ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_polynomial::getPolyDiff Interface Reference

Generate and return the vector of coefficients of the polynomial resulting from the \(k\)th-order differentiation of a univariate polynomial of arbitrary degree. More...

Detailed Description

Generate and return the vector of coefficients of the polynomial resulting from the \(k\)th-order differentiation of a univariate polynomial of arbitrary degree.

See the documentation of pm_polynomial for details of the implementation.

Parameters
[in]coef: 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 (in the order of increasing power) of the univariate polynomial whose \(k\)th-order derivative must be returned.
By definition, the degree of the coef polynomial is size(coef) - 1.
This means that the condition coef(size(coef)) /= 0. is expected to hold (although not enforced).
[in]order: The input scalar nonnegative integer of default kind IK containing the order of the derivative to compute.
(optional, default = 1)
Returns
diff : The output contiguous vector of the same type and kind as the input coef, of size size(coef) - order, containing the coefficients (in the order of increasing power) of the resulting polynomial from the \(k\)th-order differentiation of the input polynomial with coefficients coef of arbitrary degree.
By definition, the degree of the diff polynomial is size(diff) - order.


Possible calling interfaces ⛓

use pm_polynomial, only: getPolyDiff
diff(1 : size(coef) - 1) = getPolyDiff(coef(:))
diff(1 : size(coef) - order) = getPolyDiff(coef(:), order)
pm_polynomial::getPolyDiff
Generate and return the vector of coefficients of the polynomial resulting from the th-order differen...
Definition: pm_polynomial.F90:2415
pm_polynomial
This module contains procedures and generic interfaces for performing various mathematical operations...
Definition: pm_polynomial.F90:437
Warning
The condition 0 <= order 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.
See also
getPolyDiff
setPolyDiff


Example usage ⛓

1program example
2
3 use pm_kind, only: SK, IK
4 use pm_io, only: display_type
5 use pm_distUnif, only: getUnifRand
6 use pm_polynomial, only: getPolyStr
7 use pm_polynomial, only: getPolyDiff
8
9 implicit none
10
11 integer(IK) :: order
12 integer(IK) :: degree
13 type(display_type) :: disp
14 integer(IK) :: itry, ntry = 20
15 disp = display_type(file = "main.out.F90")
16
17 block
18 use pm_kind, only: TKG => RKS ! all processor real and complex kinds are supported.
19 real(TKG), allocatable :: coef(:), diff(:)
20 do itry = 1, ntry
21 call disp%show("degree = getUnifRand(0, 9_IK)")
22 degree = getUnifRand(0, 9_IK)
23 call disp%show("degree")
24 call disp%show( degree )
25 call disp%show("coef = getUnifRand(-9, 9, degree)")
26 coef = getUnifRand(-9, 9, degree)
27 call disp%show("coef")
28 call disp%show( coef )
29 call disp%show("getPolyStr(coef)")
30 call disp%show( getPolyStr(coef) )
31 call disp%show("order = getUnifRand(0, size(coef) + 1)")
32 order = getUnifRand(0, size(coef) + 1)
33 call disp%show("order")
34 call disp%show( order )
35 call disp%skip()
36 call disp%show("diff = getPolyDiff(coef, order)")
37 diff = getPolyDiff(coef, order)
38 call disp%show("diff ! derivative coefficients.")
39 call disp%show( diff )
40 call disp%show("getPolyStr(diff)")
41 call disp%show( getPolyStr(diff) )
42 call disp%skip()
43 end do
44 end block
45
46 block
47 use pm_kind, only: TKG => RKS ! all processor real and complex kinds are supported.
