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

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

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
[out]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.
[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)


Possible calling interfaces ⛓

use pm_polynomial, only: setPolyDiff
call setPolyDiff(diff(1 : size(coef) - 1), coef(:))
call setPolyDiff(diff(1 : size(coef) - order), coef(:), order)
pm_polynomial::setPolyDiff
Return the vector of coefficients of the polynomial resulting from the th-order differentiation of a ...
Definition: pm_polynomial.F90:2730
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.
The condition size(diff) == max(1, size(coef) - order) 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
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: setPolyDiff
8 use pm_arrayResize, only: setResized
9
10 implicit none
11
12 integer(IK) :: order
13 integer(IK) :: degree
14 type(display_type) :: disp
15 integer(IK) :: itry, ntry = 20
16 disp = display_type(file = "main.out.F90")
17
18 block
19 use pm_kind, only: TKG => RKS ! all processor real and complex kinds are supported.
20 real(TKG), allocatable :: coef(:), diff(:)
21 do itry = 1, ntry
22 call disp%show("degree = getUnifRand(0, 9_IK)")
23 degree = getUnifRand(0, 9_IK)
24 call disp%show("degree")
25 call disp%show( degree )
26 call disp%show("coef = getUnifRand(-9, 9, degree)")
27 coef = getUnifRand(-9, 9, degree)
28 call disp%show("coef")
29 call disp%show( coef )
30 call disp%show("getPolyStr(coef)")
31 call disp%show( getPolyStr(coef) )
32 call disp%show("order = getUnifRand(0, size(coef) + 1)")
33 order = getUnifRand(0, size(coef) + 1)
34 call disp%show("order")
35 call disp%show( order )
36 call disp%skip()
37 call disp%show("call setResized(diff, max(0_IK, size(coef, 1, IK) - order))")
38 call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
39 call disp%show("call setPolyDiff(diff, coef, order)")
40 call setPolyDiff(diff, coef, order)
41 call disp%show("diff ! derivative coefficients.")
42 call disp%show( diff )
43 call disp%show("getPolyStr(diff)")
44 call disp%show( getPolyStr(diff) )
45 call disp%skip()
46 end do
47 end block
48
49 block
50 use pm_kind, only: TKG => RKS ! all processor real and complex kinds are supported.
51 complex(TKG), allocatable :: coef(:), diff(:)
52 do itry = 1, ntry
53 call disp%show("degree = getUnifRand(0, 9_IK)")
54 degree = getUnifRand(0, 9_IK)
55 call disp%show("degree")
56 call disp%show( degree )
57 call disp%show("coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)")
58 coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
59 call disp%show("coef")
60 call disp%show( coef )
61 call disp%show("getPolyStr(coef)")
62 call disp%show( getPolyStr(coef) )
63 call disp%show("order = getUnifRand(0, size(coef) + 1)")
64 order = getUnifRand(0, size(coef) + 1)
65 call disp%show("order")
66 call disp%show( order )
67 call disp%skip()
68 call disp%show("call setResized(diff, max(0_IK, size(coef, 1, IK) - order))")
69 call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
70 call disp%show("call setPolyDiff(diff, coef, order)")
71 call setPolyDiff(diff, coef, order)
72 call disp%show("diff ! derivative coefficients.")
73 call disp%show( diff )
74 call disp%show("getPolyStr(diff)")
75 call disp%show( getPolyStr(diff) )
76 call disp%skip()
77 end do
78 end block
79
80end program example
pm_arrayResize::setResized
Allocate or resize (shrink or expand) an input allocatable scalar string or array of rank 1....
Definition: pm_arrayResize.F90:249
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_arrayResize
This module contains procedures and generic interfaces for resizing allocatable arrays of various typ...
Definition: pm_arrayResize.F90:81
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+2
4coef = getUnifRand(-9, 9, degree)
5coef
6-1.00000000, -8.00000000
7getPolyStr(coef)
8-1.x^0 - 8.x^1
9order = getUnifRand(0, size(coef) + 1)
10order
11+1
12
13call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
14call setPolyDiff(diff, coef, order)
15diff ! derivative coefficients.
