def __init__(self, perm, **kwargs):
"""
Parameters
----------
perm : list or tuple
The permutation of coefficients.
Returns
-------
A PermutationOperator instance.
Exemple
-------
>>> import numpy as np
>>> import linear_operators as lo
>>> P = lo.PermutationOperator([3, 1, 0, 2])
>>> P.todense()
array([[ 0., 0., 0., 1.],
[ 0., 1., 0., 0.],
[ 1., 0., 0., 0.],
[ 0., 0., 1., 0.]])
"""
shape = 2 * (len(perm),)
self.perm = perm
# reverse permutation
self.perm_inv = np.argsort(perm)
def matvec(x):
return np.asarray([x[pi] for pi in self.perm])
def rmatvec(x):
return np.asarray([x[pi] for pi in self.perm_inv])
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __init__(self,
shapein,
shapeout,
matvec,
rmatvec=None,
matmat=None,
rmatmat=None,
dtypein=None,
dtypeout=None,
dtype=None):
sizein = np.prod(shapein)
sizeout = np.prod(shapeout)
shape = (sizeout, sizein)
ndmatvec = lambda x: matvec(x.reshape(shapein)).ravel()
if rmatvec is not None:
ndrmatvec = lambda x: rmatvec(x.reshape(shapeout)).ravel()
else:
ndrmatvec = None
LinearOperator.__init__(self,
shape,
ndmatvec,
ndrmatvec,
dtype=dtype,
dtypein=dtypein,
dtypeout=dtypeout)
self.ndmatvec = matvec
self.ndrmatvec = rmatvec
self.shapein = shapein
self.shapeout = shapeout
def __init__(self, shape, rep_num, **kwargs):
"""
Parameters
----------
shape : length 2 tuple.
The shape of the operator.
rep_num : int
The number of replications.
Returns
-------
A ReplicationOperator instance.
Exemple
-------
>>> import numpy as np
>>> import linear_operators as lo
>>> R = lo.ReplicationOperator((4, 2), 2)
>>> R.todense()
array([[ 1., 0.],
[ 0., 1.],
[ 1., 0.],
[ 0., 1.]])
"""
self.rep_num = rep_num
# ensure coherent input
if not shape[0] == shape[1] * rep_num:
raise ValueError("Output vector should be n times the size of input vector.")
def matvec(x):
return np.tile(x, self.rep_num)
def rmatvec(x):
N = shape[1]
return sum([x[i * N:(i + 1) * N] for i in xrange(self.rep_num)])
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __init__(self, shape, slice, **kwargs):
"""
Exemple
-------
>>> S = lo.SliceOperator((2, 4), slice(None, None, 2))
>>> S.todense()
array([[ 1., 0., 0., 0.],
[ 0., 0., 1., 0.]])
>>> S.T.todense()
array([[ 1., 0.],
[ 0., 0.],
[ 0., 1.],
[ 0., 0.]])
"""
def matvec(x):
return x[slice]
def rmatvec(x):
out = np.zeros(shape[1])
out[slice] = x
return out
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __init__(self, shape, shift, **kwargs):
if shape[0] != shape[1]:
raise ValueError("Only square operator is implemented.")
if np.round(shift) != shift:
raise ValueError("The shift argument should be an integer value.")
self.shift = shift
ashift = np.abs(shift)
# square case
matvec = lambda x: np.concatenate((x[ashift:], np.zeros(ashift)))
rmatvec = lambda x: np.concatenate((np.zeros(ashift), x[:-ashift]))
if self.shift < 0:
matvec, rmatvec = rmatvec, matvec
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __init__(self, shape, shift, **kwargs):
if shape[0] != shape[1]:
raise ValueError("Only square operator is implemented.")
if np.round(shift) != shift:
raise ValueError("The shift argument should be an integer value.")
self.shift = shift
ashift = np.abs(shift)
# square case
matvec = lambda x: np.concatenate((x[ashift:], np.zeros(ashift)))
rmatvec = lambda x: np.concatenate((np.zeros(ashift), x[:-ashift]))
if self.shift < 0:
matvec, rmatvec = rmatvec, matvec
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __init__(self, shape, diag, subdiag, superdiag, **kwargs):
"""
Parameters
----------
shape : length 2 tuple.
The shape of the operator.
diag : ndarray of size shape[0]
The diagonal of the matrix.
subdiag : ndarray of size shape[0] - 1
The subdiagonal of the matrix.
superdiag : ndarray of size shape[0] - 1
The superdiagonal of the matrix.
