COND

The COND function returns the condition number of a real or complex two-dimensional array A.

By default, COND uses the L_¥ norm to compute the condition number. You may use the LNORM keyword to specify the L₁, L₂, or L_¥ norm.

For the L₁ and L_¥ norms, the condition number is computed from NORM(A)×NORM(INVERT(A)). If the inverse of A is invalid (due to the singularity of A or floating-point errors in the INVERT function), COND returns -1.

For the L₂ norm, the condition number is defined as the ratio of the largest singular value to the smallest. The singular values are computed using LA_SVD.

This routine is written in the IDL language. Its source code can be found in the file cond.pro in the lib subdirectory of the IDL distribution.

Syntax

Return Value

Returns the condition number of an n by n real or complex array A by explicitly computing NORM(A)×NORM(A^-1). If A^-1 is invalid (due to the singularity of A or floating-point errors in the INVERT function), COND returns -1.

Arguments

The two-dimensional array. For LNORM = 0 or 1, the array A must be a square and can be either real or complex. For LNORM = 2, the array A may be rectangular and can only be real.

Keywords

DOUBLE

Set this keyword to force the result to be returned as double-precision. The default is to return a single-precision result if the input is single precision, or a double-precision result otherwise. Internally, IDL performs all computations using double-precision arithmetic.

LNORM

Set this keyword to an integer value to indicate which norm to use for the computation. The possible values of this keyword are:

Table 3-6: LNORM Keyword Values

Table 3-6: LNORM Keyword Values
Value	Description
0	Use the L_¥ norm (the maximum absolute row sum norm). This is the default.
1	Use the L₁ norm (the maximum absolute column sum norm).
2	Use the L₂ norm (the spectral norm).

Examples

; Define a complex array A:  
A = [[COMPLEX(1, 0), COMPLEX(2,-2), COMPLEX(-3, 1)], $  
     [COMPLEX(1,-2), COMPLEX(2, 2), COMPLEX(1, 0)], $  
     [COMPLEX(1, 1), COMPLEX(0, 1), COMPLEX(1, 5)]]  
  
; Compute the condition number of the array using internal   
; double-precision arithmetic:  
PRINT, COND(A, /DOUBLE)

5.93773

Version History


Pre 4.0	Introduced