IDL

LA_TRISOL

LA_TRISOL

The LA_TRISOL function is used in conjunction with the LA_TRIDC procedure to solve a set of n linear equations in n unknowns, AX = B, where A is a tridiagonal array. The parameter A is input not as the original array, but as its LU decomposition, created by the routine LA_TRIDC.

The LA_TRISOL function may also be used to solve for multiple systems of linear equations, with each column of B representing a different set of equations. In this case, the result is a k-by-n array where each of the k columns represents the solution vector for that set of equations.

LA_TRISOL is based on the following LAPACK routines:

 

Output Type

LAPACK Routine

Float

sgttrs

Double

dgttrs

Complex

cgttrs

Double complex

zgttrs

Examples


For an example of using this routine see LA_TRIMPROVE.

Syntax


Result = LA_TRISOL( AL, A, AU, U2, Index, B [, /DOUBLE] )

Return Value


The result is an n-element vector or k-by-n array.

Arguments


AL

The (n - 1) elements of the lower bidiagonal array, created by the LA_TRIDC procedure.

A

The n diagonal elements of the upper triangular array, created by the LA_TRIDC procedure.

AU

The (n - 1) superdiagonal elements of the upper triangular array, created by the LA_TRIDC procedure.

U2

The (n - 2) elements of the second superdiagonal of the upper triangular array, created by the LA_TRIDC procedure.

Index

An input vector, created by the LA_TRIDC procedure, containing the row permutations which occurred as a result of partial pivoting.

B

An n-element input vector containing the right-hand side of the linear system, or a k-by-n array, where each of the k columns represents a different linear system.

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.

Version History


5.6

Introduced

Resources and References


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

See Also


LA_TRIDC, LA_TRIMPROVE, TRISOL

Notes


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