvalue Decompositon of a symmetric or Hermitian matrix G
G = V D V^{*}
Parameters
-------------------------------------
G: PitchArray, GPUArray or numpy.ndarray
if G is GPUArray or PitchArray, its gpudata will be destroyed
after calling the function
compute_z: bool
whether return eigenvectors
uplo: str
'U' or 'u' assumes the entries of G are stored
in upper triangular part,
lower off diagonal triangular part is not referenced
'L' or 'l' assumes the entries of G are stored
in lower triangular part,
upper off diagonal triangular part is not referenced
Returns
-------------------------------------
D: PitchArray
a row vector containing all eigenvalues with ascending order
V: PitchArray
if compute_z, jth column of V contains orthonormal
eigenvector associated with jth eigenvalue
Examples
D = eig_sym(G, compute_z = False)
D,V = eig_sym(G, compute_z = True)
"""
if cula._libcula_toolkit != 'premium':
raise ValueError("eigenvalue decomposition is only supported "
"in premium version of CULA")
if G.__class__ is not parray.PitchArray:
if G.__class__ is garray.GPUArray:
h_G = G.get()
del G.gpudata
A= parray.to_gpu(h_G)
elif G.__class__ is np.ndarray:
A = parray.to_gpu(G)
else:
raise TypeError("G must be either parray, or GPUArray or ndarray")
else:
A = G
if len(A.shape) != 2:
raise TypeError("eig only works on 2D matrix")
if A.shape[0] != A.shape[1]:
raise ValueError("G must be square matrix")
if uplo in ['u', 'U']:
uplo = 'L'
elif uplo in ['l', 'L']:
uplo = 'U'
else:
raise ValueError("uplo must be 'U' or 'L'")
real_dtype = np.dtype(np.float32)
if A.dtype == np.complex64:
eig_func = cula.culaDeviceCheev
elif A.dtype == np.float32:
eig_func = cula.culaDeviceSsyev
else:
if A.dtype == np.complex128:
eig_func = cula.culaDeviceZheev
elif A.dtype == np.float64:
eig_func = cula.culaDeviceDsyev
else:
raise ValueError('unsupported type')
real_dtype = np.dtype(np.float64)
D = parray.empty(A.shape[0], real_dtype)
cula.culaInitialize()
handle = cublashandle()
if compute_z:
jobz = 'V'
else:
jobz = 'N'
eig_func(handle.handle, jobz, uplo, A.shape[0], A.gpudata, A.ld, D.gpudata)
#cula.culaShutdown()
if compute_z:
return D, A.conj().T()
else:
return D
def svd(G, compute_u=True, compute_v=True, econ=False):
"""
compute Singular Value Decompositon of G
G = U*(diag(S))*V
Parameters
----------------------------------------
G: PitchArray, GPUArray or numpy.ndarray of shape (m,n)
if G is GPUArray or PitchArray, its gpudata will be
destroyed after calling the function
compute_u: bool
whether return U matrix or not
compute_v: bool
whether return V matrix or not
econ: bool
return economical matrix
Returns:
U: parray.PitchArray matrix
as U in G = U*(diag(S))*V,
if econ, returns the first min(m,n) columns of U
S: parray.PitchArray vector
a row vector containing all singular values
with descending order
V: parray.PitchArray matrix
as V in G = U*(diag(S))*V,
if econ, returns the first min(m,n) rows of V
order of output:
always obeys the order U,S,V
e.g.
