## Naming Conventions

The types of all arguments follow the notation shown below:

 ``` IMPLICIT COMPLEX (C) ``` ``` IMPLICIT DOUBLE PRECISION (D) ``` ``` IMPLICIT INTEGER (I-N) ``` ``` IMPLICIT DOUBLE COMPLEX (Z) ```

The first letter of a subroutine name identifies the type of the result. The second and third letters identify the form of the output matrix and its mode of storage in an array. The forms are shown below:

 CH Cholesky-factored GB general in banded storage GE general GT general tridiagonal HI Hermitian HP Hermitian in packed storage PB symmetric positive definite in banded storage PO symmetric positive definite PP symmetric positive definite in packed storage PT symmetric positive definite tridiagonal QR QR-factored SI symmetric SP symmetric in packed storage TR triangular

When the second and third letters indicate the type of matrix and its storage mode, the fourth and fifth letters indicate the operation that will be performed. The fourth and fifth letters mean different things for different subroutines, so you must read the description of the subroutine in order to find out exactly what it does. For example, DTRCO estimates the condition of a triangular matrix. DGECO estimates the condition of a general matrix and also determines the LU factorization. The operations are shown below:

 CO Estimate the condition number; sometimes also determine the LU or Cholesky factorization DC Decomposition DD Downdate a Cholesky factorization DI Compute the determinant of a matrix; sometimes also determine the inverse and inertia of a matrix EX Permute and update a Cholesky factorization FA Factor SL Solve a system of linear equations, usually after the matrix has been factored by a subroutine whose name ends in CO or FA UD Update a Cholesky factorization

A-1 denotes the inverse of the square matrix stored in the array A. Whenever the symbol A-1 appears it is assumed that the numerical inverse of the matrix stored in the array A exists. AT denotes the transpose of an array A and AH denotes the conjugate transpose of A for a complex matrix A.