Returns
-------
A Tridiagonal matrix operator instance.
Exemple
-------
>>> import numpy as np
>>> import linear_operators as lo
>>> T = lo.TridiagonalOperator((3, 3), [1, 2, 3], [4, 5], [6, 7])
>>> T.todense()
array([[1, 6, 0],
[4, 2, 7],
[0, 5, 3]])
"""
if shape[0] != shape[1]:
raise ValueError("Only square operator is implemented.")
self.diag = diag
self.subdiag = subdiag
self.superdiag = superdiag
self.kwargs = kwargs
def matvec(x):
out = self.diag * x
out[:-1] += self.superdiag * x[1:]
out[1:] += self.subdiag * x[:-1]
return out
def rmatvec(x):
out = self.diag * x
out[:-1] += self.subdiag * x[1:]
out[1:] += self.superdiag * x[:-1]
return out
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __init__(self, shape, diag, subdiag, superdiag, **kwargs):
"""
Parameters
----------
shape : length 2 tuple.
The shape of the operator.
diag : ndarray of size shape[0]
The diagonal of the matrix.
subdiag : ndarray of size shape[0] - 1
The subdiagonal of the matrix.
superdiag : ndarray of size shape[0] - 1
The superdiagonal of the matrix.
Returns
-------
A Tridiagonal matrix operator instance.
Exemple
-------
>>> import numpy as np
>>> import linear_operators as lo
>>> T = lo.TridiagonalOperator((3, 3), [1, 2, 3], [4, 5], [6, 7])
>>> T.todense()
array([[1, 6, 0],
[4, 2, 7],
[0, 5, 3]])
"""
if shape[0] != shape[1]:
raise ValueError("Only square operator is implemented.")
self.diag = diag
self.subdiag = subdiag
self.superdiag = superdiag
self.kwargs = kwargs
def matvec(x):
out = self.diag * x
out[:-1] += self.superdiag * x[1:]
out[1:] += self.subdiag * x[:-1]
return out
def rmatvec(x):
out = self.diag * x
out[:-1] += self.subdiag * x[1:]
out[1:] += self.superdiag * x[:-1]
return out
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def identity(shape, dtype=np.float64):
"Returns the identity linear Operator"
if shape[0] != shape[1]:
raise ValueError('Identity operators must be square')
def matvec(x):
return x
return LinearOperator(shape, matvec=matvec, rmatvec=matvec, dtype=dtype)
def __init__(self, shape, matvec, **kwargs):
"""Returns a SymmetricOperator of given shape and matvec
function.
Parameters
----------
shape : length 2 tuple
The shape of the operator. Should be square.
matvec : function
The matrix-vector operation.
Returns
-------
A SymmetricOperator instance.
"""
if shape[0] != shape[1]:
raise ValueError("Symmetric operators are square operators.")
kwargs['rmatvec'] = matvec
LinearOperator.__init__(self, shape, matvec, **kwargs)
def __init__(self, shape, matvec, **kwargs):
"""Returns a SymmetricOperator of given shape and matvec
function.
Parameters
----------
shape : length 2 tuple
The shape of the operator. Should be square.
matvec : function
The matrix-vector operation.
Returns
-------
A SymmetricOperator instance.
"""
if shape[0] != shape[1]:
raise ValueError("Symmetric operators are square operators.")
kwargs['rmatvec'] = matvec
LinearOperator.__init__(self, shape, matvec, **kwargs)
def diag(d, shape=None, dtype=None):
"Returns a diagonal Linear Operator"
if shape is None:
shape = 2 * (d.size, )
if shape[0] != shape[1]:
raise ValueError('Diagonal operators must be square')
def matvec(x):
return d * x
if dtype is None:
dtype = d.dtype
return LinearOperator(shape, matvec=matvec, rmatvec=matvec, dtype=dtype)
def __init__(self, shape, rep_num, **kwargs):
"""
Parameters
----------
shape : length 2 tuple.
The shape of the operator.
rep_num : int
The number of replications.
Returns
-------
A ReplicationOperator instance.
Exemple
-------
>>> import numpy as np
>>> import linear_operators as lo
>>> R = lo.ReplicationOperator((4, 2), 2)
>>> R.todense()
array([[ 1., 0.],
[ 0., 1.],
[ 1., 0.],
[ 0., 1.]])