16-8.00000000
17getPolyStr(diff)
18-8.x^0
19
20degree = getUnifRand(0, 9_IK)
21degree
22+4
23coef = getUnifRand(-9, 9, degree)
24coef
25+9.00000000, -5.00000000, -9.00000000, -2.00000000
26getPolyStr(coef)
279.x^0 - 5.x^1 - 9.x^2 - 2.x^3
28order = getUnifRand(0, size(coef) + 1)
29order
30+2
31
32call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
33call setPolyDiff(diff, coef, order)
34diff ! derivative coefficients.
35-18.0000000, -6.00000000
36getPolyStr(diff)
37-18.x^0 - 6.x^1
38
39degree = getUnifRand(0, 9_IK)
40degree
41+7
42coef = getUnifRand(-9, 9, degree)
43coef
44-1.00000000, -4.00000000, +3.00000000, -3.00000000, -1.00000000, -6.00000000, +4.00000000
45getPolyStr(coef)
46-1.x^0 - 4.x^1 + 3.x^2 - 3.x^3 - 1.x^4 - 6.x^5 + 4.x^6
47order = getUnifRand(0, size(coef) + 1)
48order
49+1
50
51call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
52call setPolyDiff(diff, coef, order)
53diff ! derivative coefficients.
54-4.00000000, +6.00000000, -9.00000000, -4.00000000, -30.0000000, +24.0000000
55getPolyStr(diff)
56-4.x^0 + 6.x^1 - 9.x^2 - 4.x^3 - 30.x^4 + 24.x^5
57
58degree = getUnifRand(0, 9_IK)
59degree
60+1
61coef = getUnifRand(-9, 9, degree)
62coef
63+9.00000000
64getPolyStr(coef)
659.x^0
66order = getUnifRand(0, size(coef) + 1)
67order
68+0
69
70call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
71call setPolyDiff(diff, coef, order)
72diff ! derivative coefficients.
73+9.00000000
74getPolyStr(diff)
759.x^0
76
77degree = getUnifRand(0, 9_IK)
78degree
79+1
80coef = getUnifRand(-9, 9, degree)
81coef
82+1.00000000
83getPolyStr(coef)
841.x^0
85order = getUnifRand(0, size(coef) + 1)
86order
87+0
88
89call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
90call setPolyDiff(diff, coef, order)
91diff ! derivative coefficients.
92+1.00000000
93getPolyStr(diff)
941.x^0
95
96degree = getUnifRand(0, 9_IK)
97degree
98+7
99coef = getUnifRand(-9, 9, degree)
100coef
101+8.00000000, -9.00000000, -7.00000000, +0.00000000, +4.00000000, -7.00000000, +1.00000000
102getPolyStr(coef)
1038.x^0 - 9.x^1 - 7.x^2 + 0.x^3 + 4.x^4 - 7.x^5 + 1.x^6
104order = getUnifRand(0, size(coef) + 1)
105order
106+2
107
108call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
109call setPolyDiff(diff, coef, order)
110diff ! derivative coefficients.
111-14.0000000, +0.00000000, +16.0000000, -35.0000000, +6.00000000
112getPolyStr(diff)
113-14.x^0 + 0.x^1 + 16.x^2 - 35.x^3 + 6.x^4
114
115degree = getUnifRand(0, 9_IK)
116degree
117+7
118coef = getUnifRand(-9, 9, degree)
119coef
120+5.00000000, +8.00000000, +4.00000000, +2.00000000, +5.00000000, -5.00000000, -3.00000000
121getPolyStr(coef)
1225.x^0 + 8.x^1 + 4.x^2 + 2.x^3 + 5.x^4 - 5.x^5 - 3.x^6
123order = getUnifRand(0, size(coef) + 1)
124order
125+6
126
127call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
128call setPolyDiff(diff, coef, order)
129diff ! derivative coefficients.
