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+7
4coef = getUnifRand(-9, 9, degree)
5coef
6-9.00000000, +1.00000000, +2.00000000, -1.00000000, +0.00000000, +3.00000000, -2.00000000
7getPolyStr(coef)
8-9.x^0 + 1.x^1 + 2.x^2 - 1.x^3 + 0.x^4 + 3.x^5 - 2.x^6
9order = getUnifRand(0, size(coef) + 1)
10order
11+5
12
13diff = getPolyDiff(coef, order)
14diff ! derivative coefficients.
15+15.0000000, -12.0000000
16getPolyStr(diff)
1715.x^0 - 12.x^1
18
19degree = getUnifRand(0, 9_IK)
20degree
21+1
22coef = getUnifRand(-9, 9, degree)
23coef
24-1.00000000
25getPolyStr(coef)
26-1.x^0
27order = getUnifRand(0, size(coef) + 1)
28order
29+0
30
31diff = getPolyDiff(coef, order)
32diff ! derivative coefficients.
33-1.00000000
34getPolyStr(diff)
35-1.x^0
36
37degree = getUnifRand(0, 9_IK)
38degree
39+1
40coef = getUnifRand(-9, 9, degree)
41coef
42+5.00000000
43getPolyStr(coef)
445.x^0
45order = getUnifRand(0, size(coef) + 1)
46order
47+0
48
49diff = getPolyDiff(coef, order)
50diff ! derivative coefficients.
51+5.00000000
52getPolyStr(diff)
535.x^0
54
55degree = getUnifRand(0, 9_IK)
56degree
57+2
58coef = getUnifRand(-9, 9, degree)
59coef
60-9.00000000, -5.00000000
61getPolyStr(coef)
62-9.x^0 - 5.x^1
63order = getUnifRand(0, size(coef) + 1)
64order
65+1
66
67diff = getPolyDiff(coef, order)
68diff ! derivative coefficients.
69-5.00000000
70getPolyStr(diff)
71-5.x^0
72
73degree = getUnifRand(0, 9_IK)
74degree
75+7
76coef = getUnifRand(-9, 9, degree)
77coef
78-4.00000000, -3.00000000, +5.00000000, -9.00000000, -7.00000000, +7.00000000, -3.00000000
79getPolyStr(coef)
80-4.x^0 - 3.x^1 + 5.x^2 - 9.x^3 - 7.x^4 + 7.x^5 - 3.x^6
81order = getUnifRand(0, size(coef) + 1)
82order
83+8
84
85diff = getPolyDiff(coef, order)
86diff ! derivative coefficients.
87
88getPolyStr(diff)
89
90
91degree = getUnifRand(0, 9_IK)
92degree
93+5
94coef = getUnifRand(-9, 9, degree)
95coef
96-1.00000000, -6.00000000, +8.00000000, +6.00000000, +6.00000000
97getPolyStr(coef)
98-1.x^0 - 6.x^1 + 8.x^2 + 6.x^3 + 6.x^4
99order = getUnifRand(0, size(coef) + 1)
100order
101+6
102
103diff = getPolyDiff(coef, order)
104diff ! derivative coefficients.
105
106getPolyStr(diff)
107
108
109degree = getUnifRand(0, 9_IK)
110degree
111+4
112coef = getUnifRand(-9, 9, degree)
113coef
114+1.00000000, +4.00000000, -3.00000000, +9.00000000
115getPolyStr(coef)
1161.x^0 + 4.x^1 - 3.x^2 + 9.x^3
117order = getUnifRand(0, size(coef) + 1)
118order
119+5
120
121diff = getPolyDiff(coef, order)
122diff ! derivative coefficients.
123
124getPolyStr(diff)
125
126
127degree = getUnifRand(0, 9_IK)
128degree
129+8
130coef = getUnifRand(-9, 9, degree)
131coef
132+4.00000000, -2.00000000, +1.00000000, +4.00000000, +3.00000000, -5.00000000, +6.00000000, +0.00000000
133getPolyStr(coef)
1344.x^0 - 2.x^1 + 1.x^2 + 4.x^3 + 3.x^4 - 5.x^5 + 6.x^6 + 0.x^7
135order = getUnifRand(0, size(coef) + 1)
136order
137+6
138
139diff = getPolyDiff(coef, order)
140diff ! derivative coefficients.