"""
self.rep_num = rep_num
# ensure coherent input
if not shape[0] == shape[1] * rep_num:
raise ValueError(
"Output vector should be n times the size of input vector.")
def matvec(x):
return np.tile(x, self.rep_num)
def rmatvec(x):
N = shape[1]
return sum([x[i * N:(i + 1) * N] for i in xrange(self.rep_num)])
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __init__(self, shapein, shapeout, matvec, rmatvec=None, matmat=None, rmatmat=None,
dtypein=None, dtypeout=None, dtype=np.float64):
sizein = np.prod(shapein)
sizeout = np.prod(shapeout)
shape = (sizeout, sizein)
ndmatvec = lambda x: matvec(x.reshape(shapein)).ravel()
if rmatvec is not None:
ndrmatvec = lambda x: rmatvec(x.reshape(shapeout)).ravel()
else:
ndrmatvec = None
LinearOperator.__init__(self, shape, ndmatvec, ndrmatvec, dtype=dtype,
dtypein=dtypein, dtypeout=dtypeout)
# rename to keep same interface as LinearOperator
self.ndmatvec = matvec
self.ndrmatvec = rmatvec
self.shapein = shapein
self.shapeout = shapeout
def __init__(self, shape, ab, kl, ku, **kwargs):
"""
Generate a BandOperator instance
Arguments
---------
shape : 2-tuple
The shape of the operator
ab : ndarray with ndim == 2
Store the bands of the matrix using LAPACK storage scheme.
kl : int
Number of subdiagonals
ku : int
Number of superdiagonals
"""
if ab.shape[0] != kl + ku + 1 or ab.shape[1] != shape[1]:
raise ValueError("Wrong ab shape.")
self.ab = ab
self.kl = kl
self.ku = ku
self.kwargs = kwargs
def matvec(x):
# diag
out = self.ab[ku] * x
# upper part
for i in xrange(ku):
j = ku - i
out[:-j] += self.ab[i, j:] * x[j:]
for i in xrange(ku, kl + ku):
# lower part
out[i:] += self.ab[i + 1, :-i] * x[:-i]
return out
def rmatvec(x):
rab = self._rab
rkl, rku = ku, kl
# diag
out = rab[ku] * x
# upper part
for i in xrange(rku):
j = rku - i
out[:-j] += rab[i, j:] * x[j:]
for i in xrange(rku, rkl + rku):
# lower part
out[i:] += rab[i + 1, :-i] * x[:-i]
return out
return LinearOperator.__init__(self, shape, matvec, rmatvec,
**kwargs)
def __init__(self, shape, ab, kl, ku, **kwargs):
"""
Generate a BandOperator instance
Arguments
---------
shape : 2-tuple
The shape of the operator
ab : ndarray with ndim == 2
Store the bands of the matrix using LAPACK storage scheme.
kl : int
Number of subdiagonals
ku : int
Number of superdiagonals
"""
if ab.shape[0] != kl + ku + 1 or ab.shape[1] != shape[1]:
raise ValueError("Wrong ab shape.")
self.ab = ab
self.kl = kl
self.ku = ku
self.kwargs = kwargs
def matvec(x):
# diag
out = self.ab[ku] * x
# upper part
for i in xrange(ku):
j = ku - i
out[:-j] += self.ab[i, j:] * x[j:]
for i in xrange(ku, kl + ku):
# lower part
out[i:] += self.ab[i + 1, :-i] * x[:-i]
return out
def rmatvec(x):
rab = self._rab
rkl, rku = ku, kl
# diag
out = rab[ku] * x
# upper part
for i in xrange(rku):
j = rku - i
out[:-j] += rab[i, j:] * x[j:]
for i in xrange(rku, rkl + rku):
# lower part
out[i:] += rab[i + 1, :-i] * x[:-i]
return out
return LinearOperator.__init__(self, shape, matvec, rmatvec, **kwargs)
def __init__(self, shape, slice, **kwargs):
"""
Exemple
-------
>>> S = lo.SliceOperator((2, 4), slice(None, None, 2))
>>> S.todense()
array([[ 1., 0., 0., 0.],
[ 0., 0., 1., 0.]])
>>> S.T.todense()
array([[ 1., 0.],
[ 0., 0.],
[ 0., 1.],
[ 0., 0.]])
"""
def matvec(x):
return x[slice]
def rmatvec(x):
out = np.zeros(shape[1])
out[slice] = x
return out
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __init__(self, perm, **kwargs):
"""
Parameters
----------
perm : list or tuple
The permutation of coefficients.
