pm_polynomial::setPolyMul Interface Reference

Return the vector of coefficients of the polynomial resulting from the multiplication of a polynomial with another polynomial of arbitrary degrees. More...

Detailed Description

Return the vector of coefficients of the polynomial resulting from the multiplication of a polynomial with another polynomial of arbitrary degrees.

See the documentation of pm_polynomial for details of the implementation.

Parameters

[out]	mul	: The output contiguous vector of the same type and kind as the input lhs, of size size(lhs) + size(rhs) - 1, containing the coefficients (in the order of increasing power) of the resulting polynomial from the multiplication of the polynomial lhs of arbitrary degree with another polynomial rhs of arbitrary degree. By definition, the degree of the mul polynomial is size(mul) - 1.
[in]	lhs	: The input contiguous vector of non-zero size of, type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128), or type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the coefficients of the left-hand-side polynomial in the multiplication, in the order of increasing power. By definition, the degree of the lhs polynomial is size(lhs) - 1. This means that the condition lhs(size(lhs)) /= 0. must hold.
[in]	rhs	: The input contiguous vector of non-zero size of the same type and kind as lhs, containing the coefficients of the right-hand-side polynomial in the multiplication, in the order of increasing power. By definition, the degree of the rhs polynomial is size(rhs) - 1. This means that the condition rhs(size(rhs)) /= 0. must hold.

Possible calling interfaces ⛓

use pm_polynomial, only: setPolyMul
 
call setPolyMul(mul(1 : size(lhs) + size(rhs) - 1), lhs(:), rhs(:))

Warning

The condition 0 < size(rhs) must hold for the corresponding input arguments.
The condition 0 < size(lhs) must hold for the corresponding input arguments.
The condition size(mul) == size(lhs) + size(rhs) - 1 must hold for the corresponding input arguments.
The condition lhs(size(lhs)) /= 0. must hold for the corresponding input arguments.
The condition rhs(size(rhs)) /= 0. must hold for the corresponding input arguments.
These conditions are 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.

See also

getPolySub
setPolySub
getPolySub
setPolySub
setPolyDiv
getPolyMul
setPolyMul

Example usage ⛓

! Define example template macro to avoid duplications. See the example output for actual usage.
#define SET_POLY_PROD \
block; \
    TYPE(RKG), allocatable :: Lhs(:), Rhs(:), Prod(:); \
    Lhs = LHS; \
    Rhs = RHS; \
    call disp%skip(); \
    call disp%show("getPolyStr(Lhs)"); \
    call disp%show( getPolyStr(Lhs) ); \
    call disp%show("getPolyStr(Rhs)"); \
    call disp%show( getPolyStr(Rhs) ); \
    call disp%show("allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))"); \
                    allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1))); \
    call disp%show("call setPolyMul(Prod, Lhs, Rhs)"); \
                    call setPolyMul(Prod, Lhs, Rhs); \
    call disp%show("getPolyStr(Prod)"); \
    call disp%show( getPolyStr(Prod) ); \
    call disp%skip(); \
end block;
 
program example
 
    use pm_kind, only: SK, IK
    use pm_kind, only: RKG => RKS ! all processor real and complex kinds are supported.
    use pm_io, only: display_type
    use pm_polynomial, only: setPolyMul
    use pm_polynomial, only: getPolyStr
 
    implicit none
 
    integer(IK) :: lenQuo
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
#define LHS [real(RKG) :: +1., +1.]
#define RHS [real(RKG) :: -1., +1.]
#define TYPE real
SET_POLY_PROD
 
#define LHS [real(RKG) :: 2., 3., 1.]
#define RHS [real(RKG) :: 1., 1.]
#define TYPE real
SET_POLY_PROD
 
#define LHS [real(RKG) :: -42., 0., -12., 1.]
#define RHS [real(RKG) :: 1., -2., 1.]
#define TYPE real
SET_POLY_PROD
 
#define LHS [real(RKG) :: -42., 0., -12., 1.]
#define RHS [real(RKG) :: -2., 1.]
#define TYPE real
SET_POLY_PROD
 
 
#define LHS cmplx([real(RKG) :: -4., 0., -2., 1.], -[real(RKG) :: -4., 0., -2., 1.], RKG)
#define RHS cmplx([real(RKG) :: -3., 1.], -[real(RKG) :: -3., 1.], RKG)
#define TYPE complex
SET_POLY_PROD
 
#define LHS cmplx([real(RKG) :: 2., 3., 1.], -[real(RKG) :: 2., 3., 1.], RKG)
#define RHS cmplx([real(RKG) :: 1., 1.], -[real(RKG) :: 1., 1.], RKG)
#define TYPE complex
SET_POLY_PROD
 
#define LHS cmplx([real(RKG) :: -42., 0., -12., 1.], -[real(RKG) :: -42., 0., -12., 1.], RKG)
#define RHS cmplx([real(RKG) :: 1., -2., 1.], -[real(RKG) :: 1., -2., 1.], RKG)
#define TYPE complex
SET_POLY_PROD
 
