IDL Reference Guide: Procedures and Functions

FZ_ROOTS

The FZ_ROOTS function is used to find the roots of an m-degree complex polynomial, using Laguerre's method.

FZ_ROOTS is based on the routine zroots described in section 9.5 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.

Syntax

Result = FZ_ROOTS(C [, /DOUBLE] [, EPS=value] [, /NO_POLISH] )

Return Value

Returns an m-element complex vector containing the roots of an m-degree complex polynomial.

Arguments

C

A vector of length m+1 containing the coefficients of the polynomial, in ascending order (see example). The type can be real or complex.

Keywords

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

EPS

The desired fractional accuracy. The default value is 2.0 x 10^-6.

NO_POLISH

Set this keyword to suppress the usual polishing of the roots by Laguerre's method.

Examples

Example 1: Real coefficients yielding real roots.

Find the roots of the polynomial:

P (x) = 6x3 - 7x2 - 9x - 2   

The exact roots are -1/2, -1/3, 2.0.

coeffs = [-2.0, -9.0, -7.0, 6.0]  
roots = FZ_ROOTS(coeffs)  
PRINT, roots  

IDL prints:

( -0.500000, 0.00000)( -0.333333, 0.00000)( 2.00000, 0.00000)  

Example 2: Real coefficients yielding complex roots.

Find the roots of the polynomial:

P (x) = x4 + 3x2 + 2  

The exact roots are:

coeffs = [2.0, 0.0, 3.0, 0.0, 1.0]  
roots = FZ_ROOTS(coeffs)  
PRINT, roots  

IDL Prints:

(0.00000, -1.41421)(0.00000, 1.41421)  
(0.00000, -1.00000)(0.00000, 1.00000)  

Example 3: Real and complex coefficients yielding real and complex roots.

Find the roots of the polynomial:

P (x) = x3 + (-4 - i4)x2 + s (-3 + i4)x + (18 + i24)  

The exact roots are –2.0, 3.0, (3.0 + i4.0)

coeffs = [COMPLEX(18,24), COMPLEX(-3,4), COMPLEX(-4,-4), 1.0]  
roots = FZ_ROOTS(coeffs)  
PRINT, roots  

IDL Prints:

( -2.00000, 0.00000) ( 3.00000, 0.00000) ( 3.00000, 4.00000)