The LUSOL function is used in conjunction with the LUDC procedure to solve a set of n linear equations in n unknowns Ax = b. The parameter A is input not as the original array, but as its LU decomposition, created by the routine LUDC.
LUSOL is based on the routine lubksb described in section 2.3 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.
Note: If you are working with complex inputs, use the LA_LUSOL function instead.
Examples
This example solves the linear system Ax = b using LU decomposition and back substitution:
; Define array A:
A = [[ 2.0, 1.0, 1.0], $
[ 4.0, -6.0, 0.0], $
[-2.0, 7.0, 2.0]]
; Define right-hand side vector B:
B = [3.0, -8.0, 10.0]
; Decompose A:
LUDC, A, INDEX
; Compute the solution using back substitution:
result = LUSOL(A, INDEX, B)
; Print the result:
PRINT, result
IDL prints:
1.00000 2.00000 -1.00000
This is the exact solution vector.
Syntax
Result = LUSOL(A, Index, B [, /COLUMN] [, /DOUBLE])
Return Value
The result is an n-element vector whose type is identical to A.
Arguments
A
The n by n LU decomposition of an array created by the LUDC procedure.
Note: If LUSOL is complex then only the real part is used for the computation.
Index
An input vector, created by the LUDC procedure, containing a record of the row permutations which occurred as a result of partial pivoting.
B
An n-element vector containing the right-hand side of the linear system Ax = b.
Keywords
COLUMN
Set this keyword if the input array A is in column-major format (composed of column vectors) rather than in row-major format (composed of row vectors).
DOUBLE
Set this keyword to force the computation to be done in double-precision arithmetic.
Version History
| Pre 4.0 |
Introduced |
See Also
CHOLSOL, CRAMER, GS_ITER, LA_LUSOL, LU_COMPLEX, LUDC, SVSOL, TRISOL
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