130-18.0000000
131getPolyStr(diff)
132-18.x^0
133
134degree = getUnifRand(0, 9_IK)
135degree
136+5
137coef = getUnifRand(-9, 9, degree)
138coef
139+9.00000000, -3.00000000, -1.00000000, -9.00000000, -4.00000000
140getPolyStr(coef)
1419.x^0 - 3.x^1 - 1.x^2 - 9.x^3 - 4.x^4
142order = getUnifRand(0, size(coef) + 1)
143order
144+5
145
146call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
147call setPolyDiff(diff, coef, order)
148diff ! derivative coefficients.
149
150getPolyStr(diff)
151
152
153degree = getUnifRand(0, 9_IK)
154degree
155+3
156coef = getUnifRand(-9, 9, degree)
157coef
158+2.00000000, -9.00000000, -5.00000000
159getPolyStr(coef)
1602.x^0 - 9.x^1 - 5.x^2
161order = getUnifRand(0, size(coef) + 1)
162order
163+3
164
165call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
166call setPolyDiff(diff, coef, order)
167diff ! derivative coefficients.
168
169getPolyStr(diff)
170
171
172degree = getUnifRand(0, 9_IK)
173degree
174+5
175coef = getUnifRand(-9, 9, degree)
176coef
177-1.00000000, +4.00000000, -8.00000000, -9.00000000, -1.00000000
178getPolyStr(coef)
179-1.x^0 + 4.x^1 - 8.x^2 - 9.x^3 - 1.x^4
180order = getUnifRand(0, size(coef) + 1)
181order
182+6
183
184call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
185call setPolyDiff(diff, coef, order)
186diff ! derivative coefficients.
187
188getPolyStr(diff)
189
190
191degree = getUnifRand(0, 9_IK)
192degree
193+1
194coef = getUnifRand(-9, 9, degree)
195coef
196+6.00000000
197getPolyStr(coef)
1986.x^0
199order = getUnifRand(0, size(coef) + 1)
200order
201+2
202
203call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
204call setPolyDiff(diff, coef, order)
205diff ! derivative coefficients.
206
207getPolyStr(diff)
208
209
210degree = getUnifRand(0, 9_IK)
211degree
212+7
213coef = getUnifRand(-9, 9, degree)
214coef
215-8.00000000, -2.00000000, +5.00000000, +8.00000000, +6.00000000, +4.00000000, +9.00000000
216getPolyStr(coef)
217-8.x^0 - 2.x^1 + 5.x^2 + 8.x^3 + 6.x^4 + 4.x^5 + 9.x^6
218order = getUnifRand(0, size(coef) + 1)
219order
220+5
221
222call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
223call setPolyDiff(diff, coef, order)
224diff ! derivative coefficients.
225+20.0000000, +54.0000000
226getPolyStr(diff)
22720.x^0 + 54.x^1
228
229degree = getUnifRand(0, 9_IK)
230degree
231+2
232coef = getUnifRand(-9, 9, degree)
233coef
234+9.00000000, +7.00000000
235getPolyStr(coef)
2369.x^0 + 7.x^1
237order = getUnifRand(0, size(coef) + 1)
238order
239+1
240
241call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
242call setPolyDiff(diff, coef, order)
243diff ! derivative coefficients.
244+7.00000000
245getPolyStr(diff)
2467.x^0
247
248degree = getUnifRand(0, 9_IK)
249degree
250+7
251coef = getUnifRand(-9, 9, degree)
252coef
253+4.00000000, -9.00000000, -4.00000000, -6.00000000, -9.00000000, +2.00000000, +1.00000000
254getPolyStr(coef)
2554.x^0 - 9.x^1 - 4.x^2 - 6.x^3 - 9.x^4 + 2.x^5 + 1.x^6
256order = getUnifRand(0, size(coef) + 1)
257order
258+8
259
260call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
261call setPolyDiff(diff, coef, order)
262diff ! derivative coefficients.
