func_operations module¶
Functional operations¶
Classes:
|
Composes a function with a linear operator defined by a matrix computes orig_f(Mat.dot(x)) |
|
Restrict an MDOFunction to a subset of its input vector Fixes the rest of the indices. |
- class gemseo.core.func_operations.LinerarComposition(orig_function, interp_operator)[source]¶
Bases:
gemseo.core.function.MDOFunctionComposes a function with a linear operator defined by a matrix computes orig_f(Mat.dot(x))
Constructor.
- Parameters
orig_function – the original function to restrict
interp_operator – operator matrix, the output of the function will be f(interp_operator.dot(x))
Attributes:
Accessor to the arguments list.
Accessor to the dimension.
Accessor to the expression.
Accessor to the function type.
Accessor to the func property.
Accessor to the jacobian.
Returns the number of calls to execute() which triggered the _run() multiprocessing safe.
Accessor to the name of the function.
Accessor to the array of input variable names used by the function.
Methods:
apply_operator(other_f, operator, operator_repr)Defines addition/substraction for MDOFunction Supports automatic differentiation if other_f and self have a Jacobian.
check_grad(x_vect[, method, step, error_max])Checks the gradient of self.
concatenate(functions, name[, f_type])Concatenate functions.
convex_linear_approx(x_vect[, …])Return the convex linearization of the function at a given point
evaluate(x_vect[, force_real])Evaluate the function.
generate_args(input_dim[, args])Generate the strings for a function arguments.
Returns a dict representation of self for serialization Pointers to functions are removed.
has_args()Check if MDOFunction has an args.
has_dim()Check if MDOFunction has a dimension.
has_expr()Check if MDOFunction has an expression.
Check if MDOFunction has an type.
has_jac()Check if MDOFunction has a jacobian.
Check if MDOFunction has an array of input variables.
init_from_dict_repr(**kwargs)Initalizes a new Function from a data dict typically used for deserialization.
Returns True if self.f_type is eq or ineq.
linear_approximation(x_vect[, name, f_type, …])Return the first-order Taylor polynomial of the function at a given point
offset(value)Adds an offset value to the function.
quadratic_approx(x_vect, hessian_approx[, args])Return a quadratic appproximation of the (scalar-valued) function at a given point
restrict(frozen_indexes, frozen_values, …)Return a restriction of the function
set_pt_from_database(database, design_space)self.__call__(x) returns f(x) if x is in the database and self.name in the database keys Idem for jac.
- AVAILABLE_TYPES = ['obj', 'eq', 'ineq', 'obs']¶
- COEFF_FORMAT_1D = '{:.2e}'¶
- COEFF_FORMAT_ND = '{: .2e}'¶
- DEFAULT_ARGS_BASE = 'x'¶
- DICT_REPR_ATTR = ['name', 'f_type', 'expr', 'args', 'dim', 'special_repr']¶
- INDEX_PREFIX = '!'¶
- TYPE_EQ = 'eq'¶
- TYPE_INEQ = 'ineq'¶
- TYPE_OBJ = 'obj'¶
- TYPE_OBS = 'obs'¶
- apply_operator(other_f, operator, operator_repr)¶
Defines addition/substraction for MDOFunction Supports automatic differentiation if other_f and self have a Jacobian.
- Parameters
other_f – param operator:
operator_repr – the representation as a string
operator – the operator as a function pointer
- property args¶
Accessor to the arguments list.
- check_grad(x_vect, method='FirstOrderFD', step=1e-06, error_max=1e-08)¶
Checks the gradient of self.
- Parameters
x_vect (ndarray) – the vector at which the function is checked
method (str, optional) – FirstOrderFD or ComplexStep (Default value = “FirstOrderFD”)
step (float, optional) – the step for approximation (Default value = 1e-6)
error_max (float, optional) – Default value = 1e-8)
- static concatenate(functions, name, f_type=None)¶
Concatenate functions.
- Parameters
functions (list(MDOFunction)) – functions to be concatenated
name (str) – name of the concatenation
f_type (str, optional) – type of the concatenation function
- Returns
concatenation of the functions
- Return type
- convex_linear_approx(x_vect, approx_indexes=None, sign_threshold=1e-09)¶
Return the convex linearization of the function at a given point
\(\newcommand{\xref}{\hat{x}}\newcommand{\dim}{d}\) The convex linearization of a function \(f\) at a point \(\xref\) is defined as
\[\begin{split}\newcommand{\partialder}{\frac{\partial f}{\partial x_i}(\xref)} f(x) \approx f(\xref) + \sum_{\substack{i = 1 \\ \partialder > 0}}^{\dim} \partialder \, (x_i - \xref_i) - \sum_{\substack{i = 1 \\ \partialder < 0}}^{\dim} \partialder \, \xref_i^2 \, \left(\frac{1}{x_i} - \frac{1}{\xref_i}\right).\end{split}\]\(\newcommand{\approxinds}{I}\) Optionally, one may require the convex linearization of \(f\) with respect to a subset \(x_{i \in \approxinds} \subset \{x_1, \dots, x_{\dim}\}\) of its variables rather than all of them:
\[\begin{split}f(x) = f(x_{i \in \approxinds}, x_{i \not\in \approxinds}) \approx f(\xref_{i \in \approxinds}, x_{i \not\in \approxinds}) + \sum_{\substack{i \in \approxinds \\ \partialder > 0}} \partialder \, (x_i - \xref_i) - \sum_{\substack{i \in \approxinds \\ \partialder < 0}} \partialder \, \xref_i^2 \, \left(\frac{1}{x_i} - \frac{1}{\xref_i}\right).\end{split}\]- Parameters
x_vect (ndarray) – point defining the convex linearization
approx_indexes (ndarray, optional) – array of booleans specifying w.r.t. which variables the function should be approximated (by default, all of them)
sign_threshold (float, optional) – threshold for the sign of the derivatives
- Returns
convex linearization of the function at the given point
- Return type
- property default_repr¶
- property dim¶
Accessor to the dimension.
- evaluate(x_vect, force_real=False)¶
Evaluate the function.
- Parameters
x_vect (ndarray) – the function argument
force_real (bool, optional) – if True, cast the results to real value
- Returns
the function value
- Return type
Number or ndarray
- property expr¶
Accessor to the expression.
- property f_type¶
Accessor to the function type.
- property func¶
Accessor to the func property.
- static generate_args(input_dim, args=None)¶
Generate the strings for a function arguments.
- Parameters
input_dim (int) – number of scalar input arguments
args (list(str), optional) – the initial function arguments strings
- Returns
the arguments strings
- Return type
list(str)
- get_data_dict_repr()¶
Returns a dict representation of self for serialization Pointers to functions are removed.
- Returns
a dict with attributes names as keys
- Return type
dict
- has_args()¶
Check if MDOFunction has an args.
- Returns
True if self has an args
- Return type
bool
- has_dim()¶
Check if MDOFunction has a dimension.
- Returns
True if self has a dimension
- Return type
bool
- has_expr()¶
Check if MDOFunction has an expression.
- Returns
True if self has an expression
- Return type
bool
- has_f_type()¶
Check if MDOFunction has an type.
- Returns
True if self has a type
- Return type
bool
- has_jac()¶
Check if MDOFunction has a jacobian.
- Returns
True if self has a jacobian
- Return type
bool
- has_outvars()¶
Check if MDOFunction has an array of input variables.
- Returns
True if self has a dimension
- Return type
bool
- static init_from_dict_repr(**kwargs)¶
Initalizes a new Function from a data dict typically used for deserialization.
- Parameters
kwargs – key value pairs from DICT_REPR_ATTR
- is_constraint()¶
Returns True if self.f_type is eq or ineq.
- Returns
True if and only if the function is a contraint
- Return type
bool
- property jac¶
Accessor to the jacobian.
- linear_approximation(x_vect, name=None, f_type=None, args=None)¶
Return the first-order Taylor polynomial of the function at a given point
\(\newcommand{\xref}{\hat{x}}\newcommand{\dim}{d}\) The first-order Taylor polynomial of a (possibly vector-valued) function \(f\) at a point \(\xref\) is defined as
\[\newcommand{\partialder}{\frac{\partial f}{\partial x_i}(\xref)} f(x) \approx f(\xref) + \sum_{i = 1}^{\dim} \partialder \, (x_i - \xref_i).\]- Parameters
x_vect (ndarray) – point defining the Taylor polynomial
name (str, optional) – name of the linear approximation
f_type (str, optional) – the function type of the linear approximation
args (list(str), optional) – names for each scalar variable, or a name base
- Returns
first-order Taylor polynomial of the function at the given point
- Return type
- property n_calls¶
Returns the number of calls to execute() which triggered the _run() multiprocessing safe.
- property name¶
Accessor to the name of the function.
- offset(value)¶
Adds an offset value to the function.
- Parameters
value (Number or ndarray) – the offset value
- Returns
the offset function as an MDOFunction
- Return type
- property outvars¶
Accessor to the array of input variable names used by the function.
- quadratic_approx(x_vect, hessian_approx, args=None)¶
Return a quadratic appproximation of the (scalar-valued) function at a given point
\(\newcommand{\xref}{\hat{x}}\newcommand{\dim}{d}\newcommand{ \hessapprox}{\hat{H}}\) For a given approximation \(\hessapprox\) of the Hessian matrix of a function \(f\) at a point \(\xref\), the quadratic approximation of \(f\) is defined as
\[\newcommand{\partialder}{\frac{\partial f}{\partial x_i}(\xref)} f(x) \approx f(\xref) + \sum_{i = 1}^{\dim} \partialder \, (x_i - \xref_i) + \frac{1}{2} \sum_{i = 1}^{\dim} \sum_{j = 1}^{\dim} \hessapprox_{ij} (x_i - \xref_i) (x_j - \xref_j).\]- Parameters
x_vect (ndarray) – point defining the Taylor polynomial
hessian_approx (ndarray) – approximation of the Hessian matrix at x_vect
args (list(str), optional) – names for each scalar variable, or a name base
- Returns
second-order Taylor polynomial of the function at the given point
- Return type
- restrict(frozen_indexes, frozen_values, input_dim, name=None, f_type=None, expr=None, args=None)¶
Return a restriction of the function
\(\newcommand{\frozeninds}{I}\newcommand{\xfrozen}{\hat{x}}\newcommand{ \frestr}{\hat{f}}\) For a subset \(\approxinds\) of the variables indexes of a function \(f\) to remain frozen at values \(\xfrozen_{i \in \frozeninds}\) the restriction of \(f\) is given by
\[\frestr: x_{i \not\in \approxinds} \longmapsto f(\xref_{i \in \approxinds}, x_{i \not\in \approxinds}).\]- Parameters
frozen_indexes (ndarray) – indexes of the variables that will be frozen
frozen_values (ndarray) – values of the variables that will be frozen
input_dim (int) – dimension of the function input (before restriction)
name (str, optional) – name of the restriction
f_type (str, optional) – type of the restriction
expr (str, optional) – the expression of the restriction
args (list(str), optional) – arguments names of the restriction
- Returns
restriction of the function
- Return type
- set_pt_from_database(database, design_space, normalize=False, jac=True, x_tolerance=1e-10)¶
self.__call__(x) returns f(x) if x is in the database and self.name in the database keys Idem for jac.
