Cholesky factorising a general size symmetric matrix

The Cholesky factor of a symmetric positive definite matrix $S$ is a lower triangular matrix $L$ such that

$$S = L L^{\top}$$

and we write $L={\rm chol}(S)$. The Gandalf Cholesky factorisation routines apply to all symmetric types of matrix, i.e. GAN_SYMMETRIC_MATRIX itself, GAN_DIAGONAL_MATRIX and GAN_SCALED_IDENT_MATRIX. Routines are available to compute the factorisation, with the usual options, as follows:

      Gan_SquMatrix smS, smL, *psmL; /* declare matrices S & L */

      /* ... create and fill matrix S, which must be symmetric and positive definite,
             create L ... */
      gan_symmat_cholesky_q ( &smS, &smL ); /* L = chol(S), OR */
      psmL = gan_symmat_cholesky_s ( &smS ); /* L = chol(S) */
      gan_symmat_cholesky_i ( &smS ); /* replace S = chol(S) */

The last option gan_symmat_cholesky_i() replaces $S$ in-place by ${\rm chol}(S)$.

Error detection: If $S$ is not either symmetric or positive definite in the above routines, NULL is returned and the Gandalf error handler is invoked. Another failure mode is failing to create the result matrix.