S = svd(G, compute_u = False, compute_v = False)
U,S = svd(G, compute_u = True, compute_v = False)
S,V = svd(G, compute_u = False, compute_v = True)
U,S,V = svd(G, compute_u = True, compute_v = True)
"""
if G.__class__ is not parray.PitchArray:
if G.__class__ is garray.GPUArray:
h_G = G.get()
del G.gpudata
A = parray.to_gpu(h_G)
elif G.__class__ is np.ndarray:
A = parray.to_gpu(G)
else:
raise TypeError("G must be either parray, or GPUArray or ndarray")
else:
A = G
real_dtype = np.dtype(np.float32)
if A.dtype == np.complex64:
svd_func = cula.culaDeviceCgesvd
elif A.dtype == np.float32:
svd_func = cula.culaDeviceSgesvd
else:
if cula._libcula_toolkit == 'standard':
if A.dtype == np.complex128:
svd_func = cula.culaDeviceZgesvd
elif A.dtype == np.float64:
svd_func = cula.culaDeviceDgesvd
else:
raise ValueError('unsupported type')
real_dtype = np.dtype(np.float64)
else:
raise TypeError('does not support premium double precision svd')
if len(A.shape) != 2:
raise TypeError("svd only works on 2D matrix")
S = parray.empty(min(A.shape), real_dtype)
cula.culaInitialize()
if compute_u:
if compute_v:
if econ:
if A.shape[1] <= A.shape[0]:
jobu = 'A'
jobvt = 'O'
V = parray.empty((A.shape[1], A.shape[1]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata,
A.ld, S.gpudata, V.gpudata, V.ld, 1, 1)
#cula.culaShutdown()
return A, S, V
else:
jobu = 'O'
jobvt = 'A'
U = parray.empty((A.shape[0], A.shape[0]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata,
A.ld, S.gpudata, 1, 1, U.gpudata, U.ld)
#cula.culaShutdown()
return U, S, A
else:
if A.shape[1] <= A.shape[0]:
jobu = 'O'
jobvt = 'A'
U = parray.empty((A.shape[0], A.shape[0]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata,
A.ld, S.gpudata, 1, 1, U.gpudata, U.ld)
#cula.culaShutdown()
A.shape = (A.shape[1], A.shape[1])
return U, S, A
else:
jobu = 'A'
jobvt = 'O'
V = parray.empty((A.shape[1], A.shape[1]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata,
A.ld, S.gpudata, V.gpudata, V.ld, 1, 1)
A.shape = (A.shape[0], A.shape[0])
#cula.culaShutdown()
return A, S, V
else:
if econ | (A.shape[1] >= A.shape[0]):
jobu = 'N'
jobvt = 'O'
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata, A.ld,
S.gpudata, 1, 1, 1, 1)
if (A.shape[1] > A.shape[0]):
A.shape = (A.shape[0], A.shape[0])
#cula.culaShutdown()
return A, S
else:
jobu = 'N'
jobvt = 'A'
U = parray.empty((A.shape[0], A.shape[0]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata, A.ld,
S.gpudata, 1, 1, U.gpudata, U.ld)
#cula.culaShutdown()
return U, S
else:
if compute_v:
if econ | (A.shape[1] <= A.shape[0]):
jobu = 'O'
jobvt = 'N'
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata, A.ld,
S.gpudata, 1, 1, 1, 1)
if (A.shape[1] < A.shape[0]):
A.shape = (A.shape[1], A.shape[1])
#cula.culaShutdown()
return S, A
else:
jobu = 'A'
jobvt = 'N'
V = parray.empty((A.shape[1], A.shape[1]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata, A.ld,
S.gpudata, V.gpudata, V.ld, 1, 1)
#cula.culaShutdown()
return S, V
else:
jobu = 'N'
jobvt = 'N'
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata, A.ld,
S.gpudata, 1, 1, 1, 1)
#cula.culaShutdown()
return S
def svd(G, compute_u = True, compute_v = True, econ = False):
"""
compute Singular Value Decompositon of G
G = U*(diag(S))*V
Parameters
----------------------------------------
G: PitchArray, GPUArray or numpy.ndarray of shape (m,n)
if G is GPUArray or PitchArray, its gpudata will be
destroyed after calling the function
compute_u: bool
whether return U matrix or not
compute_v: bool
whether return V matrix or not
econ: bool
return economical matrix
Returns:
U: parray.PitchArray matrix
as U in G = U*(diag(S))*V,
if econ, returns the first min(m,n) columns of U
S: parray.PitchArray vector
a row vector containing all singular values
with descending order
V: parray.PitchArray matrix
as V in G = U*(diag(S))*V,
if econ, returns the first min(m,n) rows of V
order of output:
always obeys the order U,S,V
e.g.