#define LHS cmplx([real(RKG) :: -42., 0., -12., 1.], -[real(RKG) :: -42., 0., -12., 1.], RKG)
#define RHS cmplx([real(RKG) :: -2., 1.], -[real(RKG) :: -2., 1.])
#define TYPE complex
SET_POLY_PROD
 
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 ⛓

 
getPolyStr(Lhs)
1.x^0 + 1.x^1                                                                                                                                                                                                                                 
getPolyStr(Rhs)
-1.x^0 + 1.x^1                                                                                                                                                                                                                                
allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))
call setPolyMul(Prod, Lhs, Rhs)
getPolyStr(Prod)
-1.x^0 + 0.x^1 + 1.x^2                                                                                                                                                                                                                                                                                                                                               
 
 
getPolyStr(Lhs)
2.x^0 + 3.x^1 + 1.x^2                                                                                                                                                                                                                                                                                                                                                
getPolyStr(Rhs)
1.x^0 + 1.x^1                                                                                                                                                                                                                                 
allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))
call setPolyMul(Prod, Lhs, Rhs)
getPolyStr(Prod)
2.x^0 + 5.x^1 + 4.x^2 + 1.x^3                                                                                                                                                                                                                                                                                                                                                                                                                                                               
 
 
getPolyStr(Lhs)
-42.x^0 + 0.x^1 - 12.x^2 + 1.x^3                                                                                                                                                                                                                                                                                                                                                                                                                                                              
getPolyStr(Rhs)
1.x^0 - 2.x^1 + 1.x^2                                                                                                                                                                                                                                                                                                                                                
allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))
call setPolyMul(Prod, Lhs, Rhs)
getPolyStr(Prod)
-42.x^0 + 84.x^1 - 54.x^2 + 25.x^3 - 14.x^4 + 1.x^5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
 
 
getPolyStr(Lhs)
-42.x^0 + 0.x^1 - 12.x^2 + 1.x^3                                                                                                                                                                                                                                                                                                                                                                                                                                                              
getPolyStr(Rhs)
-2.x^0 + 1.x^1                                                                                                                                                                                                                                
allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))
call setPolyMul(Prod, Lhs, Rhs)
getPolyStr(Prod)
84.x^0 - 42.x^1 + 24.x^2 - 14.x^3 + 1.x^4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              
 
 
getPolyStr(Lhs)
(-4.,4.)x^0 + (0.,-0.)x^1 + (-2.,2.)x^2 + (1.,-1.)x^3                                                                                                                                                                                                                                                                                                                                                                                                       
getPolyStr(Rhs)
(-3.,3.)x^0 + (1.,-1.)x^1                                                                                                                                                                                                     
allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))
call setPolyMul(Prod, Lhs, Rhs)
getPolyStr(Prod)
(0.,-24.)x^0 + (0.,8.)x^1 + (0.,-12.)x^2 + (0.,10.)x^3 + (0.,-2.)x^4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          
 
 
getPolyStr(Lhs)
(2.,-2.)x^0 + (3.,-3.)x^1 + (1.,-1.)x^2                                                                                                                                                                                                                                                                                                      
getPolyStr(Rhs)
(1.,-1.)x^0 + (1.,-1.)x^1                                                                                                                                                                                                     
allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))
call setPolyMul(Prod, Lhs, Rhs)
getPolyStr(Prod)
(0.,-4.)x^0 + (0.,-10.)x^1 + (0.,-8.)x^2 + (0.,-2.)x^3                                                                                                                                                                                                                                                                                                                                                                                                       
 
 
getPolyStr(Lhs)
(-42.,42.)x^0 + (0.,-0.)x^1 + (-12.,12.)x^2 + (1.,-1.)x^3                                                                                                                                                                                                                                                                                                                                                                                                       
getPolyStr(Rhs)
(1.,-1.)x^0 + (-2.,2.)x^1 + (1.,-1.)x^2                                                                                                                                                                                                                                                                                                      
allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))
call setPolyMul(Prod, Lhs, Rhs)
getPolyStr(Prod)
(0.,84.)x^0 + (0.,-168.)x^1 + (0.,108.)x^2 + (0.,-50.)x^3 + (0.,28.)x^4 + (0.,-2.)x^5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
 
 
getPolyStr(Lhs)
(-42.,42.)x^0 + (0.,-0.)x^1 + (-12.,12.)x^2 + (1.,-1.)x^3                                                                                                                                                                                                                                                                                                                                                                                                       
getPolyStr(Rhs)
(-2.,2.)x^0 + (1.,-1.)x^1                                                                                                                                                                                                     
allocate(Prod(1 : min(size(Lhs) * size(Rhs), size(Lhs) + size(Rhs) - 1)))
call setPolyMul(Prod, Lhs, Rhs)
getPolyStr(Prod)
(0.,-168.)x^0 + (0.,84.)x^1 + (0.,-48.)x^2 + (0.,28.)x^3 + (0.,-2.)x^4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          
 
 

Test:

test_pm_polynomial

Final Remarks ⛓

---

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 1997 of file pm_polynomial.F90.

---

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

• src/fortran/main/pm_polynomial.F90