Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

Programming Considerations for the SUBF Subroutine

This section describes how to design and code the subf subroutine for use by the numerical quadrature subrutines.

Designing SUBF

For the Gaussian quadrature subroutines, you must supply a separate subroutine that is callable by ESSL. You specify the name of the subroutine in the subf argument. This subroutine name is selected by you. You should design the subf subroutine so it receives, as input, a tabulated set of points at which the integrand is evaluated, and it returns, as output, the values of the integrand evaluated at these points.

Depending on the numerical quadrature subroutine that you use, the subf subroutine is defined in one of the two following ways:

• For _GLNQ, _GLGQ, _GRAQ, and _GHMQ, you define the subf subroutine with three arguments: t, y, and n, where:

  t

  is an input array, referred to as T, of tabulated Gaussian quadrature abscissas, containing n real numbers, t_i, where t_i is automatically provided by the ESSL subroutine and is determined by n and the Gaussian quadrature method chosen.

  y

  is an output array, referred to as Y, containing n real numbers, where for the integrand, the following is true: y_i = f(t_i) for i = 1, n.

  n

  is a positive integer indicating the number of elements in T and Y.

• For _GLNQ2, you define the subf subroutine with six arguments: s, n1, t, n2, z, and ldz, where:

  s

  is an input array, referred to as S, of tabulated Gaussian quadrature abscissas, containing n1 real numbers, s_i, where s_i is automatically provided by the ESSL subroutine and is determined by n1 and the Gaussian quadrature method.

  n1

  is a positive integer indicating the number of elements in S and the number of rows to be used in array Z.

  t

  is an input array, referred to as T, of tabulated Gaussian quadrature abscissas, containing n2 real numbers, t_i, where t_i is automatically provided by the ESSL subroutine and is determined by n2 and the Gaussian quadrature method.

  n2

  is a positive integer indicating the number of elements in T and the number of columns to be used in array Z.

  z

  is an ldz by (at least) n2 output array, referred to as Z, of real numbers, where for the integrand, the following is true: z_ij = f(s_i, t_j) for i = 1, n1 and j = 1, n2.

  ldz

  is a positive integer indicating the size of the leading dimension of the array Z.

Coding and Setting Up SUBF in Your Program

Examples of coding a subf subroutine in Fortran are provided for each subroutine in this chapter. Examples of coding a subf subroutine in C, C++, and PL/I are provided in Example 1.

Depending on the programming language you use for your program that calls the numerical quadrature subroutines, you have a choice of one or more languages that you can use for writing subf. These rules and other langauge-related coding rules for setting up subf in your program are described in the following sections:

• Setting Up a User-Supplied Subroutine for ESSL in Fortran
• Setting Up a User-Supplied Subroutine for ESSL in C
• Setting Up a User-Supplied Subroutine for ESSL in C++