48 complex(TKG), allocatable :: coef(:), diff(:)
49 do itry = 1, ntry
50 call disp%show("degree = getUnifRand(0, 9_IK)")
51 degree = getUnifRand(0, 9_IK)
52 call disp%show("degree")
53 call disp%show( degree )
54 call disp%show("coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)")
55 coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
56 call disp%show("coef")
57 call disp%show( coef )
58 call disp%show("getPolyStr(coef)")
59 call disp%show( getPolyStr(coef) )
60 call disp%show("order = getUnifRand(0, size(coef) + 1)")
61 order = getUnifRand(0, size(coef) + 1)
62 call disp%show("order")
63 call disp%show( order )
64 call disp%skip()
65 call disp%show("diff = getPolyDiff(coef, order)")
66 diff = getPolyDiff(coef, order)
67 call disp%show("diff ! derivative coefficients.")
68 call disp%show( diff )
69 call disp%show("getPolyStr(diff)")
70 call disp%show( getPolyStr(diff) )
71 call disp%skip()
72 end do
73 end block
74
75end program example
pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4150
pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
pm_polynomial::getPolyStr
Generate and return a string containing the polynomial expression corresponding to the input polynomi...
Definition: pm_polynomial.F90:3047
pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274
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 ⛓
1degree = getUnifRand(0, 9_IK)
2degree
3+1
4coef = getUnifRand(-9, 9, degree)
5coef
6-6.00000000
7getPolyStr(coef)
8-6.x^0
9order = getUnifRand(0, size(coef) + 1)
10order
11+0
12
13diff = getPolyDiff(coef, order)
14diff ! derivative coefficients.
15-6.00000000
16getPolyStr(diff)
17-6.x^0
18
19degree = getUnifRand(0, 9_IK)
20degree
21+6
22coef = getUnifRand(-9, 9, degree)
23coef
24+0.00000000, +5.00000000, -4.00000000, -3.00000000, +6.00000000, -2.00000000
25getPolyStr(coef)
260.x^0 + 5.x^1 - 4.x^2 - 3.x^3 + 6.x^4 - 2.x^5
27order = getUnifRand(0, size(coef) + 1)
28order
29+0
30
31diff = getPolyDiff(coef, order)
32diff ! derivative coefficients.
33+0.00000000, +5.00000000, -4.00000000, -3.00000000, +6.00000000, -2.00000000
34getPolyStr(diff)
350.x^0 + 5.x^1 - 4.x^2 - 3.x^3 + 6.x^4 - 2.x^5
36
37degree = getUnifRand(0, 9_IK)
38degree
39+0
40coef = getUnifRand(-9, 9, degree)
41coef
42
43getPolyStr(coef)
44
45order = getUnifRand(0, size(coef) + 1)
46order
47+1
48
49diff = getPolyDiff(coef, order)
50diff ! derivative coefficients.
51
52getPolyStr(diff)
53
54
55degree = getUnifRand(0, 9_IK)
56degree
57+5
58coef = getUnifRand(-9, 9, degree)
59coef
60-5.00000000, -6.00000000, +2.00000000, -3.00000000, -6.00000000
61getPolyStr(coef)
62-5.x^0 - 6.x^1 + 2.x^2 - 3.x^3 - 6.x^4
63order = getUnifRand(0, size(coef) + 1)
64order
65+0
66
67diff = getPolyDiff(coef, order)
68diff ! derivative coefficients.
69-5.00000000, -6.00000000, +2.00000000, -3.00000000, -6.00000000
70getPolyStr(diff)
71-5.x^0 - 6.x^1 + 2.x^2 - 3.x^3 - 6.x^4
72
73degree = getUnifRand(0, 9_IK)
74degree
75+6
76coef = getUnifRand(-9, 9, degree)
77coef
78+7.00000000, -8.00000000, -3.00000000, -4.00000000, -9.00000000, +4.00000000
79getPolyStr(coef)
807.x^0 - 8.x^1 - 3.x^2 - 4.x^3 - 9.x^4 + 4.x^5
81order = getUnifRand(0, size(coef) + 1)
82order
83+4
84
85diff = getPolyDiff(coef, order)
86diff ! derivative coefficients.