Returns
-------
A PermutationOperator instance.
Exemple
-------
>>> import numpy as np
>>> import linear_operators as lo
>>> P = lo.PermutationOperator([3, 1, 0, 2])
>>> P.todense()
array([[ 0., 0., 0., 1.],
[ 0., 1., 0., 0.],
[ 1., 0., 0., 0.],
[ 0., 0., 1., 0.]])
"""
shape = 2 * (len(perm), )
self.perm = perm
# reverse permutation
self.perm_inv = np.argsort(perm)
def matvec(x):
return np.asarray([x[pi] for pi in self.perm])
def rmatvec(x):
return np.asarray([x[pi] for pi in self.perm_inv])
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def masubclass(xin=None,
xout=None,
shapein=None,
shapeout=None,
classin=None,
classout=None,
dictin=None,
dictout=None,
matvec=None,
rmatvec=None,
dtype=np.float64,
dtypein=None,
dtypeout=None):
"Wrap linear operation working on ndarray subclasses in MaskedArray style"
if xin is not None:
shapein = xin.shape
classin = xin.__class__
dictin = xin.__dict__
dtype = xin.dtype
if xout is not None:
shapeout = xout.shape
classout = xout.__class__
dictout = xout.__dict__
sizein = np.prod(shapein)
sizeout = np.prod(shapeout)
shape = (sizeout, sizein)
if matvec is not None:
def ndmatvec(x):
xi = classin(x.reshape(shapein))
xi.__dict__ = dictin
return matvec(xi).reshape(sizeout)
else:
raise ValueError('Requires a matvec function')
if rmatvec is not None:
def ndrmatvec(x):
xo = classout(x.reshape(shapeout))
xo.__dict__ = dictout
return rmatvec(xo).reshape(sizein)
else:
ndrmatvec = None
return LinearOperator(shape,
matvec=ndmatvec,
rmatvec=ndrmatvec,
dtype=dtype,
dtypein=dtypein,
dtypeout=dtypeout)
def eye(shape, dtype=np.float64):
"Returns the identity linear Operator"
if shape[0] == shape[1]:
return identity(shape, dtype=dtype)
else:
def matvec(x):
return x[:shape[0]]
def rmatvec(x):
return np.concatenate(x, np.zeros(shape[0] - shape[1]))
return LinearOperator(shape,
matvec=matvec,
rmatvec=rmatvec,
dtype=dtype)
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + " and shift=%d >" % self.shift
def __repr__(self):
s = LinearOperator.__repr__(self)[:-1]
s += ",\n superdiagonal=" + self.superdiag.__repr__()
s += ",\n diagonal=" + self.diag.__repr__()
s += ",\n subdiagonal=" + self.subdiag.__repr__() + ">"
return s
def __repr__(self):
s = LinearOperator.__repr__(self)[:-1]
s += ",\n superdiagonal=" + self.superdiag.__repr__()
s += ",\n diagonal=" + self.diag.__repr__()
s += ",\n subdiagonal=" + self.subdiag.__repr__() + ">"
return s
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + ",\n diagonal=" + self.diag.__repr__() + ">"
def __init__(self, shape, **kwargs):
matvec = lambda x: np.fft.fft(x, n=shape[0]) / np.sqrt(shape[0])
rmatvec = lambda x: np.fft.ifft(x, n=shape[1]) * np.sqrt(shape[0])
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + " and shift=%d >" % self.shift
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + " and coef=%f >" % self.coef
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + "\n and diagonal=" + self.d.__repr__() + ">"
def __init__(self, shape, **kwargs):
matvec = lambda x: np.fft.fft(x, n=shape[0]) / np.sqrt(shape[0])
rmatvec = lambda x: np.fft.ifft(x, n=shape[1]) * np.sqrt(shape[0])
LinearOperator.__init__(self, shape, matvec, rmatvec=rmatvec, **kwargs)
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + ",\n permutation=" + self.perm.__repr__() + ">"
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + ",\n Replicate %i times" % self.n + ">"
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + ",\n diagonal=" + self.diag.__repr__() + ">"
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + ",\n Replicate %i times" % self.n + ">"
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + " and coef=%f >" % self.coef
def __repr__(self):
s = LinearOperator.__repr__(self)
return s[:-1] + ",\n permutation=" + self.perm.__repr__() + ">"