141+36.0000000, +0.00000000
142getPolyStr(diff)
14336.x^0 + 0.x^1
144
145degree = getUnifRand(0, 9_IK)
146degree
147+4
148coef = getUnifRand(-9, 9, degree)
149coef
150-2.00000000, -4.00000000, -9.00000000, +5.00000000
151getPolyStr(coef)
152-2.x^0 - 4.x^1 - 9.x^2 + 5.x^3
153order = getUnifRand(0, size(coef) + 1)
154order
155+1
156
157diff = getPolyDiff(coef, order)
158diff ! derivative coefficients.
159-4.00000000, -18.0000000, +15.0000000
160getPolyStr(diff)
161-4.x^0 - 18.x^1 + 15.x^2
162
163degree = getUnifRand(0, 9_IK)
164degree
165+0
166coef = getUnifRand(-9, 9, degree)
167coef
168
169getPolyStr(coef)
170
171order = getUnifRand(0, size(coef) + 1)
172order
173+0
174
175diff = getPolyDiff(coef, order)
176diff ! derivative coefficients.
177
178getPolyStr(diff)
179
180
181degree = getUnifRand(0, 9_IK)
182degree
183+9
184coef = getUnifRand(-9, 9, degree)
185coef
186-1.00000000, +3.00000000, -6.00000000, -1.00000000, -6.00000000, -8.00000000, +0.00000000, -7.00000000, -3.00000000
187getPolyStr(coef)
188-1.x^0 + 3.x^1 - 6.x^2 - 1.x^3 - 6.x^4 - 8.x^5 + 0.x^6 - 7.x^7 - 3.x^8
189order = getUnifRand(0, size(coef) + 1)
190order
191+4
192
193diff = getPolyDiff(coef, order)
194diff ! derivative coefficients.
195-24.0000000, -40.0000000, +0.00000000, -49.0000000, -24.0000000
196getPolyStr(diff)
197-24.x^0 - 40.x^1 + 0.x^2 - 49.x^3 - 24.x^4
198
199degree = getUnifRand(0, 9_IK)
200degree
201+1
202coef = getUnifRand(-9, 9, degree)
203coef
204+1.00000000
205getPolyStr(coef)
2061.x^0
207order = getUnifRand(0, size(coef) + 1)
208order
209+2
210
211diff = getPolyDiff(coef, order)
212diff ! derivative coefficients.
213
214getPolyStr(diff)
215
216
217degree = getUnifRand(0, 9_IK)
218degree
219+5
220coef = getUnifRand(-9, 9, degree)
221coef
222-8.00000000, -7.00000000, -9.00000000, +4.00000000, +9.00000000
223getPolyStr(coef)
224-8.x^0 - 7.x^1 - 9.x^2 + 4.x^3 + 9.x^4
225order = getUnifRand(0, size(coef) + 1)
226order
227+5
228
229diff = getPolyDiff(coef, order)
230diff ! derivative coefficients.
231
232getPolyStr(diff)
233
234
235degree = getUnifRand(0, 9_IK)
236degree
237+3
238coef = getUnifRand(-9, 9, degree)
239coef
240-8.00000000, -9.00000000, -4.00000000
241getPolyStr(coef)
242-8.x^0 - 9.x^1 - 4.x^2
243order = getUnifRand(0, size(coef) + 1)
244order
245+2
246
247diff = getPolyDiff(coef, order)
248diff ! derivative coefficients.
249-8.00000000
250getPolyStr(diff)
251-8.x^0
252
253degree = getUnifRand(0, 9_IK)
254degree
255+5
256coef = getUnifRand(-9, 9, degree)
257coef
258+8.00000000, +6.00000000, +2.00000000, +7.00000000, +4.00000000
259getPolyStr(coef)
2608.x^0 + 6.x^1 + 2.x^2 + 7.x^3 + 4.x^4
261order = getUnifRand(0, size(coef) + 1)
262order
263+0
264
265diff = getPolyDiff(coef, order)
266diff ! derivative coefficients.