87-36.0000000, +20.0000000
88getPolyStr(diff)
89-36.x^0 + 20.x^1
90
91degree = getUnifRand(0, 9_IK)
92degree
93+7
94coef = getUnifRand(-9, 9, degree)
95coef
96+8.00000000, +6.00000000, +8.00000000, -6.00000000, +5.00000000, -9.00000000, +5.00000000
97getPolyStr(coef)
988.x^0 + 6.x^1 + 8.x^2 - 6.x^3 + 5.x^4 - 9.x^5 + 5.x^6
99order = getUnifRand(0, size(coef) + 1)
100order
101+5
102
103diff = getPolyDiff(coef, order)
104diff ! derivative coefficients.
105-45.0000000, +30.0000000
106getPolyStr(diff)
107-45.x^0 + 30.x^1
108
109degree = getUnifRand(0, 9_IK)
110degree
111+4
112coef = getUnifRand(-9, 9, degree)
113coef
114-4.00000000, +7.00000000, -1.00000000, +0.00000000
115getPolyStr(coef)
116-4.x^0 + 7.x^1 - 1.x^2 + 0.x^3
117order = getUnifRand(0, size(coef) + 1)
118order
119+0
120
121diff = getPolyDiff(coef, order)
122diff ! derivative coefficients.
123-4.00000000, +7.00000000, -1.00000000, +0.00000000
124getPolyStr(diff)
125-4.x^0 + 7.x^1 - 1.x^2 + 0.x^3
126
127degree = getUnifRand(0, 9_IK)
128degree
129+2
130coef = getUnifRand(-9, 9, degree)
131coef
132-6.00000000, +4.00000000
133getPolyStr(coef)
134-6.x^0 + 4.x^1
135order = getUnifRand(0, size(coef) + 1)
136order
137+0
138
139diff = getPolyDiff(coef, order)
140diff ! derivative coefficients.
141-6.00000000, +4.00000000
142getPolyStr(diff)
143-6.x^0 + 4.x^1
144
145degree = getUnifRand(0, 9_IK)
146degree
147+8
148coef = getUnifRand(-9, 9, degree)
149coef
150+2.00000000, -4.00000000, -3.00000000, +2.00000000, -8.00000000, +9.00000000, +8.00000000, +4.00000000
151getPolyStr(coef)
1522.x^0 - 4.x^1 - 3.x^2 + 2.x^3 - 8.x^4 + 9.x^5 + 8.x^6 + 4.x^7
153order = getUnifRand(0, size(coef) + 1)
154order
155+2
156
157diff = getPolyDiff(coef, order)
158diff ! derivative coefficients.
159-6.00000000, +6.00000000, -32.0000000, +45.0000000, +48.0000000, +28.0000000
160getPolyStr(diff)
161-6.x^0 + 6.x^1 - 32.x^2 + 45.x^3 + 48.x^4 + 28.x^5
162
163degree = getUnifRand(0, 9_IK)
164degree
165+3
166coef = getUnifRand(-9, 9, degree)
167coef
168+8.00000000, -1.00000000, -8.00000000
169getPolyStr(coef)
1708.x^0 - 1.x^1 - 8.x^2
171order = getUnifRand(0, size(coef) + 1)
172order
173+4
174
175diff = getPolyDiff(coef, order)
176diff ! derivative coefficients.
177
178getPolyStr(diff)
179
180
181degree = getUnifRand(0, 9_IK)
182degree
183+8
184coef = getUnifRand(-9, 9, degree)
185coef
186-2.00000000, +7.00000000, -8.00000000, +2.00000000, +3.00000000, +0.00000000, +2.00000000, +7.00000000
187getPolyStr(coef)
188-2.x^0 + 7.x^1 - 8.x^2 + 2.x^3 + 3.x^4 + 0.x^5 + 2.x^6 + 7.x^7
189order = getUnifRand(0, size(coef) + 1)
190order
191+1
192
193diff = getPolyDiff(coef, order)
194diff ! derivative coefficients.
