def norm(x, order=None):
'''Matrix or vector norm
x -- input array
ord -- None = Frobenius | 2-norm
'fro' = Frobenius | n/a
inf = max(sum(abs(x),axis=1)) | max(abs(x))
-inf = min(sum(abs(x),axis=1)) | min(abs(x))
0 = n/a | sum(x != 0)
1 = max(sum(abs(x),axis=0)) | as below
-1 = min(sum(abs(x),axis=0)) | as below
2 = 2-norm (largest s.v.) | as below
-2 = smallest singular value | as below
other = n/a | sum(abs(x)**ord)**(1./ord)
Return norm
'''
if order is None:
return _linalg.norm(x)
if order == 'fro':
order = _normorder.FROBENIUS # @UndefinedVariable
elif _isinf(order):
if order > 0:
order = _normorder.POS_INFINITY # @UndefinedVariable
else:
order = _normorder.NEG_INFINITY # @UndefinedVariable
try:
return _linalg.norm(x, order)
except Exception, e:
raise LinAlgError(e)
def norm(x, order=None):
"""Matrix or vector norm
x -- input array
ord -- None = Frobenius | 2-norm
'fro' = Frobenius | n/a
inf = max(sum(abs(x),axis=1)) | max(abs(x))
-inf = min(sum(abs(x),axis=1)) | min(abs(x))
0 = n/a | sum(x != 0)
1 = max(sum(abs(x),axis=0)) | as below
-1 = min(sum(abs(x),axis=0)) | as below
2 = 2-norm (largest s.v.) | as below
-2 = smallest singular value | as below
other = n/a | sum(abs(x)**ord)**(1./ord)
Return norm
"""
if order is None:
return _linalg.norm(x)
if order == "fro":
order = _normorder.FROBENIUS # @UndefinedVariable
elif _isinf(order):
if order > 0:
order = _normorder.POS_INFINITY # @UndefinedVariable
else:
order = _normorder.NEG_INFINITY # @UndefinedVariable
try:
return _linalg.norm(x, order)
except Exception, e:
raise LinAlgError(e)
def tensordot(a, b, axes=2):
'''Tensor dot product of two arrays
'''
if isinstance(axes, int):
bx = range(axes)
ao = a.getRank() - axes
ax = [ ao + i for i in bx ]
else:
t = type(axes)
if t is _types.ListType or t is _types.TupleType:
if len(axes) == 0:
raise ValueError, "Given axes sequence should be non-empty"
if len(axes) == 1:
ax = axes[0]
bx = axes[0]
else:
ax = axes[0]
bx = axes[1]
ta = type(ax)
tal = ta is _types.ListType or ta is _types.TupleType
tb = type(bx)
tbl = tb is _types.ListType or tb is _types.TupleType
if tal != tbl:
if tal:
bx = list(bx)
else:
ax = list(ax)
else:
raise ValueError, "Given axes has wrong type"
return _linalg.tensorDotProduct(a, b, ax, bx)
def svd(a, full_matrices=1, compute_uv=1):
"""Singular value decomposition
"""
try:
return _linalg.calcSingularValueDecomposition(a)
except Exception, e:
raise LinAlgError(e)
def tensordot(a, b, axes=2):
'''Tensor dot product of two arrays
'''
if isinstance(axes, int):
bx = range(axes)
ao = a.getRank() - axes
ax = [ao + i for i in bx]
else:
t = type(axes)
if t is _types.ListType or t is _types.TupleType:
if len(axes) == 0:
raise ValueError, "Given axes sequence should be non-empty"
if len(axes) == 1:
ax = axes[0]
bx = axes[0]
else:
ax = axes[0]
bx = axes[1]
ta = type(ax)
tal = ta is _types.ListType or ta is _types.TupleType
tb = type(bx)
tbl = tb is _types.ListType or tb is _types.TupleType
if tal != tbl:
if tal:
bx = list(bx)
else:
ax = list(ax)
else:
raise ValueError, "Given axes has wrong type"
return _linalg.tensorDotProduct(a, b, ax, bx)
def trace(a, offset=0, axis1=0, axis2=1, dtype=None):
if dtype is None:
dtype = a.getDtype()
else:
dtype = dtype.value
return _linalg.trace(a, offset).cast(dtype)
def svd(a, full_matrices=1, compute_uv=1):
'''Singular value decomposition
'''
try:
return _linalg.calcSingularValueDecomposition(a)
except Exception, e:
raise LinAlgError(e)
def qr(a, mode='full'):
'''QR decomposition
'''
try:
return _linalg.calcQRDecomposition(a)
except Exception, e:
raise LinAlgError(e)
def cholesky(a):
'''Cholesky decomposition
'''
try:
return _linalg.calcCholeskyDecomposition(a)
except Exception, e:
raise LinAlgError(e)
def eigvals(a):
'''Eigenvalues
'''
try:
return _linalg.calcEigenvalues(a)
except Exception, e:
raise LinAlgError(e)
def eig(a):
'''Eigen decomposition
'''
try:
return _linalg.calcEigenDecomposition(a)
except Exception, e:
raise LinAlgError(e)
def matrix_power(a, n):
'''Raise matrix to given power
'''
try:
return _linalg.power(a, n)
except Exception, e:
raise LinAlgError(e)
def pinv(a, rcond=1e-15):
'''Pseudo-inverse of array
'''
try:
return _linalg.calcPseudoInverse(a)
except Exception, e:
raise LinAlgError(e)
