Generate and return the vector of coefficients of the polynomial resulting from the multiplication of a polynomial with another polynomial of arbitrary degrees.
More...
Generate and 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
-
[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.
|
- Returns
mul
: The output contiguous
vector of the same type and kind as the input lhs
, of size max(0, min(size(lhs) * size(rhs), 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
.
Possible calling interfaces ⛓
mul(
1 :
size(lhs)
+ size(rhs)
- 1)
= getPolyMul(lhs(:), rhs(:))
Generate and return the vector of coefficients of the polynomial resulting from the multiplication of...
This module contains procedures and generic interfaces for performing various mathematical operations...
- Note
- The additional minimax criterion in size requirement of
mul(1:max(0, min(size(lhs) * size(rhs), size(lhs) + size(rhs) - 1)))
is to ensure the that the procedures of this generic interface can gracefully handle input polynomials coefficient vectors lhs
and rhs
of zero sizes.
A zero-sized polynomial coefficient vector is equivalent to the scalar zero.
Such cases can occur in polynomial division operations where the output quotient or the remainder of the division is an empty vector.
The specific size definition of mul
enhances the flexibility and utility of the procedures of this generic interface in quick concise polynomial arithmetic.
Note, however, that the same flexibility does not hold for the procedures of setPolyMul generic interface.
- Warning
- 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 ⛓
4 TYPE(RKG),
allocatable :: Lhs(:), Rhs(:), Prod(:); \
8 call disp
%show(
"getPolyStr(Lhs)"); \
10 call disp
%show(
"getPolyStr(Rhs)"); \
12 call disp
%show(
"Prod = getPolyMul(Lhs, Rhs)"); \
14 call disp
%show(
"getPolyStr(Prod)"); \
30 type(display_type) :: disp
33#define LHS [real(RKG) :: ]
34#define RHS [real(RKG) :: ]
38#define LHS [real(RKG) :: ]
39#define RHS [real(RKG) :: -1., +1.]
43#define LHS [real(RKG) :: -1., +1.]
44#define RHS [real(RKG) :: ]
48#define LHS [real(RKG) :: +1., +1.]
49#define RHS [real(RKG) :: -1., +1.]
53#define LHS [real(RKG) :: 2., 3., 1.]
54#define RHS [real(RKG) :: 1., 1.]
58#define LHS [real(RKG) :: -42., 0., -12., 1.]
59#define RHS [real(RKG) :: 1., -2., 1.]
63#define LHS [real(RKG) :: -42., 0., -12., 1.]
64#define RHS [real(RKG) :: -2., 1.]
69#define LHS [complex(RKG) :: ]
70#define RHS [complex(RKG) :: ]
74#define LHS [complex(RKG) :: ]
75#define RHS cmplx([real(RKG) :: -1., +1.], -[real(RKG) :: -1., +1.], RKG)
79#define LHS cmplx([real(RKG) :: -1., +1.], -[real(RKG) :: -1., +1.], RKG)
80#define RHS [complex(RKG) :: ]
84#define LHS cmplx([real(RKG) :: -4., 0., -2., 1.], -[real(RKG) :: -4., 0., -2., 1.], RKG)
85#define RHS cmplx([real(RKG) :: -3., 1.], -[real(RKG) :: -3., 1.], RKG)
89#define LHS cmplx([real(RKG) :: 2., 3., 1.], -[real(RKG) :: 2., 3., 1.], RKG)
90#define RHS cmplx([real(RKG) :: 1., 1.], -[real(RKG) :: 1., 1.], RKG)
94#define LHS cmplx([real(RKG) :: -42., 0., -12., 1.], -[real(RKG) :: -42., 0., -12., 1.], RKG)
95#define RHS cmplx([real(RKG) :: 1., -2., 1.], -[real(RKG) :: 1., -2., 1.], RKG)
99#define LHS cmplx([real(RKG) :: -42., 0., -12., 1.], -[real(RKG) :: -42., 0., -12., 1.], RKG)
100#define RHS cmplx([real(RKG) :: -2., 1.], -[real(RKG) :: -2., 1.])
Generate and return a string containing the polynomial expression corresponding to the input polynomi...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
442.x^
0 + 5.x^
1 + 4.x^
2 + 1.x^
3
48-42.x^
0 + 0.x^
1 - 12.x^
2 + 1.x^
3
53-42.x^
0 + 84.x^
1 - 54.x^
2 + 25.x^
3 - 14.x^
4 + 1.x^
5
57-42.x^
0 + 0.x^
1 - 12.x^
2 + 1.x^
3
6284.x^
0 - 42.x^
1 + 24.x^
2 - 14.x^
3 + 1.x^
4
77(
-1.,
1.)x^
0 + (
1.,
-1.)x^
1
84(
-1.,
1.)x^
0 + (
1.,
-1.)x^
1
93(
-4.,
4.)x^
0 + (
0.,
-0.)x^
1 + (
-2.,
2.)x^
2 + (
1.,
-1.)x^
3
95(
-3.,
3.)x^
0 + (
1.,
-1.)x^
1
98(
0.,
-24.)x^
0 + (
0.,
8.)x^
1 + (
0.,
-12.)x^
2 + (
0.,
10.)x^
3 + (
0.,
-2.)x^
4
102(
2.,
-2.)x^
0 + (
3.,
-3.)x^
1 + (
1.,
-1.)x^
2
104(
1.,
-1.)x^
0 + (
1.,
-1.)x^
1
107(
0.,
-4.)x^
0 + (
0.,
-10.)x^
1 + (
0.,
-8.)x^
2 + (
0.,
-2.)x^
3
111(
-42.,
42.)x^
0 + (
0.,
-0.)x^
1 + (
-12.,
12.)x^
2 + (
1.,
-1.)x^
3
113(
1.,
-1.)x^
0 + (
-2.,
2.)x^
1 + (
1.,
-1.)x^
2
116(
0.,
84.)x^
0 + (
0.,
-168.)x^
1 + (
0.,
108.)x^
2 + (
0.,
-50.)x^
3 + (
0.,
28.)x^
4 + (
0.,
-2.)x^
5
120(
-42.,
42.)x^
0 + (
0.,
-0.)x^
1 + (
-12.,
12.)x^
2 + (
1.,
-1.)x^
3
122(
-2.,
2.)x^
0 + (
1.,
-1.)x^
1
125(
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.
-
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.
-
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 1793 of file pm_polynomial.F90.