Fixed size matrix inverse

All types of square matrices can be inverted in Gandalf. If the matrix is singular, NULL is normally returned and an error condition set using gan_err_register() (see Section 2.9). The routines to invert a $3\times 3$ matrix are

      Gan_Matrix33 m33A, m33B;

      /* ... set up m33A using e.g. gan_mat33_fill_q() ... */
      gan_mat33_invert_q ( &m33A, &m33B ); /* B = A^-1, OR */
      m33B = gan_mat33_invert_s ( &m33A ); /* B = A^-1, OR */
      gan_mat33_invert_i ( &m33A ); /* A = A^-1, in-place in A */

Note that the routine gan_mat33_invert_s() returns the structure, rather than a pointer value, so cannot return an error condition. Do not use it unless you are SURE that your matrix is non-singular! The basic routines gan_mat33_invert_[qs]() are implemented as functions rather than macros, because they require temporary variables. There are similar routines for symmetric matrices

      Gan_SquMatrix33 sm33Sa, sm33Sb;

      /* ... set up sm33Sa using e.g. gan_symmat33_fill_q() ... */
      gan_symmat33_invert_q ( &sm33Sa, &sm33Sb ); /* Sb = Sa^-1, OR */
      sm33Sb = gan_symmat33_invert_s ( &sm33Sa ); /* Sb = Sa^-1, OR */
      gan_symmat33_invert_i ( &sm33Sa ); /* Sa = Sa^-1, in-place in Sa */

and for triangular matrices

      Gan_SquMatrix33 sm33La, sm33Lb;

      /* ... set up sm33La using e.g. gan_ltmat33_fill_q() ... */
      gan_ltmat33_invert_q ( &sm33La, &sm33Lb ); /* Lb = La^-1, OR */
      sm33Lb = gan_ltmat33_invert_s ( &sm33La ); /* Lb = La^-1, OR */
      gan_ltmat33_invert_i ( &sm33La ); /* La = La^-1, in-place in La */

If you don't want to invoke the error package when inversion is attempted on a singular matrix, there is a set of routines which allows to instead to return the error condition as part of the result. For instance the code fragment

      Gan_Matrix33 m33A, m33B;
      int error_code;

      /* ... set up m33A using e.g. gan_mat33_fill_q() ... */
      if ( gan_mat33_invert ( &m33A, &m33B, &error_code ) == NULL )
      {
         /* error found, act on it ... */
      }

      /* no error found */

attempts to invert matrix $A$, and if an error is found, returns NULL, with the error condition returned in the error_code variable. For singular matrices the error condition is GAN_ERROR_SINGULAR_MATRIX. There are similar routines gan_symmat33_invert() and gan_ltmat33_invert() for symmetric and triangular matrices respectively.