267+8.00000000, +6.00000000, +2.00000000, +7.00000000, +4.00000000
268getPolyStr(diff)
2698.x^0 + 6.x^1 + 2.x^2 + 7.x^3 + 4.x^4
270
271degree = getUnifRand(0, 9_IK)
272degree
273+1
274coef = getUnifRand(-9, 9, degree)
275coef
276+3.00000000
277getPolyStr(coef)
2783.x^0
279order = getUnifRand(0, size(coef) + 1)
280order
281+2
282
283diff = getPolyDiff(coef, order)
284diff ! derivative coefficients.
285
286getPolyStr(diff)
287
288
289degree = getUnifRand(0, 9_IK)
290degree
291+8
292coef = getUnifRand(-9, 9, degree)
293coef
294+7.00000000, +0.00000000, +0.00000000, +5.00000000, -8.00000000, +7.00000000, +2.00000000, -9.00000000
295getPolyStr(coef)
2967.x^0 + 0.x^1 + 0.x^2 + 5.x^3 - 8.x^4 + 7.x^5 + 2.x^6 - 9.x^7
297order = getUnifRand(0, size(coef) + 1)
298order
299+5
300
301diff = getPolyDiff(coef, order)
302diff ! derivative coefficients.
303+35.0000000, +12.0000000, -63.0000000
304getPolyStr(diff)
30535.x^0 + 12.x^1 - 63.x^2
306
307degree = getUnifRand(0, 9_IK)
308degree
309+8
310coef = getUnifRand(-9, 9, degree)
311coef
312+2.00000000, -7.00000000, +8.00000000, -3.00000000, -3.00000000, +3.00000000, +4.00000000, +6.00000000
313getPolyStr(coef)
3142.x^0 - 7.x^1 + 8.x^2 - 3.x^3 - 3.x^4 + 3.x^5 + 4.x^6 + 6.x^7
315order = getUnifRand(0, size(coef) + 1)
316order
317+0
318
319diff = getPolyDiff(coef, order)
320diff ! derivative coefficients.
321+2.00000000, -7.00000000, +8.00000000, -3.00000000, -3.00000000, +3.00000000, +4.00000000, +6.00000000
322getPolyStr(diff)
3232.x^0 - 7.x^1 + 8.x^2 - 3.x^3 - 3.x^4 + 3.x^5 + 4.x^6 + 6.x^7
324
325degree = getUnifRand(0, 9_IK)
326degree
327+6
328coef = getUnifRand(-9, 9, degree)
329coef
330+5.00000000, +1.00000000, -7.00000000, +3.00000000, -6.00000000, -7.00000000
331getPolyStr(coef)
3325.x^0 + 1.x^1 - 7.x^2 + 3.x^3 - 6.x^4 - 7.x^5
333order = getUnifRand(0, size(coef) + 1)
334order
335+1
336
337diff = getPolyDiff(coef, order)
338diff ! derivative coefficients.
339+1.00000000, -14.0000000, +9.00000000, -24.0000000, -35.0000000
340getPolyStr(diff)
3411.x^0 - 14.x^1 + 9.x^2 - 24.x^3 - 35.x^4
342
343degree = getUnifRand(0, 9_IK)
344degree
345+1
346coef = getUnifRand(-9, 9, degree)
347coef
348+7.00000000
349getPolyStr(coef)
3507.x^0
351order = getUnifRand(0, size(coef) + 1)
352order
353+1
354
355diff = getPolyDiff(coef, order)
356diff ! derivative coefficients.
357
358getPolyStr(diff)
359
360
361degree = getUnifRand(0, 9_IK)
362degree
363+3
364coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
365coef
366(+7.00000000, -9.00000000), (+9.00000000, +5.00000000), (-2.00000000, +9.00000000)
367getPolyStr(coef)
368(7.,-9.)x^0 + (9.,5.)x^1 + (-2.,9.)x^2
369order = getUnifRand(0, size(coef) + 1)
370order
371+4
372
373diff = getPolyDiff(coef, order)
374diff ! derivative coefficients.
375
376getPolyStr(diff)
377
378
379degree = getUnifRand(0, 9_IK)
380degree
381+5
382coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
383coef
384(+3.00000000, +7.00000000), (+7.00000000, +2.00000000), (-7.00000000, -3.00000000), (-9.00000000, -5.00000000), (+1.00000000, +0.00000000)
385getPolyStr(coef)
386(3.,7.)x^0 + (7.,2.)x^1 + (-7.,-3.)x^2 + (-9.,-5.)x^3 + (1.,0.)x^4
387order = getUnifRand(0, size(coef) + 1)
388order
389+1
390
391diff = getPolyDiff(coef, order)
392diff ! derivative coefficients.