195+7.00000000, -16.0000000, +6.00000000, +12.0000000, +0.00000000, +12.0000000, +49.0000000
196getPolyStr(diff)
1977.x^0 - 16.x^1 + 6.x^2 + 12.x^3 + 0.x^4 + 12.x^5 + 49.x^6
198
199degree = getUnifRand(0, 9_IK)
200degree
201+9
202coef = getUnifRand(-9, 9, degree)
203coef
204-7.00000000, +1.00000000, +8.00000000, +5.00000000, -6.00000000, -2.00000000, -9.00000000, +0.00000000, +1.00000000
205getPolyStr(coef)
206-7.x^0 + 1.x^1 + 8.x^2 + 5.x^3 - 6.x^4 - 2.x^5 - 9.x^6 + 0.x^7 + 1.x^8
207order = getUnifRand(0, size(coef) + 1)
208order
209+2
210
211diff = getPolyDiff(coef, order)
212diff ! derivative coefficients.
213+16.0000000, +15.0000000, -24.0000000, -10.0000000, -54.0000000, +0.00000000, +8.00000000
214getPolyStr(diff)
21516.x^0 + 15.x^1 - 24.x^2 - 10.x^3 - 54.x^4 + 0.x^5 + 8.x^6
216
217degree = getUnifRand(0, 9_IK)
218degree
219+3
220coef = getUnifRand(-9, 9, degree)
221coef
222+2.00000000, -5.00000000, +6.00000000
223getPolyStr(coef)
2242.x^0 - 5.x^1 + 6.x^2
225order = getUnifRand(0, size(coef) + 1)
226order
227+1
228
229diff = getPolyDiff(coef, order)
230diff ! derivative coefficients.
231-5.00000000, +12.0000000
232getPolyStr(diff)
233-5.x^0 + 12.x^1
234
235degree = getUnifRand(0, 9_IK)
236degree
237+1
238coef = getUnifRand(-9, 9, degree)
239coef
240+8.00000000
241getPolyStr(coef)
2428.x^0
243order = getUnifRand(0, size(coef) + 1)
244order
245+1
246
247diff = getPolyDiff(coef, order)
248diff ! derivative coefficients.
249
250getPolyStr(diff)
251
252
253degree = getUnifRand(0, 9_IK)
254degree
255+6
256coef = getUnifRand(-9, 9, degree)
257coef
258+1.00000000, -7.00000000, -5.00000000, +0.00000000, -4.00000000, +4.00000000
259getPolyStr(coef)
2601.x^0 - 7.x^1 - 5.x^2 + 0.x^3 - 4.x^4 + 4.x^5
261order = getUnifRand(0, size(coef) + 1)
262order
263+3
264
265diff = getPolyDiff(coef, order)
266diff ! derivative coefficients.
267+0.00000000, -16.0000000, +20.0000000
268getPolyStr(diff)
2690.x^0 - 16.x^1 + 20.x^2
270
271degree = getUnifRand(0, 9_IK)
272degree
273+9
274coef = getUnifRand(-9, 9, degree)
275coef
276+4.00000000, -3.00000000, -2.00000000, +9.00000000, +2.00000000, +3.00000000, -6.00000000, +4.00000000, -3.00000000
277getPolyStr(coef)
2784.x^0 - 3.x^1 - 2.x^2 + 9.x^3 + 2.x^4 + 3.x^5 - 6.x^6 + 4.x^7 - 3.x^8
279order = getUnifRand(0, size(coef) + 1)
280order
281+9
282
283diff = getPolyDiff(coef, order)
284diff ! derivative coefficients.
285
286getPolyStr(diff)
287
288
289degree = getUnifRand(0, 9_IK)
290degree
291+0
292coef = getUnifRand(-9, 9, degree)
293coef
294
295getPolyStr(coef)
296
297order = getUnifRand(0, size(coef) + 1)
298order
299+0
300
301diff = getPolyDiff(coef, order)
302diff ! derivative coefficients.
