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.

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)

IDL prints:

5.93773

Syntax

Result = COND( A [, /DOUBLE] [, LNORM={0 | 1 | 2}])

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

A

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:

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).

Version History

Pre 4.0

Introduced