393(+7.00000000, +2.00000000), (-14.0000000, -6.00000000), (-27.0000000, -15.0000000), (+4.00000000, +0.00000000)
394getPolyStr(diff)
395(7.,2.)x^0 + (-14.,-6.)x^1 + (-27.,-15.)x^2 + (4.,0.)x^3
396
397degree = getUnifRand(0, 9_IK)
398degree
399+9
400coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
401coef
402(+0.00000000, +4.00000000), (+8.00000000, -8.00000000), (+3.00000000, -2.00000000), (-3.00000000, -2.00000000), (+7.00000000, +7.00000000), (+7.00000000, -9.00000000), (+9.00000000, -7.00000000), (+2.00000000, -1.00000000), (+7.00000000, +9.00000000)
403getPolyStr(coef)
404(0.,4.)x^0 + (8.,-8.)x^1 + (3.,-2.)x^2 + (-3.,-2.)x^3 + (7.,7.)x^4 + (7.,-9.)x^5 + (9.,-7.)x^6 + (2.,-1.)x^7 + (7.,9.)x^8
405order = getUnifRand(0, size(coef) + 1)
406order
407+3
408
409diff = getPolyDiff(coef, order)
410diff ! derivative coefficients.
411(-9.00000000, -6.00000000), (+28.0000000, +28.0000000), (+35.0000000, -45.0000000), (+54.0000000, -42.0000000), (+14.0000000, -7.00000000), (+56.0000000, +72.0000000)
412getPolyStr(diff)
413(-9.,-6.)x^0 + (28.,28.)x^1 + (35.,-45.)x^2 + (54.,-42.)x^3 + (14.,-7.)x^4 + (56.,72.)x^5
414
415degree = getUnifRand(0, 9_IK)
416degree
417+4
418coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
419coef
420(+3.00000000, -1.00000000), (+0.00000000, +4.00000000), (-3.00000000, +2.00000000), (-9.00000000, +4.00000000)
421getPolyStr(coef)
422(3.,-1.)x^0 + (0.,4.)x^1 + (-3.,2.)x^2 + (-9.,4.)x^3
423order = getUnifRand(0, size(coef) + 1)
424order
425+3
426
427diff = getPolyDiff(coef, order)
428diff ! derivative coefficients.
429(-27.0000000, +12.0000000)
430getPolyStr(diff)
431(-27.,12.)x^0
432
433degree = getUnifRand(0, 9_IK)
434degree
435+7
436coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
437coef
438(+6.00000000, +7.00000000), (+6.00000000, +6.00000000), (-2.00000000, -5.00000000), (-2.00000000, +1.00000000), (-4.00000000, -5.00000000), (+1.00000000, +4.00000000), (-3.00000000, -6.00000000)
439getPolyStr(coef)
440(6.,7.)x^0 + (6.,6.)x^1 + (-2.,-5.)x^2 + (-2.,1.)x^3 + (-4.,-5.)x^4 + (1.,4.)x^5 + (-3.,-6.)x^6
441order = getUnifRand(0, size(coef) + 1)
442order
443+7
444
445diff = getPolyDiff(coef, order)
446diff ! derivative coefficients.
447
448getPolyStr(diff)
449
450
451degree = getUnifRand(0, 9_IK)
452degree
453+9
454coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
455coef
456(+6.00000000, +5.00000000), (-2.00000000, +5.00000000), (+4.00000000, -7.00000000), (+7.00000000, +8.00000000), (+0.00000000, -8.00000000), (+6.00000000, -2.00000000), (-3.00000000, -9.00000000), (-9.00000000, -4.00000000), (-4.00000000, -3.00000000)
457getPolyStr(coef)
458(6.,5.)x^0 + (-2.,5.)x^1 + (4.,-7.)x^2 + (7.,8.)x^3 + (0.,-8.)x^4 + (6.,-2.)x^5 + (-3.,-9.)x^6 + (-9.,-4.)x^7 + (-4.,-3.)x^8
459order = getUnifRand(0, size(coef) + 1)
460order
461+1
462
463diff = getPolyDiff(coef, order)
464diff ! derivative coefficients.