263
264getPolyStr(diff)
265
266
267degree = getUnifRand(0, 9_IK)
268degree
269+0
270coef = getUnifRand(-9, 9, degree)
271coef
272
273getPolyStr(coef)
274
275order = getUnifRand(0, size(coef) + 1)
276order
277+0
278
279call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
280call setPolyDiff(diff, coef, order)
281diff ! derivative coefficients.
282
283getPolyStr(diff)
284
285
286degree = getUnifRand(0, 9_IK)
287degree
288+4
289coef = getUnifRand(-9, 9, degree)
290coef
291-8.00000000, +7.00000000, +1.00000000, -6.00000000
292getPolyStr(coef)
293-8.x^0 + 7.x^1 + 1.x^2 - 6.x^3
294order = getUnifRand(0, size(coef) + 1)
295order
296+1
297
298call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
299call setPolyDiff(diff, coef, order)
300diff ! derivative coefficients.
301+7.00000000, +2.00000000, -18.0000000
302getPolyStr(diff)
3037.x^0 + 2.x^1 - 18.x^2
304
305degree = getUnifRand(0, 9_IK)
306degree
307+3
308coef = getUnifRand(-9, 9, degree)
309coef
310+7.00000000, +0.00000000, +6.00000000
311getPolyStr(coef)
3127.x^0 + 0.x^1 + 6.x^2
313order = getUnifRand(0, size(coef) + 1)
314order
315+1
316
317call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
318call setPolyDiff(diff, coef, order)
319diff ! derivative coefficients.
320+0.00000000, +12.0000000
321getPolyStr(diff)
3220.x^0 + 12.x^1
323
324degree = getUnifRand(0, 9_IK)
325degree
326+5
327coef = getUnifRand(-9, 9, degree)
328coef
329+5.00000000, +6.00000000, -6.00000000, +1.00000000, +9.00000000
330getPolyStr(coef)
3315.x^0 + 6.x^1 - 6.x^2 + 1.x^3 + 9.x^4
332order = getUnifRand(0, size(coef) + 1)
333order
334+1
335
336call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
337call setPolyDiff(diff, coef, order)
338diff ! derivative coefficients.
339+6.00000000, -12.0000000, +3.00000000, +36.0000000
340getPolyStr(diff)
3416.x^0 - 12.x^1 + 3.x^2 + 36.x^3
342
343degree = getUnifRand(0, 9_IK)
344degree
345+0
346coef = getUnifRand(-9, 9, degree)
347coef
348
349getPolyStr(coef)
350
351order = getUnifRand(0, size(coef) + 1)
352order
353+1
354
355call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
356call setPolyDiff(diff, coef, order)
357diff ! derivative coefficients.
358
359getPolyStr(diff)
360
361
362degree = getUnifRand(0, 9_IK)
363degree
364+5
365coef = getUnifRand(-9, 9, degree)
366coef
367-7.00000000, +4.00000000, +2.00000000, -3.00000000, +7.00000000
368getPolyStr(coef)
369-7.x^0 + 4.x^1 + 2.x^2 - 3.x^3 + 7.x^4
370order = getUnifRand(0, size(coef) + 1)
371order
372+2
373
374call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
375call setPolyDiff(diff, coef, order)
376diff ! derivative coefficients.
377+4.00000000, -9.00000000, +28.0000000
378getPolyStr(diff)
3794.x^0 - 9.x^1 + 28.x^2
380
381degree = getUnifRand(0, 9_IK)
382degree
383+1
384coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
385coef
386(+4.00000000, +4.00000000)
387getPolyStr(coef)
388(4.,4.)x^0
389order = getUnifRand(0, size(coef) + 1)
390order
391+2
392
393call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
394call setPolyDiff(diff, coef, order)
395diff ! derivative coefficients.
