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Zero and Identity - Useful for writing derivatives.
These should work with sparse matrices and numpy arrays. ```python z = Zero() z*A == 0 o = Identity() o*A == A ```
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@@ -396,4 +396,60 @@ def diagEst(matFun, n, k=None, approach='Probing'):
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return d
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class Zero(object):
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def __add__(self, v):return v
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def __radd__(self, v):return v
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def __sub__(self, v):return -v
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def __rsub__(self, v):return v
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def __mul__(self, v):return self
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def __rmul__(self, v):return self
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def __div__(self, v): return self
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def __truediv__(self, v): return self
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def __rdiv__(self, v): raise ZeroDivisionError('Cannot divide by zero.')
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def __pos__(self):return self
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def __neg__(self):return self
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def __lt__(self, v):return 0 < v
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def __le__(self, v):return 0 <= v
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def __eq__(self, v):return v == 0
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def __ne__(self, v):return not (0 == v)
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def __ge__(self, v):return 0 >= v
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def __gt__(self, v):return 0 > v
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class Identity(object):
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_positive = True
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def __init__(self, positive=True):
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self._positive = positive is True
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def __pos__(self):return self
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def __neg__(self):return Identity(not self._positive)
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def __add__(self, v):
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if sp.issparse(v):
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return v + speye(v.shape[0]) if self._positive else v - speye(v.shape[0])
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return v + 1 if self._positive else v - 1
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def __radd__(self, v):
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return self.__add__(v)
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def __sub__(self, v): return self+-v
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def __rsub__(self, v):return -self+v
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def __mul__(self, v): return v if self._positive else -v
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def __rmul__(self, v):return v if self._positive else -v
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def __div__(self, v):
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if sp.issparse(v): raise NotImplementedError('Sparse arrays not divisibile.')
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return 1/v if self._positive else -1/v
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def __truediv__(self, v):
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if sp.issparse(v): raise NotImplementedError('Sparse arrays not divisibile.')
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return 1.0/v if self._positive else -1.0/v
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def __rdiv__(self, v):
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return v if self._positive else -v
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def __lt__(self, v):return 1 < v if self._positive else -1 < v
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def __le__(self, v):return 1 <= v if self._positive else -1 <= v
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def __eq__(self, v):return v == 1 if self._positive else v == -1
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def __ne__(self, v):return (not (1 == v))if self._positive else (not (-1 == v))
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def __ge__(self, v):return 1 >= v if self._positive else -1 >= v
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def __gt__(self, v):return 1 > v if self._positive else -1 > v
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