465(-2.00000000, +5.00000000), (+8.00000000, -14.0000000), (+21.0000000, +24.0000000), (+0.00000000, -32.0000000), (+30.0000000, -10.0000000), (-18.0000000, -54.0000000), (-63.0000000, -28.0000000), (-32.0000000, -24.0000000)
466getPolyStr(diff)
467(-2.,5.)x^0 + (8.,-14.)x^1 + (21.,24.)x^2 + (0.,-32.)x^3 + (30.,-10.)x^4 + (-18.,-54.)x^5 + (-63.,-28.)x^6 + (-32.,-24.)x^7
468
469degree = getUnifRand(0, 9_IK)
470degree
471+9
472coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
473coef
474(+3.00000000, -8.00000000), (-2.00000000, +1.00000000), (-5.00000000, +5.00000000), (+1.00000000, -1.00000000), (+2.00000000, -9.00000000), (+6.00000000, +0.00000000), (-2.00000000, -3.00000000), (+6.00000000, -7.00000000), (+6.00000000, +5.00000000)
475getPolyStr(coef)
476(3.,-8.)x^0 + (-2.,1.)x^1 + (-5.,5.)x^2 + (1.,-1.)x^3 + (2.,-9.)x^4 + (6.,0.)x^5 + (-2.,-3.)x^6 + (6.,-7.)x^7 + (6.,5.)x^8
477order = getUnifRand(0, size(coef) + 1)
478order
479+2
480
481diff = getPolyDiff(coef, order)
482diff ! derivative coefficients.
483(-10.0000000, +10.0000000), (+3.00000000, -3.00000000), (+8.00000000, -36.0000000), (+30.0000000, +0.00000000), (-12.0000000, -18.0000000), (+42.0000000, -49.0000000), (+48.0000000, +40.0000000)
484getPolyStr(diff)
485(-10.,10.)x^0 + (3.,-3.)x^1 + (8.,-36.)x^2 + (30.,0.)x^3 + (-12.,-18.)x^4 + (42.,-49.)x^5 + (48.,40.)x^6
486
487degree = getUnifRand(0, 9_IK)
488degree
489+5
490coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
491coef
492(+3.00000000, +1.00000000), (-7.00000000, +4.00000000), (-1.00000000, +2.00000000), (+3.00000000, -1.00000000), (+2.00000000, +8.00000000)
493getPolyStr(coef)
494(3.,1.)x^0 + (-7.,4.)x^1 + (-1.,2.)x^2 + (3.,-1.)x^3 + (2.,8.)x^4
495order = getUnifRand(0, size(coef) + 1)
496order
497+2
498
499diff = getPolyDiff(coef, order)
500diff ! derivative coefficients.
501(-2.00000000, +4.00000000), (+9.00000000, -3.00000000), (+8.00000000, +32.0000000)
502getPolyStr(diff)
503(-2.,4.)x^0 + (9.,-3.)x^1 + (8.,32.)x^2
504
505degree = getUnifRand(0, 9_IK)
506degree
507+5
508coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
509coef
510(+7.00000000, +4.00000000), (+2.00000000, -8.00000000), (+0.00000000, +5.00000000), (+6.00000000, +2.00000000), (-4.00000000, -6.00000000)
511getPolyStr(coef)
512(7.,4.)x^0 + (2.,-8.)x^1 + (0.,5.)x^2 + (6.,2.)x^3 + (-4.,-6.)x^4
513order = getUnifRand(0, size(coef) + 1)
514order
515+1
516
517diff = getPolyDiff(coef, order)
518diff ! derivative coefficients.
519(+2.00000000, -8.00000000), (+0.00000000, +10.0000000), (+18.0000000, +6.00000000), (-16.0000000, -24.0000000)
520getPolyStr(diff)
521(2.,-8.)x^0 + (0.,10.)x^1 + (18.,6.)x^2 + (-16.,-24.)x^3
522
523degree = getUnifRand(0, 9_IK)
524degree
525+4
526coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
527coef
528(-6.00000000, +8.00000000), (-9.00000000, +5.00000000), (+6.00000000, +4.00000000), (+5.00000000, -1.00000000)
529getPolyStr(coef)
530(-6.,8.)x^0 + (-9.,5.)x^1 + (6.,4.)x^2 + (5.,-1.)x^3
531order = getUnifRand(0, size(coef) + 1)
532order
533+2
534
535diff = getPolyDiff(coef, order)
536diff ! derivative coefficients.