S = svd(G, compute_u = False, compute_v = False)
U,S = svd(G, compute_u = True, compute_v = False)
S,V = svd(G, compute_u = False, compute_v = True)
U,S,V = svd(G, compute_u = True, compute_v = True)
"""
if G.__class__ is not parray.PitchArray:
if G.__class__ is garray.GPUArray:
h_G = G.get()
del G.gpudata
A= parray.to_gpu(h_G)
elif G.__class__ is np.ndarray:
A = parray.to_gpu(G)
else:
raise TypeError("G must be either parray, or GPUArray or ndarray")
else:
A = G
real_dtype = np.dtype(np.float32)
if A.dtype == np.complex64:
svd_func = cula.culaDeviceCgesvd
elif A.dtype == np.float32:
svd_func = cula.culaDeviceSgesvd
else:
if cula._libcula_toolkit == 'standard':
if A.dtype == np.complex128:
svd_func = cula.culaDeviceZgesvd
elif A.dtype == np.float64:
svd_func = cula.culaDeviceDgesvd
else:
raise ValueError('unsupported type')
real_dtype = np.dtype(np.float64)
else:
raise TypeError('does not support premium double precision svd')
if len(A.shape) != 2:
raise TypeError("svd only works on 2D matrix")
S = parray.empty(min(A.shape), real_dtype)
cula.culaInitialize()
if compute_u:
if compute_v:
if econ:
if A.shape[1] <= A.shape[0]:
jobu = 'A'
jobvt = 'O'
V = parray.empty((A.shape[1], A.shape[1]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0],
A.gpudata, A.ld, S.gpudata, V.gpudata,
V.ld, 1, 1)
#cula.culaShutdown()
return A,S,V
else:
jobu = 'O'
jobvt = 'A'
U = parray.empty((A.shape[0], A.shape[0]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0],
A.gpudata, A.ld, S.gpudata, 1, 1,
U.gpudata, U.ld)
#cula.culaShutdown()
return U,S,A
else:
if A.shape[1] <= A.shape[0]:
jobu = 'O'
jobvt = 'A'
U = parray.empty((A.shape[0], A.shape[0]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0],
A.gpudata, A.ld, S.gpudata, 1, 1,
U.gpudata, U.ld)
#cula.culaShutdown()
A.shape = (A.shape[1],A.shape[1])
return U,S,A
else:
jobu = 'A'
jobvt = 'O'
V = parray.empty((A.shape[1], A.shape[1]), A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0],
A.gpudata, A.ld, S.gpudata, V.gpudata,
V.ld, 1, 1)
A.shape = (A.shape[0], A.shape[0])
#cula.culaShutdown()
return A,S,V
else:
if econ | (A.shape[1] >= A.shape[0]):
jobu = 'N'
jobvt = 'O'
svd_func(jobu, jobvt, A.shape[1], A.shape[0],
A.gpudata, A.ld, S.gpudata, 1, 1, 1, 1)
if (A.shape[1] > A.shape[0]):
A.shape = (A.shape[0], A.shape[0])
#cula.culaShutdown()
return A,S
else:
jobu = 'N'
jobvt = 'A'
U = parray.empty((A.shape[0],A.shape[0]),A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0],
A.gpudata, A.ld, S.gpudata, 1, 1, U.gpudata, U.ld)
#cula.culaShutdown()
return U,S
else:
if compute_v:
if econ | (A.shape[1] <= A.shape[0]):
jobu = 'O'
jobvt = 'N'
svd_func(jobu, jobvt, A.shape[1], A.shape[0],
A.gpudata, A.ld, S.gpudata, 1, 1, 1, 1)
if (A.shape[1] < A.shape[0]):
A.shape = (A.shape[1], A.shape[1])
#cula.culaShutdown()
return S,A
else:
jobu = 'A'
jobvt = 'N'
V = parray.empty((A.shape[1],A.shape[1]),A.dtype)
svd_func(jobu, jobvt, A.shape[1], A.shape[0],
A.gpudata, A.ld, S.gpudata, V.gpudata, V.ld, 1, 1)
#cula.culaShutdown()
return S,V
else:
jobu = 'N'
jobvt = 'N'
svd_func(jobu, jobvt, A.shape[1], A.shape[0], A.gpudata,
A.ld, S.gpudata, 1, 1, 1, 1)
#cula.culaShutdown()
return S