pymor.functions package¶
Submodules¶
basic module¶
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class
pymor.functions.basic.ConstantFunction(value=array(1.0), dim_domain=1, name=None)[source]¶ Bases:
pymor.functions.basic.FunctionBaseA constant
Functionf: R^d -> R^shape(c), f(x) = c
Parameters
- value
- The constant c.
- dim_domain
- The dimension d.
- name
- The name of the function.
Methods
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class
pymor.functions.basic.ExpressionFunction(expression, dim_domain=1, shape_range=(), parameter_type=None, name=None)[source]¶ Bases:
pymor.functions.basic.GenericFunctionTurns a Python expression given as a string into a
Function.Some
NumPyarithmetic functions like ‘sin’, ‘log’, ‘min’ are supported. For a full list see thefunctionsclass attribute.Warning
evalis used to evaluate the given expression. Using this class with expression strings from untrusted sources will cause mayhem and destruction!Parameters
- expression
- A Python expression of one variable
xand a parametermugiven as a string. - dim_domain
- The dimension of the domain.
- shape_range
- The shape of the values returned by the expression.
- parameter_type
- The
ParameterTypethe expression accepts. - name
- The name of the function.
Methods
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class
pymor.functions.basic.FunctionBase[source]¶ Bases:
pymor.functions.interfaces.FunctionInterfaceBase class for
Functionsproviding some common functionality.Methods
Attributes
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__add__(other)[source]¶ Returns a new
LincombFunctionrepresenting the sum of two functions, or of one function and a constant.
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__mul__(other)[source]¶ Returns a new
LincombFunctionrepresenting the product of a function by a scalar.
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__neg__()[source]¶ Returns a new
LincombFunctionrepresenting the function scaled by -1.
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__radd__(other)¶ Returns a new
LincombFunctionrepresenting the sum of two functions, or of one function and a constant.
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__rmul__(other)¶ Returns a new
LincombFunctionrepresenting the product of a function by a scalar.
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__sub__(other)[source]¶ Returns a new
LincombFunctionrepresenting the difference of two functions, or of one function and a constant.
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class
pymor.functions.basic.GenericFunction(mapping, dim_domain=1, shape_range=(), parameter_type=None, name=None)[source]¶ Bases:
pymor.functions.basic.FunctionBaseWrapper making an arbitrary Python function between
NumPy arraysa properFunction.Note that a
GenericFunctioncan only bepickledif the function it is wrapping can be pickled (cf.dumps_function). For this reason, it is usually preferable to useExpressionFunctioninstead ofGenericFunction.Parameters
- mapping
The function to wrap. If
parameter_typeisNone, the function is of the formmapping(x). Ifparameter_typeis notNone, the function has to have the signaturemapping(x, mu). Moreover, the function is expected to be vectorized, i.e.:mapping(x).shape == x.shape[:-1] + shape_range.
- dim_domain
- The dimension of the domain.
- shape_range
- The shape of the values returned by the mapping.
- parameter_type
- The
ParameterTypethe mapping accepts. - name
- The name of the function.
Methods
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class
pymor.functions.basic.LincombFunction(functions, coefficients, name=None)[source]¶ Bases:
pymor.functions.basic.FunctionBaseA
Functionrepresenting a linear combination ofFunctions.The linear coefficients can be provided either as scalars or as
ParameterFunctionals.Parameters
- functions
- List of
Functionswhose linear combination is formed. - coefficients
- A list of linear coefficients. A linear coefficient can
either be a fixed number or a
ParameterFunctional. - name
- Name of the function.
Methods
Attributes
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functions¶
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coefficients¶
bitmap module¶
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class
pymor.functions.bitmap.BitmapFunction(filename, bounding_box=[[0.0, 0.0], [1.0, 1.0]], range=[0.0, 1.0])[source]¶ Bases:
pymor.functions.basic.FunctionBaseDefine a 2D
Functionvia a grayscale image.Parameters
- filename
- Path of the image representing the function.
- bounding_box
- Lower left and upper right coordinates of the domain of the function.
- range
- A pixel of value p is mapped to
(p / 255.) * range[1] + range[0].
Methods
interfaces module¶
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class
pymor.functions.interfaces.FunctionInterface[source]¶ Bases:
pymor.core.interfaces.ImmutableInterface,pymor.parameters.base.ParametricInterface for
Parameterdependent analytical functions.Every
Functionis a map of the formf(μ): Ω ⊆ R^d -> R^(shape_range)
The returned values are
NumPy arraysof arbitrary (but fixed) shape. Note that NumPy distinguishes between one-dimensional arrays of length 1 (with shape(1,)) and zero-dimensional scalar arrays (with shape()). In pyMOR, we usually expect scalar-valued functions to haveshape_range == ().While the function might raise an error if it is evaluated for an argument not in the domain Ω, the exact behavior is left undefined.
Functions are vectorized in the sense, that if
x.ndim == k, thenf(x, μ)[i0, i1, ..., i(k-2)] == f(x[i0, i1, ..., i(k-2)], μ).
In particular,
f(x, μ).shape == x.shape[:-1] + shape_range.Methods
Attributes
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dim_domain¶ The dimension d > 0.
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shape_range¶ The shape of the function values.
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