/usr/include/openturns/swig/QuadraticFunction_doc.i is in libopenturns-dev 1.9-5.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | %feature("docstring") OT::QuadraticFunction
"Quadratic function.
Available constructors:
QuadraticFunction(*center, constant, linear, quadratic*)
Parameters
----------
center : sequence of float
Vector :math:`\\\\vect{b}`.
constant : sequence of float
Vector :math:`\\\\vect{c}`.
linear : :class:`~openturns.Matrix`
Matrix :math:`\\\\mat{A}`.
quadratic : :class:`~openturns.SymmetricTensor`
Tensor :math:`\\\\underline{\\\\underline{\\\\underline{M}}}`.
Notes
-----
This implements a quadratic function :math:`f` defined as:
.. math::
f : & \\\\Rset^n \\\\rightarrow \\\\Rset^p \\\\\\\\
& \\\\vect{X} \\\\mapsto \\\\mat{A} ( \\\\vect{X} - \\\\vect{b} ) + \\\\vect{c} + \\\\frac{1}{2} \\\\vect{X}^T \\\\times \\\\underline{\\\\underline{\\\\underline{M}}} \\\\times \\\\vect{X}
where:
- :math:`\\\\mat{A}` is the :math:`\\\\Rset^p \\\\times \\\\Rset^n` matrix defined by *linear*,
- :math:`\\\\vect{b}` is the :math:`\\\\Rset^n` vector defined by *center*,
- :math:`\\\\vect{c}` is the :math:`\\\\Rset^p` vector defined by *constant*.
- :math:`\\\\underline{\\\\underline{\\\\underline{M}}}` is a :math:`\\\\Rset^p \\\\times \\\\Rset^n \\\\times \\\\Rset^n` symmetric tensor defined by *quadratic*.
Examples
--------
>>> import openturns as ot
>>> inputDimension = 3
>>> outputDimension = 2
>>> center = [1.0] * inputDimension
>>> constant = [-1.0, 2.0]
>>> linear = ot.Matrix(inputDimension, outputDimension)
>>> quadratic = ot.SymmetricTensor(inputDimension, outputDimension)
>>> function = ot.QuadraticFunction(center, constant, linear, quadratic)
>>> inP = [7.0, 8.0, 9.0]
>>> print(function(inP))
[-1,2]"
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