aerosandbox.numpy.linalg
========================

.. py:module:: aerosandbox.numpy.linalg


Functions
---------

.. autoapisummary::

   aerosandbox.numpy.linalg.inner
   aerosandbox.numpy.linalg.outer
   aerosandbox.numpy.linalg.solve
   aerosandbox.numpy.linalg.inv
   aerosandbox.numpy.linalg.pinv
   aerosandbox.numpy.linalg.det
   aerosandbox.numpy.linalg.norm
   aerosandbox.numpy.linalg.inv_symmetric_3x3


Module Contents
---------------

.. py:function:: inner(x, y, manual=False)

   Inner product of two arrays.

   See syntax here: https://numpy.org/doc/stable/reference/generated/numpy.inner.html


.. py:function:: outer(x, y, manual=False)

   Compute the outer product of two vectors.

   See syntax here: https://numpy.org/doc/stable/reference/generated/numpy.outer.html


.. py:function:: solve(A, b)

   Solve the linear system Ax=b for x.
   :param A: A square matrix.
   :param b: A vector representing the RHS of the linear system.

   Returns: The solution vector x.



.. py:function:: inv(A)

   Returns the inverse of the matrix A.

   See: https://numpy.org/doc/stable/reference/generated/numpy.linalg.inv.html


.. py:function:: pinv(A)

   Returns the Moore-Penrose pseudoinverse of the matrix A.

   See: https://numpy.org/doc/stable/reference/generated/numpy.linalg.pinv.html


.. py:function:: det(A)

   Returns the determinant of the matrix A.

   See: https://numpy.org/doc/stable/reference/generated/numpy.linalg.det.html


.. py:function:: norm(x, ord=None, axis=None, keepdims=False)

   Matrix or vector norm.

   See syntax here: https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html


.. py:function:: inv_symmetric_3x3(m11, m22, m33, m12, m23, m13)

   Explicitly computes the inverse of a symmetric 3x3 matrix.

   Input matrix (note symmetry):

   [m11, m12, m13]
   [m12, m22, m23]
   [m13, m23, m33]

   Output matrix (note symmetry):

   [a11, a12, a13]
   [a12, a22, a23]
   [a13, a23, a33]

   From https://math.stackexchange.com/questions/233378/inverse-of-a-3-x-3-covariance-matrix-or-any-positive-definite-pd-matrix