303
304getPolyStr(diff)
305
306
307degree = getUnifRand(0, 9_IK)
308degree
309+4
310coef = getUnifRand(-9, 9, degree)
311coef
312-3.00000000, +6.00000000, -7.00000000, +6.00000000
313getPolyStr(coef)
314-3.x^0 + 6.x^1 - 7.x^2 + 6.x^3
315order = getUnifRand(0, size(coef) + 1)
316order
317+1
318
319diff = getPolyDiff(coef, order)
320diff ! derivative coefficients.
321+6.00000000, -14.0000000, +18.0000000
322getPolyStr(diff)
3236.x^0 - 14.x^1 + 18.x^2
324
325degree = getUnifRand(0, 9_IK)
326degree
327+7
328coef = getUnifRand(-9, 9, degree)
329coef
330+7.00000000, +3.00000000, -7.00000000, -1.00000000, +5.00000000, +2.00000000, +8.00000000
331getPolyStr(coef)
3327.x^0 + 3.x^1 - 7.x^2 - 1.x^3 + 5.x^4 + 2.x^5 + 8.x^6
333order = getUnifRand(0, size(coef) + 1)
334order
335+0
336
337diff = getPolyDiff(coef, order)
338diff ! derivative coefficients.
339+7.00000000, +3.00000000, -7.00000000, -1.00000000, +5.00000000, +2.00000000, +8.00000000
340getPolyStr(diff)
3417.x^0 + 3.x^1 - 7.x^2 - 1.x^3 + 5.x^4 + 2.x^5 + 8.x^6
342
343degree = getUnifRand(0, 9_IK)
344degree
345+6
346coef = getUnifRand(-9, 9, degree)
347coef
348+5.00000000, +8.00000000, -7.00000000, -3.00000000, -1.00000000, +5.00000000
349getPolyStr(coef)
3505.x^0 + 8.x^1 - 7.x^2 - 3.x^3 - 1.x^4 + 5.x^5
351order = getUnifRand(0, size(coef) + 1)
352order
353+0
354
355diff = getPolyDiff(coef, order)
356diff ! derivative coefficients.
357+5.00000000, +8.00000000, -7.00000000, -3.00000000, -1.00000000, +5.00000000
358getPolyStr(diff)
3595.x^0 + 8.x^1 - 7.x^2 - 3.x^3 - 1.x^4 + 5.x^5
360
361degree = getUnifRand(0, 9_IK)
362degree
363+8
364coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
365coef
366(+4.00000000, +8.00000000), (-6.00000000, +8.00000000), (+1.00000000, -8.00000000), (-5.00000000, +3.00000000), (+3.00000000, +2.00000000), (+5.00000000, -8.00000000), (+9.00000000, +2.00000000), (-7.00000000, +2.00000000)
367getPolyStr(coef)
368(4.,8.)x^0 + (-6.,8.)x^1 + (1.,-8.)x^2 + (-5.,3.)x^3 + (3.,2.)x^4 + (5.,-8.)x^5 + (9.,2.)x^6 + (-7.,2.)x^7
369order = getUnifRand(0, size(coef) + 1)
370order
371+1
372
373diff = getPolyDiff(coef, order)
374diff ! derivative coefficients.
375(-6.00000000, +8.00000000), (+2.00000000, -16.0000000), (-15.0000000, +9.00000000), (+12.0000000, +8.00000000), (+25.0000000, -40.0000000), (+54.0000000, +12.0000000), (-49.0000000, +14.0000000)
376getPolyStr(diff)
377(-6.,8.)x^0 + (2.,-16.)x^1 + (-15.,9.)x^2 + (12.,8.)x^3 + (25.,-40.)x^4 + (54.,12.)x^5 + (-49.,14.)x^6
378
379degree = getUnifRand(0, 9_IK)
380degree
381+8
382coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
383coef
384(+3.00000000, +0.00000000), (-8.00000000, -5.00000000), (-1.00000000, -5.00000000), (+4.00000000, -4.00000000), (-4.00000000, -3.00000000), (+9.00000000, +9.00000000), (+7.00000000, -2.00000000), (+7.00000000, -7.00000000)
385getPolyStr(coef)
386(3.,0.)x^0 + (-8.,-5.)x^1 + (-1.,-5.)x^2 + (4.,-4.)x^3 + (-4.,-3.)x^4 + (9.,9.)x^5 + (7.,-2.)x^6 + (7.,-7.)x^7
387order = getUnifRand(0, size(coef) + 1)
388order
389+6
390
391diff = getPolyDiff(coef, order)
392diff ! derivative coefficients.
