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quadroots

Determine roots of a quadratic equation [ a*x^2 + b*x + c].

Prototype

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"  ; This library is automatically loaded
                                                             ; from NCL V6.2.0 onward.
                                                             ; No need for user to explicitly load.

	function quadroots (
		a [1] : numeric,  
		b [1] : numeric,  
		c [1] : numeric   
	)

	return_val [3] :  double if any input is type double, otherwise float

Arguments

coefficient of x^2

coefficient of x

constant term

Return value

A one-dimensional array of length 3. If the roots are real, the first two elements contain the real roots. The third element is set to zero and should be ignored. If the roots are complex, the first element contains the real part while the second and third elements contain the imaginary roots.

Description

Solves the standard quadratic formula. The discriminant ( b^2-4*a*c ) and the root type ("real" or "complex") are returned as attributes.

Examples

The following require that contributed.ncl be loaded prior to invoking the function.

       load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"

Example 1: real roots

  q1 = quadroots( 1,  3, -4)   ; x^2 + 3*x -4 
  print(q1)                                       ; (1,-4)

  q2 = quadroots( 2, -4d0, -3)  ; 2*x^2 -4*x -3
  print(q2)

The output looks like:

Variable: q1
Type: float
Total Size: 8 bytes
            2 values
Number of Dimensions: 1
Dimensions and sizes:   [3]
Coordinates:
Number Of Attributes: 2
  root :          real
  discriminant :        25

(0)      1
(1)     -4
(2)      0                            <== ignore

and

Variable: q2
Type: double
Total Size: 16 bytes
            2 values
Number of Dimensions: 1
Dimensions and sizes:   [3]
Coordinates:
Number Of Attributes: 2
  root :        real
  discriminant :          40

(0)     2.58113883008419
(1     -0.5811388300841898
(2)     0                             <== ignore

Example 2: complex roots

  q3 = quadroots(-1, -2, -3)   ; -x^2 -2*x -3
  print(q3)       

  q4 = quadroots( 1d0,-10, 34) ;  x^2 -10*x +  34
  print(q4)

yields

Variable: q3
Type: float
Total Size: 12 bytes
            3 values
Number of Dimensions: 1
Dimensions and sizes:   [3]
Coordinates:
Number Of Attributes: 2
  root :        complex
  discriminant :        -8
(0)     -1
(1)     -1.414214
(2)      1.414214

So the roots are:

-1 - i 1.414214
and
-1 + i 1.414214

Variable: q4
Type: double
Total Size: 24 bytes
            3 values
Number of Dimensions: 1
Dimensions and sizes:   [3]
Coordinates:
Number Of Attributes: 2
  root :        complex
  discriminant :         -36
(0)        5
(1)        3
(2)       -3

So the roots are:

5 + i 3 and 5 - i 3