Generate and return the vector of coefficients of the polynomial resulting from the multiplication of a polynomial with another polynomial of arbitrary degrees. More...

Detailed Description

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 ⛓

: use pm_polynomial, only: getPolyMul

mul(1 : size(lhs) + size(rhs) - 1) = getPolyMul(lhs(:), rhs(:))

pm_polynomial::getPolyMul
Generate and return the vector of coefficients of the polynomial resulting from the multiplication of...
Definition: pm_polynomial.F90:1792

pm_polynomial
This module contains procedures and generic interfaces for performing various mathematical operations...
Definition: pm_polynomial.F90:437

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 ⛓

: 1! Define example template macro to avoid duplications. See the example output for actual usage.

2#define SET_POLY_PROD \

3block; \

4 TYPE(RKG), allocatable :: Lhs(:), Rhs(:), Prod(:); \

5 Lhs = LHS; \

6 Rhs = RHS; \

7 call disp%skip(); \

8 call disp%show("getPolyStr(Lhs)"); \

9 call disp%show( getPolyStr(Lhs) ); \

10 call disp%show("getPolyStr(Rhs)"); \

11 call disp%show( getPolyStr(Rhs) ); \

12 call disp%show("Prod = getPolyMul(Lhs, Rhs)"); \

13 Prod = getPolyMul(Lhs, Rhs); \

14 call disp%show("getPolyStr(Prod)"); \

15 call disp%show( getPolyStr(Prod) ); \

16 call disp%skip(); \

17end block;

18

19program example

20

21 use pm_kind, only: SK, IK

22 use pm_kind, only: RKG => RKS ! all processor real and complex kinds are supported.

23 use pm_io, only: display_type

24 use pm_polynomial, only: getPolyMul

25 use pm_polynomial, only: getPolyStr

26

27 implicit none

28

29 integer(IK) :: lenQuo

30 type(display_type) :: disp

31 disp = display_type(file = "main.out.F90")

32

33#define LHS [real(RKG) :: ]

34#define RHS [real(RKG) :: ]

35#define TYPE real

36SET_POLY_PROD

37

38#define LHS [real(RKG) :: ]

39#define RHS [real(RKG) :: -1., +1.]

40#define TYPE real

41SET_POLY_PROD

42

43#define LHS [real(RKG) :: -1., +1.]

44#define RHS [real(RKG) :: ]

45#define TYPE real

46SET_POLY_PROD

47

48#define LHS [real(RKG) :: +1., +1.]

49#define RHS [real(RKG) :: -1., +1.]

50#define TYPE real

51SET_POLY_PROD

52

53#define LHS [real(RKG) :: 2., 3., 1.]

54#define RHS [real(RKG) :: 1., 1.]

55#define TYPE real

56SET_POLY_PROD

57

58#define LHS [real(RKG) :: -42., 0., -12., 1.]

59#define RHS [real(RKG) :: 1., -2., 1.]

60#define TYPE real

61SET_POLY_PROD

62

63#define LHS [real(RKG) :: -42., 0., -12., 1.]

64#define RHS [real(RKG) :: -2., 1.]

65#define TYPE real

66SET_POLY_PROD

67

68

69#define LHS [complex(RKG) :: ]

70#define RHS [complex(RKG) :: ]

71#define TYPE complex

72SET_POLY_PROD

73

74#define LHS [complex(RKG) :: ]

75#define RHS cmplx([real(RKG) :: -1., +1.], -[real(RKG) :: -1., +1.], RKG)

76#define TYPE complex

77SET_POLY_PROD

78

79#define LHS cmplx([real(RKG) :: -1., +1.], -[real(RKG) :: -1., +1.], RKG)

80#define RHS [complex(RKG) :: ]

81#define TYPE complex

82SET_POLY_PROD

83

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)

86#define TYPE complex

87SET_POLY_PROD

88

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)

91#define TYPE complex

92SET_POLY_PROD

93

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)

96#define TYPE complex

97SET_POLY_PROD

98

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.])