393(+42.0000000, -12.0000000), (+49.0000000, -49.0000000)
394getPolyStr(diff)
395(42.,-12.)x^0 + (49.,-49.)x^1
396
397degree = getUnifRand(0, 9_IK)
398degree
399+0
400coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
401coef
402
403getPolyStr(coef)
404
405order = getUnifRand(0, size(coef) + 1)
406order
407+1
408
409diff = getPolyDiff(coef, order)
410diff ! derivative coefficients.
411
412getPolyStr(diff)
413
414
415degree = getUnifRand(0, 9_IK)
416degree
417+9
418coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
419coef
420(+0.00000000, -4.00000000), (+4.00000000, +6.00000000), (+4.00000000, -5.00000000), (-8.00000000, +2.00000000), (-3.00000000, +5.00000000), (-5.00000000, +5.00000000), (-2.00000000, -3.00000000), (-3.00000000, -4.00000000), (-3.00000000, +7.00000000)
421getPolyStr(coef)
422(0.,-4.)x^0 + (4.,6.)x^1 + (4.,-5.)x^2 + (-8.,2.)x^3 + (-3.,5.)x^4 + (-5.,5.)x^5 + (-2.,-3.)x^6 + (-3.,-4.)x^7 + (-3.,7.)x^8
423order = getUnifRand(0, size(coef) + 1)
424order
425+7
426
427diff = getPolyDiff(coef, order)
428diff ! derivative coefficients.
429(-21.0000000, -28.0000000), (-24.0000000, +56.0000000)
430getPolyStr(diff)
431(-21.,-28.)x^0 + (-24.,56.)x^1
432
433degree = getUnifRand(0, 9_IK)
434degree
435+0
436coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
437coef
438
439getPolyStr(coef)
440
441order = getUnifRand(0, size(coef) + 1)
442order
443+1
444
445diff = getPolyDiff(coef, order)
446diff ! derivative coefficients.
447
448getPolyStr(diff)
449
450
451degree = getUnifRand(0, 9_IK)
452degree
453+4
454coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
455coef
456(-7.00000000, +0.00000000), (-7.00000000, -8.00000000), (+5.00000000, +2.00000000), (-2.00000000, +3.00000000)
457getPolyStr(coef)
458(-7.,0.)x^0 + (-7.,-8.)x^1 + (5.,2.)x^2 + (-2.,3.)x^3
459order = getUnifRand(0, size(coef) + 1)
460order
461+3
462
463diff = getPolyDiff(coef, order)
464diff ! derivative coefficients.
465(-6.00000000, +9.00000000)
466getPolyStr(diff)
467(-6.,9.)x^0
468
469degree = getUnifRand(0, 9_IK)
470degree
471+9
472coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
473coef
474(+0.00000000, +2.00000000), (-8.00000000, +1.00000000), (-9.00000000, +2.00000000), (-3.00000000, -7.00000000), (+9.00000000, -3.00000000), (+3.00000000, -8.00000000), (+5.00000000, +9.00000000), (-1.00000000, +1.00000000), (-9.00000000, +5.00000000)
475getPolyStr(coef)
476(0.,2.)x^0 + (-8.,1.)x^1 + (-9.,2.)x^2 + (-3.,-7.)x^3 + (9.,-3.)x^4 + (3.,-8.)x^5 + (5.,9.)x^6 + (-1.,1.)x^7 + (-9.,5.)x^8
477order = getUnifRand(0, size(coef) + 1)
478order
479+10
480
481diff = getPolyDiff(coef, order)
482diff ! derivative coefficients.