def inv(a):
'''Inverse of square array
'''
try:
return _linalg.calcInverse(a)
except Exception, e:
raise LinAlgError(e)
def solve(a, b):
'''Solve equation a x = b
'''
try:
return _linalg.solve(a, b)
except Exception, e:
raise LinAlgError(e)
def trace(a, offset=0, axis1=0, axis2=1, dtype=None):
if dtype is None:
dtype = a.getDtype()
else:
dtype = dtype.value
return _linalg.trace(a, offset).cast(dtype)
def qr(a, mode="full"):
"""QR decomposition
"""
try:
return _linalg.calcQRDecomposition(a)
except Exception, e:
raise LinAlgError(e)
def cholesky(a):
"""Cholesky decomposition
"""
try:
return _linalg.calcCholeskyDecomposition(a)
except Exception, e:
raise LinAlgError(e)
def eig(a):
"""Eigen decomposition
"""
try:
return _linalg.calcEigenDecomposition(a)
except Exception, e:
raise LinAlgError(e)
def eigvals(a):
"""Eigenvalues
"""
try:
return _linalg.calcEigenvalues(a)
except Exception, e:
raise LinAlgError(e)
def pinv(a, rcond=1e-15):
"""Pseudo-inverse of array
"""
try:
return _linalg.calcPseudoInverse(a)
except Exception, e:
raise LinAlgError(e)
def matrix_power(a, n):
"""Raise matrix to given power
"""
try:
return _linalg.power(a, n)
except Exception, e:
raise LinAlgError(e)
def inv(a):
"""Inverse of square array
"""
try:
return _linalg.calcInverse(a)
except Exception, e:
raise LinAlgError(e)
def solve(a, b):
"""Solve equation a x = b
"""
try:
return _linalg.solve(a, b)
except Exception, e:
raise LinAlgError(e)
def det(a):
"""Determinant
"""
try:
return _linalg.calcDeterminant(a)
except Exception, e:
raise LinAlgError(e)
def det(a):
'''Determinant
'''
try:
return _linalg.calcDeterminant(a)
except Exception, e:
raise LinAlgError(e)
def cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None):
'''Cross product of two (arrays of vectors)
a -- first vector
b -- second vector
axisa -- axis of a that defines the vector(s)
axisb -- axis of b that defines the vector(s)
axisc -- axis of c that will contain the cross product(s)
axis -- override all values of axis values
'''
if axis is not None:
axisa = axisb = axisc = axis
return _linalg.crossProduct(a, b, axisa, axisb, axisc)
def cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None):
'''Cross product of two (arrays of vectors)
a -- first vector
b -- second vector
axisa -- axis of a that defines the vector(s)
axisb -- axis of b that defines the vector(s)
axisc -- axis of c that will contain the cross product(s)
axis -- override all values of axis values
'''
if axis is not None:
axisa = axisb = axisc = axis
return _linalg.crossProduct(a, b, axisa, axisb, axisc)
def cond(a, order=None):
"""Condition number
x -- input array
ord -- None = 2-norm computed directly using SVD
'fro' = Frobenius norm
inf = max(sum(abs(x),axis=1))
-inf = min(sum(abs(x),axis=1))
0 = n/a | sum(x != 0)
1 = max(sum(abs(x),axis=0))
-1 = min(sum(abs(x),axis=0))
2 = 2-norm (largest s.v.)
-2 = smallest singular value
other = n/a
Return norm
"""
if order is None:
try:
return _linalg.calcConditionNumber(_jinput(a))
except Exception, e:
raise LinAlgError(e)
def cond(a, order=None):
'''Condition number
x -- input array
ord -- None = 2-norm computed directly using SVD
'fro' = Frobenius norm
inf = max(sum(abs(x),axis=1))
-inf = min(sum(abs(x),axis=1))
0 = n/a | sum(x != 0)
1 = max(sum(abs(x),axis=0))
-1 = min(sum(abs(x),axis=0))
2 = 2-norm (largest s.v.)
-2 = smallest singular value
other = n/a
Return norm
'''
if order is None:
try:
return _linalg.calcConditionNumber(_jinput(a))
except Exception, e:
raise LinAlgError(e)
def dot(a, b):
'''Dot product of two arrays'''
return _linalg.dotProduct(a, b)
def vdot(a, b):
'''Dot product of two vectors with first vector conjugated if complex'''
return _linalg.dotProduct(conjugate(a.flatten()), b.flatten())
def inner(a, b):
'''Inner product of two arrays (sum product over last dimensions)'''
return _linalg.tensorDotProduct(a, b, -1, -1)
def vdot(a, b):
'''Dot product of two vectors with first vector conjugated if complex'''
return _linalg.dotProduct(conjugate(a.flatten()), b.flatten())
def dot(a, b):
'''Dot product of two arrays'''
return _linalg.dotProduct(a, b)
def inner(a, b):
'''Inner product of two arrays (sum product over last dimensions)'''
return _linalg.tensorDotProduct(a, b, -1, -1)