537(+12.0000000, +8.00000000), (+15.0000000, -3.00000000)
538getPolyStr(diff)
539(12.,8.)x^0 + (15.,-3.)x^1
540
541degree = getUnifRand(0, 9_IK)
542degree
543+2
544coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
545coef
546(-3.00000000, +1.00000000), (+5.00000000, +8.00000000)
547getPolyStr(coef)
548(-3.,1.)x^0 + (5.,8.)x^1
549order = getUnifRand(0, size(coef) + 1)
550order
551+0
552
553diff = getPolyDiff(coef, order)
554diff ! derivative coefficients.
555(-3.00000000, +1.00000000), (+5.00000000, +8.00000000)
556getPolyStr(diff)
557(-3.,1.)x^0 + (5.,8.)x^1
558
559degree = getUnifRand(0, 9_IK)
560degree
561+8
562coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
563coef
564(+0.00000000, +8.00000000), (-4.00000000, -8.00000000), (+0.00000000, -8.00000000), (-3.00000000, +4.00000000), (-2.00000000, -2.00000000), (+1.00000000, +9.00000000), (-8.00000000, +5.00000000), (+5.00000000, +1.00000000)
565getPolyStr(coef)
566(0.,8.)x^0 + (-4.,-8.)x^1 + (0.,-8.)x^2 + (-3.,4.)x^3 + (-2.,-2.)x^4 + (1.,9.)x^5 + (-8.,5.)x^6 + (5.,1.)x^7
567order = getUnifRand(0, size(coef) + 1)
568order
569+0
570
571diff = getPolyDiff(coef, order)
572diff ! derivative coefficients.
573(+0.00000000, +8.00000000), (-4.00000000, -8.00000000), (+0.00000000, -8.00000000), (-3.00000000, +4.00000000), (-2.00000000, -2.00000000), (+1.00000000, +9.00000000), (-8.00000000, +5.00000000), (+5.00000000, +1.00000000)
574getPolyStr(diff)
575(0.,8.)x^0 + (-4.,-8.)x^1 + (0.,-8.)x^2 + (-3.,4.)x^3 + (-2.,-2.)x^4 + (1.,9.)x^5 + (-8.,5.)x^6 + (5.,1.)x^7
576
577degree = getUnifRand(0, 9_IK)
578degree
579+3
580coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
581coef
582(-8.00000000, +5.00000000), (-2.00000000, -7.00000000), (-4.00000000, +0.00000000)
583getPolyStr(coef)
584(-8.,5.)x^0 + (-2.,-7.)x^1 + (-4.,0.)x^2
585order = getUnifRand(0, size(coef) + 1)
586order
587+4
588
589diff = getPolyDiff(coef, order)
590diff ! derivative coefficients.
591
592getPolyStr(diff)
593
594
595degree = getUnifRand(0, 9_IK)
596degree
597+2
598coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
599coef
600(-9.00000000, -7.00000000), (+0.00000000, +6.00000000)
601getPolyStr(coef)
602(-9.,-7.)x^0 + (0.,6.)x^1
603order = getUnifRand(0, size(coef) + 1)
604order
605+0
606
607diff = getPolyDiff(coef, order)
608diff ! derivative coefficients.
609(-9.00000000, -7.00000000), (+0.00000000, +6.00000000)
610getPolyStr(diff)
611(-9.,-7.)x^0 + (0.,6.)x^1
612
613degree = getUnifRand(0, 9_IK)
614degree
615+0
616coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
617coef
618
619getPolyStr(coef)
620
621order = getUnifRand(0, size(coef) + 1)
622order
623+1
624
625diff = getPolyDiff(coef, order)
626diff ! derivative coefficients.
