Fixed size vector outer products (original) (raw)

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Fixed size vector outer products

The outer product operation on two fixed size vectors ${\bf x}$ and ${\bf y}$ is the matrix

$\begin{displaymath}A = {\bf x}{\bf y}^{\top} \end{displaymath}$

In Gandalf, any pair of vectors can be combined in this way3.1. The operation on a 3-vector and a 4-vector produces a $3\times 4$ matrix, using either of the routines

  Gan_Vector3 v3x;
  Gan_Vector4 v4y;
  Gan_Matrix34 m34A;

  /* ... set up v3x and v4y using e.g. gan_vec[34]_fill_q() ... */
  gan_vec34_outer_q ( &v3x, &v4y, &m34A ); /* macro, or */
  m34A = gan_vec34_outer_s ( &v3x, &v4y ); /* function call */

Similar routines gan_vec33_outer_[qs]() enable the computation of the outer product of two 3-vectors, resulting in a $3\times 3$ matrix. If ${\bf x}={\bf y}$ , the result of the outer product is a symmetric matrix

$\begin{displaymath}S = {\bf x}{\bf x}^{\top} \end{displaymath}$

Gandalf has special routines for this case:

  Gan_Vector3 v3x;
  Gan_SquMatrix33 sm33S;

  /* ... set up v3x using e.g. gan_vec3_fill_q() ... */
  gan_vec33_outer_sym_q ( &v3x, &sm33S ); /* macro, or */
  sm33S = gan_vec33_outer_sym_s ( &v3x ); /* function call */

2006-03-17