101#define TYPE complex

102SET_POLY_PROD

103

104end program example

pm_polynomial::getPolyStr
Generate and return a string containing the polynomial expression corresponding to the input polynomi...
Definition: pm_polynomial.F90:3047

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1

2getPolyStr(Lhs)

3

4getPolyStr(Rhs)

5

6Prod = getPolyMul(Lhs, Rhs)

7getPolyStr(Prod)

8

9

10

11getPolyStr(Lhs)

12

13getPolyStr(Rhs)

14-1.x^0 + 1.x^1

15Prod = getPolyMul(Lhs, Rhs)

16getPolyStr(Prod)

17

18

19

20getPolyStr(Lhs)

21-1.x^0 + 1.x^1

22getPolyStr(Rhs)

23

24Prod = getPolyMul(Lhs, Rhs)

25getPolyStr(Prod)

26

27

28

29getPolyStr(Lhs)

301.x^0 + 1.x^1

31getPolyStr(Rhs)

32-1.x^0 + 1.x^1

33Prod = getPolyMul(Lhs, Rhs)

34getPolyStr(Prod)

35-1.x^0 + 0.x^1 + 1.x^2

36

37

38getPolyStr(Lhs)

392.x^0 + 3.x^1 + 1.x^2

40getPolyStr(Rhs)

411.x^0 + 1.x^1

42Prod = getPolyMul(Lhs, Rhs)

43getPolyStr(Prod)

442.x^0 + 5.x^1 + 4.x^2 + 1.x^3

45

46

47getPolyStr(Lhs)

48-42.x^0 + 0.x^1 - 12.x^2 + 1.x^3

49getPolyStr(Rhs)

501.x^0 - 2.x^1 + 1.x^2

51Prod = getPolyMul(Lhs, Rhs)

52getPolyStr(Prod)

53-42.x^0 + 84.x^1 - 54.x^2 + 25.x^3 - 14.x^4 + 1.x^5

54

55

56getPolyStr(Lhs)

57-42.x^0 + 0.x^1 - 12.x^2 + 1.x^3

58getPolyStr(Rhs)

59-2.x^0 + 1.x^1

60Prod = getPolyMul(Lhs, Rhs)

61getPolyStr(Prod)

6284.x^0 - 42.x^1 + 24.x^2 - 14.x^3 + 1.x^4

63

64

65getPolyStr(Lhs)

66

67getPolyStr(Rhs)

68

69Prod = getPolyMul(Lhs, Rhs)

70getPolyStr(Prod)

71

72

73

74getPolyStr(Lhs)

75

76getPolyStr(Rhs)

77(-1.,1.)x^0 + (1.,-1.)x^1

78Prod = getPolyMul(Lhs, Rhs)

79getPolyStr(Prod)

80

81

82

83getPolyStr(Lhs)

84(-1.,1.)x^0 + (1.,-1.)x^1

85getPolyStr(Rhs)

86

87Prod = getPolyMul(Lhs, Rhs)

88getPolyStr(Prod)

89

90

91

92getPolyStr(Lhs)

93(-4.,4.)x^0 + (0.,-0.)x^1 + (-2.,2.)x^2 + (1.,-1.)x^3

94getPolyStr(Rhs)

95(-3.,3.)x^0 + (1.,-1.)x^1

96Prod = getPolyMul(Lhs, Rhs)

97getPolyStr(Prod)

98(0.,-24.)x^0 + (0.,8.)x^1 + (0.,-12.)x^2 + (0.,10.)x^3 + (0.,-2.)x^4

99

100

101getPolyStr(Lhs)

102(2.,-2.)x^0 + (3.,-3.)x^1 + (1.,-1.)x^2

103getPolyStr(Rhs)

104(1.,-1.)x^0 + (1.,-1.)x^1

105Prod = getPolyMul(Lhs, Rhs)

106getPolyStr(Prod)

107(0.,-4.)x^0 + (0.,-10.)x^1 + (0.,-8.)x^2 + (0.,-2.)x^3

108

109

110getPolyStr(Lhs)

111(-42.,42.)x^0 + (0.,-0.)x^1 + (-12.,12.)x^2 + (1.,-1.)x^3

112getPolyStr(Rhs)

113(1.,-1.)x^0 + (-2.,2.)x^1 + (1.,-1.)x^2

114Prod = getPolyMul(Lhs, Rhs)

115getPolyStr(Prod)

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

117

118

119getPolyStr(Lhs)

120(-42.,42.)x^0 + (0.,-0.)x^1 + (-12.,12.)x^2 + (1.,-1.)x^3

121getPolyStr(Rhs)

122(-2.,2.)x^0 + (1.,-1.)x^1

123Prod = getPolyMul(Lhs, Rhs)

124getPolyStr(Prod)

125(0.,-168.)x^0 + (0.,84.)x^1 + (0.,-48.)x^2 + (0.,28.)x^3 + (0.,-2.)x^4

126

127

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 1792 of file pm_polynomial.F90.

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

src/fortran/main/pm_polynomial.F90