483
484getPolyStr(diff)
485
486
487degree = getUnifRand(0, 9_IK)
488degree
489+9
490coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
491coef
492(-3.00000000, -6.00000000), (+1.00000000, +3.00000000), (+3.00000000, +4.00000000), (+1.00000000, +9.00000000), (-5.00000000, -1.00000000), (-4.00000000, -5.00000000), (-6.00000000, +0.00000000), (-7.00000000, -1.00000000), (-7.00000000, -3.00000000)
493getPolyStr(coef)
494(-3.,-6.)x^0 + (1.,3.)x^1 + (3.,4.)x^2 + (1.,9.)x^3 + (-5.,-1.)x^4 + (-4.,-5.)x^5 + (-6.,0.)x^6 + (-7.,-1.)x^7 + (-7.,-3.)x^8
495order = getUnifRand(0, size(coef) + 1)
496order
497+2
498
499diff = getPolyDiff(coef, order)
500diff ! derivative coefficients.
501(+6.00000000, +8.00000000), (+3.00000000, +27.0000000), (-20.0000000, -4.00000000), (-20.0000000, -25.0000000), (-36.0000000, +0.00000000), (-49.0000000, -7.00000000), (-56.0000000, -24.0000000)
502getPolyStr(diff)
503(6.,8.)x^0 + (3.,27.)x^1 + (-20.,-4.)x^2 + (-20.,-25.)x^3 + (-36.,0.)x^4 + (-49.,-7.)x^5 + (-56.,-24.)x^6
504
505degree = getUnifRand(0, 9_IK)
506degree
507+2
508coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
509coef
510(-5.00000000, +0.00000000), (-1.00000000, -8.00000000)
511getPolyStr(coef)
512(-5.,0.)x^0 + (-1.,-8.)x^1
513order = getUnifRand(0, size(coef) + 1)
514order
515+2
516
517diff = getPolyDiff(coef, order)
518diff ! derivative coefficients.
519
520getPolyStr(diff)
521
522
523degree = getUnifRand(0, 9_IK)
524degree
525+4
526coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
527coef
528(+5.00000000, -8.00000000), (-1.00000000, -7.00000000), (+5.00000000, +9.00000000), (-9.00000000, -8.00000000)
529getPolyStr(coef)
530(5.,-8.)x^0 + (-1.,-7.)x^1 + (5.,9.)x^2 + (-9.,-8.)x^3
531order = getUnifRand(0, size(coef) + 1)
532order
533+1
534
535diff = getPolyDiff(coef, order)
536diff ! derivative coefficients.
537(-1.00000000, -7.00000000), (+10.0000000, +18.0000000), (-27.0000000, -24.0000000)
538getPolyStr(diff)
539(-1.,-7.)x^0 + (10.,18.)x^1 + (-27.,-24.)x^2
540
541degree = getUnifRand(0, 9_IK)
542degree
543+2
544coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
545coef
546(+4.00000000, +0.00000000), (+6.00000000, +8.00000000)
547getPolyStr(coef)
548(4.,0.)x^0 + (6.,8.)x^1
549order = getUnifRand(0, size(coef) + 1)
550order
551+3
552
553diff = getPolyDiff(coef, order)
554diff ! derivative coefficients.
555
556getPolyStr(diff)
557
558
559degree = getUnifRand(0, 9_IK)
560degree
561+0
562coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
563coef
564
565getPolyStr(coef)
566
567order = getUnifRand(0, size(coef) + 1)
568order
569+0
570
571diff = getPolyDiff(coef, order)
572diff ! derivative coefficients.
573
574getPolyStr(diff)
575
576
577degree = getUnifRand(0, 9_IK)
578degree
579+1
580coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
581coef
582(-8.00000000, -5.00000000)
583getPolyStr(coef)
584(-8.,-5.)x^0
585order = getUnifRand(0, size(coef) + 1)
586order
587+1
588
589diff = getPolyDiff(coef, order)
590diff ! derivative coefficients.
