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

SGTNPS, DGTNPS, CGTNPS, and ZGTNPS--General Tridiagonal Matrix Solve with No Pivoting

These subroutines solve a tridiagonal system of equations using the factorization of matrix A, stored in tridiagonal storage mode, produced by SGTNPF, DGTNPF, CGTNPF, or ZGTNPF, respectively.

Table 113. Data Types

Note:

The input to these solve subroutines must be the output from the factorization subroutines SGTNPF, DGTNPF, CGTNPF, and ZGTNPF, respectively.

Syntax

On Entry

n

is the order n of tridiagonal matrix A. Specified as: a fullword integer; n >= 0.

c

is the vector c, containing part of the factorization of matrix A from SGTNPF, DGTNPF, CGTNPF, and ZGTNPF, respectively, in an array, referred to as C. Specified as: a one-dimensional array of (at least) length n, containing numbers of the data type indicated in Table 113.

d

is the vector d, containing part of the factorization of matrix A from SGTNPF, DGTNPF, CGTNPF, and ZGTNPF, respectively, in an array, referred to as D. Specified as: a one-dimensional array of (at least) length n, containing numbers of the data type indicated in Table 113.

e

is the vector e, containing part of the factorization of matrix A from SGTNPF, DGTNPF, CGTNPF, and ZGTNPF, respectively, in an array, referred to as E. Specified as: a one-dimensional array of (at least) length n, containing numbers of the data type indicated in Table 113.

bx

is the vector b, containing the right-hand side of the system in the first n positions in an array, referred to as BX. Specified as: a one-dimensional array of (at least) length n, containing numbers of the data type indicated in Table 113.

On Return

bx

is the solution vector x of length n, containing the solution of the tridiagonal system in the first n positions in an array, referred to as BX. Returned as: a one-dimensional array of (at least) length n, containing numbers of the data type indicated in Table 113.

Note

For a description of how tridiagonal matrices are stored, see General Tridiagonal Matrix.

Function

The solution of tridiagonal system Ax = b is computed using the factorization produced by SGTNPF, DGTNPF, CGTNPF, or ZGTNPF, respectively. The factorization is based on Gaussian elimination. See reference [77].

Error Conditions

Computational Errors

None

Input-Argument Errors

n < 0

Example 1

This example finds the solution of tridiagonal system Ax = b, where matrix A is the same matrix factored in Example 1 for SGTNPF and DGTNPF. b is:

                    (2.0, 4.0, 5.0, 2.0)

and x is:

                    (1.0, 1.0, 1.0, 1.0)

Call Statement and Input

             N   C   D   E   BX
             |   |   |   |   |
CALL DGTNPS( 4 , C , D , E , BX )
 

Output

BX       =  (1.0, 1.0, 1.0, 1.0)

Example 2

This example finds the solution of tridiagonal system Ax = b, where matrix A is the same matrix factored in Example 2 for CGTNPF and ZGTNPF. b is:

          ((-11.0,19.0), (-14.0,50.0), (-17.0,93.0), (-13.0,85.0))

and x is:

          ((0.0,1.0), (1.0,2.0), (2.0,3.0), (3.0,4.0))

Call Statement and Input

             N   C   D   E   BX
             |   |   |   |   |
CALL ZGTNPS( 4 , C , D , E , BX )
 

Output

BX       =  ((0.0, 1.0), (1.0, 2.0), (2.0, 3.0), (3.0, 4.0))