396
397getPolyStr(diff)
398
399
400degree = getUnifRand(0, 9_IK)
401degree
402+7
403coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
404coef
405(-9.00000000, +8.00000000), (+7.00000000, +5.00000000), (-7.00000000, -6.00000000), (+2.00000000, +8.00000000), (-8.00000000, +5.00000000), (-3.00000000, -6.00000000), (+3.00000000, -9.00000000)
406getPolyStr(coef)
407(-9.,8.)x^0 + (7.,5.)x^1 + (-7.,-6.)x^2 + (2.,8.)x^3 + (-8.,5.)x^4 + (-3.,-6.)x^5 + (3.,-9.)x^6
408order = getUnifRand(0, size(coef) + 1)
409order
410+4
411
412call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
413call setPolyDiff(diff, coef, order)
414diff ! derivative coefficients.
415(-32.0000000, +20.0000000), (-15.0000000, -30.0000000), (+18.0000000, -54.0000000)
416getPolyStr(diff)
417(-32.,20.)x^0 + (-15.,-30.)x^1 + (18.,-54.)x^2
418
419degree = getUnifRand(0, 9_IK)
420degree
421+7
422coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
423coef
424(-2.00000000, -6.00000000), (-5.00000000, -2.00000000), (-4.00000000, -1.00000000), (-4.00000000, -6.00000000), (+1.00000000, +9.00000000), (+2.00000000, +8.00000000), (+2.00000000, +4.00000000)
425getPolyStr(coef)
426(-2.,-6.)x^0 + (-5.,-2.)x^1 + (-4.,-1.)x^2 + (-4.,-6.)x^3 + (1.,9.)x^4 + (2.,8.)x^5 + (2.,4.)x^6
427order = getUnifRand(0, size(coef) + 1)
428order
429+5
430
431call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
432call setPolyDiff(diff, coef, order)
433diff ! derivative coefficients.
434(+10.0000000, +40.0000000), (+12.0000000, +24.0000000)
435getPolyStr(diff)
436(10.,40.)x^0 + (12.,24.)x^1
437
438degree = getUnifRand(0, 9_IK)
439degree
440+7
441coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
442coef
443(-2.00000000, +7.00000000), (+8.00000000, -4.00000000), (-1.00000000, +0.00000000), (-7.00000000, +2.00000000), (-1.00000000, -7.00000000), (+0.00000000, +4.00000000), (+4.00000000, +7.00000000)
444getPolyStr(coef)
445(-2.,7.)x^0 + (8.,-4.)x^1 + (-1.,0.)x^2 + (-7.,2.)x^3 + (-1.,-7.)x^4 + (0.,4.)x^5 + (4.,7.)x^6
446order = getUnifRand(0, size(coef) + 1)
447order
448+0
449
450call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
451call setPolyDiff(diff, coef, order)
452diff ! derivative coefficients.
453(-2.00000000, +7.00000000), (+8.00000000, -4.00000000), (-1.00000000, +0.00000000), (-7.00000000, +2.00000000), (-1.00000000, -7.00000000), (+0.00000000, +4.00000000), (+4.00000000, +7.00000000)
454getPolyStr(diff)
455(-2.,7.)x^0 + (8.,-4.)x^1 + (-1.,0.)x^2 + (-7.,2.)x^3 + (-1.,-7.)x^4 + (0.,4.)x^5 + (4.,7.)x^6
456
457degree = getUnifRand(0, 9_IK)
458degree
459+9
460coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
461coef
462(+2.00000000, -9.00000000), (-4.00000000, +1.00000000), (-5.00000000, -5.00000000), (-9.00000000, +0.00000000), (+7.00000000, +9.00000000), (+0.00000000, +3.00000000), (+1.00000000, +0.00000000), (-6.00000000, +4.00000000), (-3.00000000, -5.00000000)
463getPolyStr(coef)
464(2.,-9.)x^0 + (-4.,1.)x^1 + (-5.,-5.)x^2 + (-9.,0.)x^3 + (7.,9.)x^4 + (0.,3.)x^5 + (1.,0.)x^6 + (-6.,4.)x^7 + (-3.,-5.)x^8
465order = getUnifRand(0, size(coef) + 1)
466order
467+4
468
469call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
470call setPolyDiff(diff, coef, order)
471diff ! derivative coefficients.
