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LA_TRIDC

Syntax | Arguments | Keywords | Examples | Version History | See Also

The LA_TRIDC procedure computes the LU decomposition of a tridiagonal (n x n) array as Array = L U, where L is a product of permutation and unit lower bidiagonal arrays, and U is upper triangular with nonzero elements only in the main diagonal and the first two superdiagonals.

LA_TRIDC is based on the following LAPACK routines:

For more details, see Anderson et al., LAPACK Users' Guide, 3rd ed., SIAM, 1999.

Syntax

LA_TRIDC, AL, A, AU, U2, Index [, /DOUBLE] [, STATUS=variable]

Arguments

AL

A named vector of length (n - 1) containing the subdiagonal elements of an array. This procedure returns AL as the (n - 1) elements of the lower bidiagonal array from the LU decomposition.

A

A named vector of length n containing the main diagonal elements of an array. This procedure returns A as the n diagonal elements of the upper array from the LU decomposition.

AU

A named vector of length (n - 1) containing the superdiagonal elements of an array. This procedure returns AU as the (n - 1) superdiagonal elements of the upper array.

U2

An output vector that contains the (n - 2) elements of the second superdiagonal of the upper array.

Index

An output vector that records the row permutations which occurred as a result of partial pivoting. For 1 < j < n, row j of the matrix was interchanged with row Index[j].

Note: Row numbers within Index start at one rather than zero.

Keywords

DOUBLE

Set this keyword to use double-precision for computations and to return a double-precision (real or complex) result. Set DOUBLE = 0 to use single-precision for computations and to return a single-precision (real or complex) result. The default is /DOUBLE if AL is double precision, otherwise the default is DOUBLE = 0.

STATUS

Set this keyword to a named variable that will contain the status of the computation. Possible values are:

• STATUS = 0: The computation was successful.
• STATUS > 0: One of the diagonal elements of U is zero. The STATUS value specifies which value along the diagonal (starting at one) is zero.

Note: If STATUS is not specified, any error messages will output to the screen.

Examples

The example la_tridc_doc.pro computes the LU decomposition of a tridiagonal array. This example file is installed in the IDL installation’s /examples/doc/language directory. To view the example code, enter .edit la_tridc_doc.pro at the IDL command line. To execute the code, enter la_tridc_doc at the IDL command line.

When this program is compiled and run, IDL prints:

LA_TRIDC error: 1.50427e-008

Version History

See Also

LA_TRIMPROVE , LA_TRISOL