591
592getPolyStr(diff)
593
594
595degree = getUnifRand(0, 9_IK)
596degree
597+1
598coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
599coef
600(-6.00000000, +6.00000000)
601getPolyStr(coef)
602(-6.,6.)x^0
603order = getUnifRand(0, size(coef) + 1)
604order
605+1
606
607diff = getPolyDiff(coef, order)
608diff ! derivative coefficients.
609
610getPolyStr(diff)
611
612
613degree = getUnifRand(0, 9_IK)
614degree
615+5
616coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
617coef
618(+8.00000000, -6.00000000), (+0.00000000, +0.00000000), (-8.00000000, -8.00000000), (-7.00000000, -3.00000000), (+2.00000000, -9.00000000)
619getPolyStr(coef)
620(8.,-6.)x^0 + (0.,0.)x^1 + (-8.,-8.)x^2 + (-7.,-3.)x^3 + (2.,-9.)x^4
621order = getUnifRand(0, size(coef) + 1)
622order
623+5
624
625diff = getPolyDiff(coef, order)
626diff ! derivative coefficients.
627
628getPolyStr(diff)
629
630
631degree = getUnifRand(0, 9_IK)
632degree
633+0
634coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
635coef
636
637getPolyStr(coef)
638
639order = getUnifRand(0, size(coef) + 1)
640order
641+1
642
643diff = getPolyDiff(coef, order)
644diff ! derivative coefficients.
645
646getPolyStr(diff)
647
648
649degree = getUnifRand(0, 9_IK)
650degree
651+0
652coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
653coef
654
655getPolyStr(coef)
656
657order = getUnifRand(0, size(coef) + 1)
658order
659+1
660
661diff = getPolyDiff(coef, order)
662diff ! derivative coefficients.
663
664getPolyStr(diff)
665
666
667degree = getUnifRand(0, 9_IK)
668degree
669+0
670coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
671coef
672
673getPolyStr(coef)
674
675order = getUnifRand(0, size(coef) + 1)
676order
677+0
678
679diff = getPolyDiff(coef, order)
680diff ! derivative coefficients.
681
682getPolyStr(diff)
683
684
685degree = getUnifRand(0, 9_IK)
686degree
687+5
688coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
689coef
690(+3.00000000, -3.00000000), (-4.00000000, +5.00000000), (-4.00000000, +7.00000000), (+6.00000000, -4.00000000), (+4.00000000, +8.00000000)
691getPolyStr(coef)
692(3.,-3.)x^0 + (-4.,5.)x^1 + (-4.,7.)x^2 + (6.,-4.)x^3 + (4.,8.)x^4
693order = getUnifRand(0, size(coef) + 1)
694order
695+4
696
697diff = getPolyDiff(coef, order)
698diff ! derivative coefficients.
699(+16.0000000, +32.0000000)
700getPolyStr(diff)
701(16.,32.)x^0
702
703degree = getUnifRand(0, 9_IK)
704degree
705+4
706coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
707coef
708(-6.00000000, -2.00000000), (+1.00000000, +5.00000000), (-8.00000000, -5.00000000), (-9.00000000, -1.00000000)
709getPolyStr(coef)
710(-6.,-2.)x^0 + (1.,5.)x^1 + (-8.,-5.)x^2 + (-9.,-1.)x^3
711order = getUnifRand(0, size(coef) + 1)
712order
713+1
714
715diff = getPolyDiff(coef, order)
716diff ! derivative coefficients.
717(+1.00000000, +5.00000000), (-16.0000000, -10.0000000), (-27.0000000, -3.00000000)
718getPolyStr(diff)
719(1.,5.)x^0 + (-16.,-10.)x^1 + (-27.,-3.)x^2
720
721
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.
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For details on the naming conventions, see this page.
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Copyright
Computational Data Science Lab
Author:
Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 2415 of file pm_polynomial.F90.

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