polynomialroots

Module

Description

PURPOSE - Solve for the roots of a polynomial equation with real

coefficients, up to quartic order. Returns a code indicating the nature of the roots found.

Quick access

Variables:

cuberoot, czero, dp, four, fourth, half, one, onelargetwosmall, outputcode, polyroots_version, sp, three, two, zero

Routines:

cubicroots(), linearroot(), quadraticroots(), quarticroots(), selectsort(), solvepolynomial(), swapdouble(), swapsingle()

Variables

  • polynomialroots/cuberoot [private]
  • polynomialroots/czero [complex,private/parameter/optional/default=(0.d0,0.d0)]
  • polynomialroots/dp [integer,private/parameter/optional/default=selected_real_kind(12)]
  • polynomialroots/eps [real,private/parameter/optional/default=epsilon(one)]
  • polynomialroots/four [real,private/parameter/optional/default=4.0d0]
  • polynomialroots/fourth [real,private/parameter/optional/default=0.25d0]
  • polynomialroots/half [real,private/parameter/optional/default=0.5d0]
  • polynomialroots/one [real,private/parameter/optional/default=1.0d0]
  • polynomialroots/onelargetwosmall [private]
  • polynomialroots/outputcode [integer,private]
  • polynomialroots/polyroots_version [character,public/parameter/optional/default="1.3 (4 jan 1999)"]
  • polynomialroots/sp [integer,private/parameter/optional/default=selected_real_kind(6)]
  • polynomialroots/three [real,private/parameter/optional/default=3.0d0]
  • polynomialroots/two [real,private/parameter/optional/default=2.0d0]
  • polynomialroots/zero [real,private/parameter/optional/default=0.0d0]

Subroutines and functions

subroutine  polynomialroots/linearroot(a, z)
PURPOSE - COMPUTES THE ROOTS OF THE REAL POLYNOMIAL

A(1) + A(2)*Z

AND STORES THE RESULTS IN Z. It is assumed that a(2) is non-zero.

Parameters:

  • a (*) [real,in]

  • z [real,out]

subroutine  polynomialroots/quadraticroots(a, z)
PURPOSE - COMPUTES THE ROOTS OF THE REAL POLYNOMIAL

A(1) + A(2)*Z + A(3)*Z**2

AND STORES THE RESULTS IN Z. IT IS ASSUMED THAT A(3) IS NONZERO.

Parameters:

  • a (*) [real,in] :: negative discriminant => roots are complex

  • z (*) [complex,out] :: one root is obviously zero

Called from:

cubicroots(), solvepolynomial()

subroutine  polynomialroots/cubicroots(a, z)
PURPOSE - Compute the roots of the real polynomial

A(1) + A(2)*Z + A(3)*Z**2 + A(4)*Z**3

Parameters:

  • a (*) [real,in]

  • z (*) [complex,out] :: one root is obviously zero

Called from:

quarticroots(), solvepolynomial()

Call to:

quadraticroots()

subroutine  polynomialroots/quarticroots(a, z)
PURPOSE - Compute the roots of the real polynomial

A(1) + A(2)*Z + … + A(5)*Z**4

Parameters:

  • a (*) [real,in]

  • z (*) [complex,out] :: one root is obviously zero

Called from:

solvepolynomial()

Call to:

cubicroots(), selectsort()

subroutine  polynomialroots/selectsort(a)

PURPOSE - Reorder the elements of in increasing order.

Parameters:

a (*) [real,inout]

Called from:

quarticroots()

subroutine  polynomialroots/solvepolynomial(quarticcoeff, cubiccoeff, quadraticcoeff, linearcoeff, constantcoeff, code, root1, root2, root3, root4)
Parameters:

  • quarticcoeff [real,in]

  • cubiccoeff [real,in]

  • quadraticcoeff [real,in]

  • linearcoeff [real,in]

  • constantcoeff [real,in]

  • code [integer,out]

  • root1 [complex,out]

  • root2 [complex,out]

  • root3 [complex,out]

  • root4 [complex,out]

Call to:

quarticroots(), cubicroots(), quadraticroots()

subroutine  polynomialroots/swapdouble(a, b)

PURPOSE - Interchange the contents of a and b

Parameters:

  • a [real,inout]

  • b [real,inout]

subroutine  polynomialroots/swapsingle(a, b)

PURPOSE - Interchange the contents of a and b

Parameters:

  • a [real,inout]

  • b [real,inout]