627
628getPolyStr(diff)
629
630
631degree = getUnifRand(0, 9_IK)
632degree
633+9
634coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
635coef
636(+9.00000000, +1.00000000), (+7.00000000, +3.00000000), (+1.00000000, -8.00000000), (+7.00000000, -1.00000000), (+6.00000000, -7.00000000), (+7.00000000, -6.00000000), (-5.00000000, -4.00000000), (-3.00000000, +5.00000000), (-1.00000000, +0.00000000)
637getPolyStr(coef)
638(9.,1.)x^0 + (7.,3.)x^1 + (1.,-8.)x^2 + (7.,-1.)x^3 + (6.,-7.)x^4 + (7.,-6.)x^5 + (-5.,-4.)x^6 + (-3.,5.)x^7 + (-1.,0.)x^8
639order = getUnifRand(0, size(coef) + 1)
640order
641+3
642
643diff = getPolyDiff(coef, order)
644diff ! derivative coefficients.
645(+21.0000000, -3.00000000), (+24.0000000, -28.0000000), (+35.0000000, -30.0000000), (-30.0000000, -24.0000000), (-21.0000000, +35.0000000), (-8.00000000, +0.00000000)
646getPolyStr(diff)
647(21.,-3.)x^0 + (24.,-28.)x^1 + (35.,-30.)x^2 + (-30.,-24.)x^3 + (-21.,35.)x^4 + (-8.,0.)x^5
648
649degree = getUnifRand(0, 9_IK)
650degree
651+4
652coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
653coef
654(+1.00000000, -2.00000000), (-8.00000000, +5.00000000), (-3.00000000, +1.00000000), (-7.00000000, -3.00000000)
655getPolyStr(coef)
656(1.,-2.)x^0 + (-8.,5.)x^1 + (-3.,1.)x^2 + (-7.,-3.)x^3
657order = getUnifRand(0, size(coef) + 1)
658order
659+0
660
661diff = getPolyDiff(coef, order)
662diff ! derivative coefficients.
663(+1.00000000, -2.00000000), (-8.00000000, +5.00000000), (-3.00000000, +1.00000000), (-7.00000000, -3.00000000)
664getPolyStr(diff)
665(1.,-2.)x^0 + (-8.,5.)x^1 + (-3.,1.)x^2 + (-7.,-3.)x^3
666
667degree = getUnifRand(0, 9_IK)
668degree
669+4
670coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
671coef
672(+6.00000000, +5.00000000), (+6.00000000, -8.00000000), (-2.00000000, -1.00000000), (-8.00000000, -7.00000000)
673getPolyStr(coef)
674(6.,5.)x^0 + (6.,-8.)x^1 + (-2.,-1.)x^2 + (-8.,-7.)x^3
675order = getUnifRand(0, size(coef) + 1)
676order
677+5
678
679diff = getPolyDiff(coef, order)
680diff ! derivative coefficients.
681
682getPolyStr(diff)
683
684
685degree = getUnifRand(0, 9_IK)
686degree
687+6
688coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
689coef
690(-6.00000000, +1.00000000), (+7.00000000, -2.00000000), (+4.00000000, +9.00000000), (-8.00000000, -6.00000000), (+4.00000000, -4.00000000), (+5.00000000, -9.00000000)
691getPolyStr(coef)
692(-6.,1.)x^0 + (7.,-2.)x^1 + (4.,9.)x^2 + (-8.,-6.)x^3 + (4.,-4.)x^4 + (5.,-9.)x^5
693order = getUnifRand(0, size(coef) + 1)
694order
695+6
696
697diff = getPolyDiff(coef, order)
698diff ! derivative coefficients.
699
700getPolyStr(diff)
701
702
703degree = getUnifRand(0, 9_IK)
704degree
705+3
706coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
707coef
708(+9.00000000, -5.00000000), (-5.00000000, -2.00000000), (+3.00000000, +5.00000000)
709getPolyStr(coef)
710(9.,-5.)x^0 + (-5.,-2.)x^1 + (3.,5.)x^2
711order = getUnifRand(0, size(coef) + 1)
712order
713+1
714
715diff = getPolyDiff(coef, order)
716diff ! derivative coefficients.
717(-5.00000000, -2.00000000), (+6.00000000, +10.0000000)
718getPolyStr(diff)
719(-5.,-2.)x^0 + (6.,10.)x^1
720
721
Test:
test_pm_polynomial


Final Remarks ⛓

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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: