gemseo.core.mdo_functions.mdo_linear_function module#

A linear function defined from coefficients and offset matrices.

class MDOLinearFunction(coefficients, name, f_type=FunctionType.NONE, input_names=(), value_at_zero=0.0, output_names=(), expr=None)[source]#

Bases: MDOFunction

Linear multivariate function defined by.

  • a matrix \(A\) of first-order coefficients \((a_{ij})_{\substack{i = 1, \dots m \\ j = 1, \dots n}}\)

  • and a vector \(b\) of zero-order coefficients \((b_i)_{i = 1, \dots m}\)

\[\begin{split}F(x) = Ax + b = \begin{bmatrix} a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{m1} & \cdots & a_{mn} \end{bmatrix} \begin{bmatrix} x_1 \\ \vdots \\ x_n \end{bmatrix} + \begin{bmatrix} b_1 \\ \vdots \\ b_m \end{bmatrix}.\end{split}\]
Parameters:

  • coefficients (SparseOrDenseRealArray) -- The coefficient matrix \(A\) of the linear function.

  • value_at_zero (OutputType) --

    The value \(b\) of the linear function output at zero.

    By default it is set to 0.0.

  • expr (str | None) -- The expression of the function, if any. If None, create an expression from the coefficients and the value at zero.

  • name (str)

  • f_type (MDOFunction.FunctionType) --

    By default it is set to "".

  • input_names (Sequence[str]) --

    By default it is set to ().

  • output_names (Sequence[str]) --

    By default it is set to ().

normalize(input_space)[source]#

Create a linear function using a scaled input vector.

Parameters:

input_space (DesignSpace) -- The input space.

Returns:

The scaled linear function.

Return type:

MDOLinearFunction

offset(value)[source]#

Add an offset value to the function.

Parameters:

value (ndarray[Any, dtype[number[Any]]] | Complex) -- The offset value.

Returns:

The offset function.

Return type:

MDOLinearFunction

restrict(frozen_indexes, frozen_values)[source]#

Build a restriction of the linear function.

Parameters:

  • frozen_indexes (ndarray[int]) -- The indexes of the inputs that will be frozen.

  • frozen_values (NumberArray) -- The values of the inputs that will be frozen.

Returns:

The restriction of the linear function.

Raises:

ValueError -- If the frozen indexes and values have different shapes.

Return type:

MDOLinearFunction

property coefficients: NumberArray#

The coefficient matrix of the linear function.

This is the matrix \(A\) in the expression \(y=Ax+b\).

property value_at_zero: NumberArray#

The value of the function at zero.

This is the vector \(b\) in the expression \(y=Ax+b\).

Raises:

ValueError -- If the value at zero is neither a ndarray nor a number.