Description

S3L_gen_trid_factor factors a tridiagonal matrix, whose diagonal is stored in vector D. The first upper subdiagonal is stored in U, and the first lower subdiagonal in L.

On return, the integer factors contains a pointer to an internal setup structure that holds the factorization. Subsequent calls to S3L_gen_trid_solve use the value in factors to access the factorization results.

The contents of the vectors D, U, and L may be altered. These altered vectors, along with the factors parameter, have to be passed to a subsequent call to S3L_gen_trid_solve to produce the solution to a tridiagonal system.

D, U, and L must have the same extents and type. If they are one-dimensional, all three must be of length n. The first n-1 entries of U contain the elements of the superdiagonal. The last n-1 entries of L contain the elements of the first subdiagonal. The last element of U and the first element of L are not referenced and can be initialized arbitrarily.

If D, U and L have more than one dimension, axis_d is the axis along which the multidimensional arrays are factored. If they are one-dimensional, axis_d must be 0 in C/C++ programs and 1 in F77/F90 programs.

S3L_gen_trid_factor is based on the ScaLAPACK routines pxdttrf, where x is single, double, complex, or double complex. It does no pivoting; consequently, the matrix has to be positive definite for the factorization to be stable.

For one-dimensional arrays, the routine is more efficient when D, U, and L are block distributed. For multiple dimensions, the routine is more efficient when axis_d is a local axis.