pm_polynomial::getPolyVal Interface Reference

Generate and return the value of the polynomial of arbitrary degree whose coefficients are specified by the user in the order of increasing power.
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Detailed Description

Generate and return the value of the polynomial of arbitrary degree whose coefficients are specified by the user in the order of increasing power.

See the documentation of pm_polynomial for details of the implementation.

Parameters

[in]	coef	: The input array of, type complex of the same kind as the kind of the input x of type complex, or type real of the same kind as the kind of the input x of type complex, or type real of the same kind as the kind of the input x of type real, containing the coefficients of the polynomial in the order of increasing power. By definition, the degree of the polynomial is size(coef) - 1.
[in]	x	: The input scalar of, type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128), type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), representing the point at which the polynomial must be computed.

Returns

poly : The output scalar of the same type and kind as the input x containing the polynomial value at the specified point.

Possible calling interfaces ⛓

use pm_polynomial, only: getPolyVal
 
poly = getPolyVal(coef(:), x)
poly(1:size(x)) = getPolyVal(coef(:), x(:))

Warning

The condition 0 < size(coef) must hold for the corresponding input arguments.
This condition is verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Note

The current interface requirements of either,

1. (complex :: coef, complex :: x), or
   
2. (real :: coef, complex :: x), or
   
3. (real :: coef, real :: x)
   

are in line with the fact that polynomial coefficients of type real frequently have complex roots.
In particular, the interface (real :: coef, complex :: x) allows seamless integration of the polynomial evaluations of this module with various polynomial root-finding algorithm of the ParaMonte library.

See also

getPolyRoot
setPolyRoot

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK, RKH
    use pm_polynomial, only: getPolyVal
    use pm_io, only: display_type
 
    implicit none
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    block
        use pm_kind, only: TKG => RKH ! all processor kinds are supported.
        call disp%skip()
        call disp%show("getPolyVal([real(TKG) :: 1, 3, 0, 2], x = 2._TKG) ! 23.")
        call disp%show( getPolyVal([real(TKG) :: 1, 3, 0, 2], x = 2._TKG) )
        call disp%skip()
        call disp%show("getPolyVal([real(TKG) :: -19.0, 7.0, -4.0, 6.0], x = 3._TKG) ! 128.")
        call disp%show( getPolyVal([real(TKG) :: -19.0, 7.0, -4.0, 6.0], x = 3._TKG) )
        call disp%skip()
        call disp%show("getPolyVal([real(TKG) :: -19.0, 7.0, -4.0, 6.0], x = (3._TKG, 0._TKG)) ! (128., 0.)")
        call disp%show( getPolyVal([real(TKG) :: -19.0, 7.0, -4.0, 6.0], x = (3._TKG, 0._TKG)) )
        call disp%skip()
    end block
 
    block
        use pm_kind, only: TKG => RKS ! all processor kinds are supported.
        call disp%skip()
        call disp%show("getPolyVal([complex(TKG) :: (+2., +4.), (+24., +12.), (-28., +36.), (-15., +0.), (+24., -42.), (-7., +0.)], x = (2._TKG, -2._TKG))")
        call disp%show( getPolyVal([complex(TKG) :: (+2., +4.), (+24., +12.), (-28., +36.), (-15., +0.), (+24., -42.), (-7., +0.)], x = (2._TKG, -2._TKG)) )
        call disp%skip()
    end block
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
getPolyVal([real(TKG) :: 1, 3, 0, 2], x = 2._TKG) ! 23.
+23.0000000000000000000000000000000000
 
getPolyVal([real(TKG) :: -19.0, 7.0, -4.0, 6.0], x = 3._TKG) ! 128.
+128.000000000000000000000000000000000
 
getPolyVal([real(TKG) :: -19.0, 7.0, -4.0, 6.0], x = (3._TKG, 0._TKG)) ! (128., 0.)
(+128.000000000000000000000000000000000, +0.00000000000000000000000000000000000)
 
 
getPolyVal([complex(TKG) :: (+2., +4.), (+24., +12.), (-28., +36.), (-15., +0.), (+24., -42.), (-7., +0.)], x = (2._TKG, -2._TKG))
(-38.0000000, +2236.00000)
 
 

Test:

test_pm_polynomial

Final Remarks ⛓

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If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
   

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 518 of file pm_polynomial.F90.

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The documentation for this interface was generated from the following file:

• src/fortran/main/pm_polynomial.F90