- Parameters
database (Database) – the database to read
design_space (DesignSpace) – the design space used for normalization
normalize (bool, optional) – if True, x_n is unnormalized before call
jac (bool, optional) – if True, a jacobian pointer is also generated
x_tolerance (float, optional) – tolerance on the distance between inputs
- class gemseo.core.func_operations.RestrictedFunction(orig_function, restriction_indices, restriction_values)[source]¶
Bases:
gemseo.core.function.MDOFunctionRestrict an MDOFunction to a subset of its input vector Fixes the rest of the indices.
Constructor.
- Parameters
orig_function – the original function to restrict
restriction_indices – indices array of the input vector to fix
restriction_values – the values of the input vector at indices ‘restriction_indices’ are set to restriction_values
Attributes:
Accessor to the arguments list.
Accessor to the dimension.
Accessor to the expression.
Accessor to the function type.
Accessor to the func property.
Accessor to the jacobian.
Returns the number of calls to execute() which triggered the _run() multiprocessing safe.
Accessor to the name of the function.
Accessor to the array of input variable names used by the function.
Methods:
apply_operator(other_f, operator, operator_repr)Defines addition/substraction for MDOFunction Supports automatic differentiation if other_f and self have a Jacobian.
check_grad(x_vect[, method, step, error_max])Checks the gradient of self.
concatenate(functions, name[, f_type])Concatenate functions.
convex_linear_approx(x_vect[, …])Return the convex linearization of the function at a given point
evaluate(x_vect[, force_real])Evaluate the function.
generate_args(input_dim[, args])Generate the strings for a function arguments.
Returns a dict representation of self for serialization Pointers to functions are removed.
has_args()Check if MDOFunction has an args.
has_dim()Check if MDOFunction has a dimension.
has_expr()Check if MDOFunction has an expression.
Check if MDOFunction has an type.
has_jac()Check if MDOFunction has a jacobian.
Check if MDOFunction has an array of input variables.
init_from_dict_repr(**kwargs)Initalizes a new Function from a data dict typically used for deserialization.
Returns True if self.f_type is eq or ineq.
linear_approximation(x_vect[, name, f_type, …])Return the first-order Taylor polynomial of the function at a given point
offset(value)Adds an offset value to the function.
quadratic_approx(x_vect, hessian_approx[, args])Return a quadratic appproximation of the (scalar-valued) function at a given point
restrict(frozen_indexes, frozen_values, …)Return a restriction of the function
set_pt_from_database(database, design_space)self.__call__(x) returns f(x) if x is in the database and self.name in the database keys Idem for jac.
- AVAILABLE_TYPES = ['obj', 'eq', 'ineq', 'obs']¶
- COEFF_FORMAT_1D = '{:.2e}'¶
- COEFF_FORMAT_ND = '{: .2e}'¶
- DEFAULT_ARGS_BASE = 'x'¶
- DICT_REPR_ATTR = ['name', 'f_type', 'expr', 'args', 'dim', 'special_repr']¶
- INDEX_PREFIX = '!'¶
- TYPE_EQ = 'eq'¶
- TYPE_INEQ = 'ineq'¶
- TYPE_OBJ = 'obj'¶
- TYPE_OBS = 'obs'¶
- apply_operator(other_f, operator, operator_repr)¶
Defines addition/substraction for MDOFunction Supports automatic differentiation if other_f and self have a Jacobian.
- Parameters
other_f – param operator:
operator_repr – the representation as a string
operator – the operator as a function pointer
- property args¶
Accessor to the arguments list.
- check_grad(x_vect, method='FirstOrderFD', step=1e-06, error_max=1e-08)¶
Checks the gradient of self.
- Parameters
x_vect (ndarray) – the vector at which the function is checked
method (str, optional) – FirstOrderFD or ComplexStep (Default value = “FirstOrderFD”)
step (float, optional) – the step for approximation (Default value = 1e-6)
error_max (float, optional) – Default value = 1e-8)
- static concatenate(functions, name, f_type=None)¶
Concatenate functions.
- Parameters
functions (list(MDOFunction)) – functions to be concatenated
name (str) – name of the concatenation
f_type (str, optional) – type of the concatenation function
- Returns
concatenation of the functions
- Return type
- convex_linear_approx(x_vect, approx_indexes=None, sign_threshold=1e-09)¶
Return the convex linearization of the function at a given point
\(\newcommand{\xref}{\hat{x}}\newcommand{\dim}{d}\) The convex linearization of a function \(f\) at a point \(\xref\) is defined as
\[\begin{split}\newcommand{\partialder}{\frac{\partial f}{\partial x_i}(\xref)} f(x) \approx f(\xref) + \sum_{\substack{i = 1 \\ \partialder > 0}}^{\dim} \partialder \, (x_i - \xref_i) - \sum_{\substack{i = 1 \\ \partialder < 0}}^{\dim} \partialder \, \xref_i^2 \, \left(\frac{1}{x_i} - \frac{1}{\xref_i}\right).\end{split}\]\(\newcommand{\approxinds}{I}\) Optionally, one may require the convex linearization of \(f\) with respect to a subset \(x_{i \in \approxinds} \subset \{x_1, \dots, x_{\dim}\}\) of its variables rather than all of them:
\[\begin{split}f(x) = f(x_{i \in \approxinds}, x_{i \not\in \approxinds}) \approx f(\xref_{i \in \approxinds}, x_{i \not\in \approxinds}) + \sum_{\substack{i \in \approxinds \\ \partialder > 0}} \partialder \, (x_i - \xref_i) - \sum_{\substack{i \in \approxinds \\ \partialder < 0}} \partialder \, \xref_i^2 \, \left(\frac{1}{x_i} - \frac{1}{\xref_i}\right).\end{split}\]- Parameters
x_vect (ndarray) – point defining the convex linearization
approx_indexes (ndarray, optional) – array of booleans specifying w.r.t. which variables the function should be approximated (by default, all of them)
sign_threshold (float, optional) – threshold for the sign of the derivatives
- Returns
convex linearization of the function at the given point
- Return type
- property default_repr¶
- property dim¶
Accessor to the dimension.
- evaluate(x_vect, force_real=False)¶
Evaluate the function.
- Parameters
x_vect (ndarray) – the function argument
force_real (bool, optional) – if True, cast the results to real value
- Returns
the function value
- Return type
Number or ndarray
- property expr¶
Accessor to the expression.
- property f_type¶
Accessor to the function type.
- property func¶
Accessor to the func property.
- static generate_args(input_dim, args=None)¶
Generate the strings for a function arguments.
- Parameters
input_dim (int) – number of scalar input arguments
args (list(str), optional) – the initial function arguments strings
- Returns
the arguments strings
- Return type
list(str)
- get_data_dict_repr()¶
Returns a dict representation of self for serialization Pointers to functions are removed.
- Returns
a dict with attributes names as keys
- Return type
dict
- has_args()¶
Check if MDOFunction has an args.
- Returns
True if self has an args
- Return type
bool
- has_dim()¶
Check if MDOFunction has a dimension.
- Returns
True if self has a dimension
- Return type
bool
- has_expr()¶
Check if MDOFunction has an expression.
- Returns
True if self has an expression
- Return type
bool
- has_f_type()¶
Check if MDOFunction has an type.
- Returns
True if self has a type
- Return type
bool
- has_jac()¶
Check if MDOFunction has a jacobian.
- Returns
True if self has a jacobian
- Return type
bool
- has_outvars()¶
Check if MDOFunction has an array of input variables.
- Returns
True if self has a dimension
- Return type
bool
- static init_from_dict_repr(**kwargs)¶
Initalizes a new Function from a data dict typically used for deserialization.
- Parameters
kwargs – key value pairs from DICT_REPR_ATTR
- is_constraint()¶
Returns True if self.f_type is eq or ineq.
- Returns
True if and only if the function is a contraint
- Return type
bool
- property jac¶
Accessor to the jacobian.
