IDL Reference Guide: Procedures and Functions

LA_LUDC

The LA_LUDC procedure computes the LU decomposition of an n-column by m-row array as:

A = P L U

where P is a permutation matrix, L is lower trapezoidal with unit diagonal elements (lower triangular if n = m), and U is upper trapezoidal (upper triangular if n = m).

LA_LUDC is based on the following LAPACK routines:

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

Syntax

LA_LUDC, Array, Index [, /DOUBLE] [, STATUS=variable]

Arguments

Array

A named variable containing the real or complex array to decompose. This procedure returns Array as its LU decomposition.

Index

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

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 Array 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:

Examples

The following example uses the LU decomposition on a given array, then determines the residual error of using the resulting lower and upper arrays to recompute the original array:

PRO ExLA_LUDC  
; Create a random array:  
n = 20  
seed = 12321  
array = RANDOMN(seed, n, n)  
  
; Compute LU decomposition.  
aludc = array           ; make a copy  
LA_LUDC, aludc, index  
  
; Extract the lower and upper triangular arrays.  
l = IDENTITY(n)  
u = FLTARR(n, n)  
FOR j = 1,n - 1 DO l[0:j-1,j] = aludc[0:j-1,j]  
FOR j=0,n - 1 DO u[j:*,j] = aludc[j:*,j]  
  
; Reconstruct array, but with rows permuted.  
arecon = l ## u  
; Adjust from LAPACK back to IDL indexing.  
Index = Index - 1  
; Permute the array rows back into correct order.  
; Note that we need to loop in reverse order.  
FOR i = n - 1,0,-1 DO BEGIN & $  
temp = arecon[*,i]  
arecon[*, i] = arecon[*,index[i]]  
arecon[*, index[i]] = temp  
ENDFOR  
PRINT, 'LA_LUDC Error:', MAX(ABS(arecon - array))  
END  

When this program is compiled and run, IDL prints:

LA_LUDC error: 4.76837e-007