NAG FL Interface
c02ajf (quadratic_​real)

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1 Purpose

c02ajf determines the roots of a quadratic equation with real coefficients.

2 Specification

Fortran Interface
Subroutine c02ajf ( a, b, c, zsm, zlg, ifail)
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: a, b, c
Real (Kind=nag_wp), Intent (Out) :: zsm(2), zlg(2)
C Header Interface
#include <nag.h>
void  c02ajf_ (const double *a, const double *b, const double *c, double zsm[], double zlg[], Integer *ifail)
The routine may be called by the names c02ajf or nagf_zeros_quadratic_real.

3 Description

c02ajf attempts to find the roots of the quadratic equation az2+bz+c=0 (where a, b and c are real coefficients), by carefully evaluating the ‘standard’ closed formula
z=-b±b2-4ac 2a .  
It is based on the routine QDRTC from Smith (1967).
Note:  it is not necessary to scale the coefficients prior to calling the routine.

4 References

Smith B T (1967) ZERPOL: a zero finding algorithm for polynomials using Laguerre's method Technical Report Department of Computer Science, University of Toronto, Canada

5 Arguments

1: a Real (Kind=nag_wp) Input
On entry: must contain a, the coefficient of z2.
2: b Real (Kind=nag_wp) Input
On entry: must contain b, the coefficient of z.
3: c Real (Kind=nag_wp) Input
On entry: must contain c, the constant coefficient.
4: zsm(2) Real (Kind=nag_wp) array Output
On exit: the real and imaginary parts of the smallest root in magnitude are stored in zsm(1) and zsm(2) respectively.
5: zlg(2) Real (Kind=nag_wp) array Output
On exit: the real and imaginary parts of the largest root in magnitude are stored in zlg(1) and zlg(2) respectively.
6: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
Note: if ifail>0 on exit, then zlg(1) contains the largest machine representable number (see x02alf) and zlg(2) contains zero.
ifail=1
On entry, a=0.0.
ifail=2
On entry, a=0.0 and b=0.0.
ifail=3
On entry, a=0.0 and the root -c/b overflows: a=value, c=value and b=value.
ifail=4
On entry, c=0.0 and the root -b/a overflows: c=value, b=value and a=value.
ifail=5
On entry, b is so large that b2 is indistinguishable from (b2-4×a×c) and the root -b/a overflows: b=value, a=value and c=value.
ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
ifail=-399
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
ifail=-999
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

If ifail=0 on exit, then the computed roots should be accurate to within a small multiple of the machine precision except when underflow (or overflow) occurs, in which case the true roots are within a small multiple of the underflow (or overflow) threshold of the machine.

8 Parallelism and Performance

c02ajf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example finds the roots of the quadratic equation z2+3z-10=0.

10.1 Program Text

Program Text (c02ajfe.f90)

10.2 Program Data

Program Data (c02ajfe.d)

10.3 Program Results

Program Results (c02ajfe.r)