- linear_approximation(x_vect, name=None, f_type=None, args=None)¶
Return the first-order Taylor polynomial of the function at a given point
\(\newcommand{\xref}{\hat{x}}\newcommand{\dim}{d}\) The first-order Taylor polynomial of a (possibly vector-valued) function \(f\) at a point \(\xref\) is defined as
\[\newcommand{\partialder}{\frac{\partial f}{\partial x_i}(\xref)} f(x) \approx f(\xref) + \sum_{i = 1}^{\dim} \partialder \, (x_i - \xref_i).\]- Parameters
x_vect (ndarray) – point defining the Taylor polynomial
name (str, optional) – name of the linear approximation
f_type (str, optional) – the function type of the linear approximation
args (list(str), optional) – names for each scalar variable, or a name base
- Returns
first-order Taylor polynomial of the function at the given point
- Return type
- property n_calls¶
Returns the number of calls to execute() which triggered the _run() multiprocessing safe.
- property name¶
Accessor to the name of the function.
- offset(value)¶
Adds an offset value to the function.
- Parameters
value (Number or ndarray) – the offset value
- Returns
the offset function as an MDOFunction
- Return type
- property outvars¶
Accessor to the array of input variable names used by the function.
- quadratic_approx(x_vect, hessian_approx, args=None)¶
Return a quadratic appproximation of the (scalar-valued) function at a given point
\(\newcommand{\xref}{\hat{x}}\newcommand{\dim}{d}\newcommand{ \hessapprox}{\hat{H}}\) For a given approximation \(\hessapprox\) of the Hessian matrix of a function \(f\) at a point \(\xref\), the quadratic approximation of \(f\) is defined as
\[\newcommand{\partialder}{\frac{\partial f}{\partial x_i}(\xref)} f(x) \approx f(\xref) + \sum_{i = 1}^{\dim} \partialder \, (x_i - \xref_i) + \frac{1}{2} \sum_{i = 1}^{\dim} \sum_{j = 1}^{\dim} \hessapprox_{ij} (x_i - \xref_i) (x_j - \xref_j).\]- Parameters
x_vect (ndarray) – point defining the Taylor polynomial
hessian_approx (ndarray) – approximation of the Hessian matrix at x_vect
args (list(str), optional) – names for each scalar variable, or a name base
- Returns
second-order Taylor polynomial of the function at the given point
- Return type
- restrict(frozen_indexes, frozen_values, input_dim, name=None, f_type=None, expr=None, args=None)¶
Return a restriction of the function
\(\newcommand{\frozeninds}{I}\newcommand{\xfrozen}{\hat{x}}\newcommand{ \frestr}{\hat{f}}\) For a subset \(\approxinds\) of the variables indexes of a function \(f\) to remain frozen at values \(\xfrozen_{i \in \frozeninds}\) the restriction of \(f\) is given by
\[\frestr: x_{i \not\in \approxinds} \longmapsto f(\xref_{i \in \approxinds}, x_{i \not\in \approxinds}).\]- Parameters
frozen_indexes (ndarray) – indexes of the variables that will be frozen
frozen_values (ndarray) – values of the variables that will be frozen
input_dim (int) – dimension of the function input (before restriction)
name (str, optional) – name of the restriction
f_type (str, optional) – type of the restriction
expr (str, optional) – the expression of the restriction
args (list(str), optional) – arguments names of the restriction
- Returns
restriction of the function
- Return type
- set_pt_from_database(database, design_space, normalize=False, jac=True, x_tolerance=1e-10)¶
self.__call__(x) returns f(x) if x is in the database and self.name in the database keys Idem for jac.
- Parameters
database (Database) – the database to read
design_space (DesignSpace) – the design space used for normalization
normalize (bool, optional) – if True, x_n is unnormalized before call
jac (bool, optional) – if True, a jacobian pointer is also generated
x_tolerance (float, optional) – tolerance on the distance between inputs