472(+28.0000000, +36.0000000), (+0.00000000, +15.0000000), (+6.00000000, +0.00000000), (-42.0000000, +28.0000000), (-24.0000000, -40.0000000)
473getPolyStr(diff)
474(28.,36.)x^0 + (0.,15.)x^1 + (6.,0.)x^2 + (-42.,28.)x^3 + (-24.,-40.)x^4
475
476degree = getUnifRand(0, 9_IK)
477degree
478+2
479coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
480coef
481(+4.00000000, -2.00000000), (-4.00000000, -4.00000000)
482getPolyStr(coef)
483(4.,-2.)x^0 + (-4.,-4.)x^1
484order = getUnifRand(0, size(coef) + 1)
485order
486+1
487
488call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
489call setPolyDiff(diff, coef, order)
490diff ! derivative coefficients.
491(-4.00000000, -4.00000000)
492getPolyStr(diff)
493(-4.,-4.)x^0
494
495degree = getUnifRand(0, 9_IK)
496degree
497+9
498coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
499coef
500(-3.00000000, -8.00000000), (+2.00000000, +8.00000000), (-1.00000000, -6.00000000), (-4.00000000, +2.00000000), (+8.00000000, +9.00000000), (+5.00000000, -6.00000000), (+2.00000000, +4.00000000), (-5.00000000, +1.00000000), (+3.00000000, +8.00000000)
501getPolyStr(coef)
502(-3.,-8.)x^0 + (2.,8.)x^1 + (-1.,-6.)x^2 + (-4.,2.)x^3 + (8.,9.)x^4 + (5.,-6.)x^5 + (2.,4.)x^6 + (-5.,1.)x^7 + (3.,8.)x^8
503order = getUnifRand(0, size(coef) + 1)
504order
505+4
506
507call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
508call setPolyDiff(diff, coef, order)
509diff ! derivative coefficients.
510(+32.0000000, +36.0000000), (+25.0000000, -30.0000000), (+12.0000000, +24.0000000), (-35.0000000, +7.00000000), (+24.0000000, +64.0000000)
511getPolyStr(diff)
512(32.,36.)x^0 + (25.,-30.)x^1 + (12.,24.)x^2 + (-35.,7.)x^3 + (24.,64.)x^4
513
514degree = getUnifRand(0, 9_IK)
515degree
516+3
517coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
518coef
519(+2.00000000, +0.00000000), (+7.00000000, -1.00000000), (+6.00000000, +9.00000000)
520getPolyStr(coef)
521(2.,0.)x^0 + (7.,-1.)x^1 + (6.,9.)x^2
522order = getUnifRand(0, size(coef) + 1)
523order
524+2
525
526call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
527call setPolyDiff(diff, coef, order)
528diff ! derivative coefficients.
529(+12.0000000, +18.0000000)
530getPolyStr(diff)
531(12.,18.)x^0
532
533degree = getUnifRand(0, 9_IK)
534degree
535+9
536coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
537coef
538(-7.00000000, -9.00000000), (+4.00000000, +9.00000000), (-5.00000000, +0.00000000), (-3.00000000, +1.00000000), (+0.00000000, -3.00000000), (-3.00000000, -6.00000000), (+9.00000000, +4.00000000), (+2.00000000, +1.00000000), (-7.00000000, -9.00000000)
539getPolyStr(coef)
540(-7.,-9.)x^0 + (4.,9.)x^1 + (-5.,0.)x^2 + (-3.,1.)x^3 + (0.,-3.)x^4 + (-3.,-6.)x^5 + (9.,4.)x^6 + (2.,1.)x^7 + (-7.,-9.)x^8
541order = getUnifRand(0, size(coef) + 1)
542order
543+1
544
545call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
546call setPolyDiff(diff, coef, order)
547diff ! derivative coefficients.
548(+4.00000000, +9.00000000), (-10.0000000, +0.00000000), (-9.00000000, +3.00000000), (+0.00000000, -12.0000000), (-15.0000000, -30.0000000), (+54.0000000, +24.0000000), (+14.0000000, +7.00000000), (-56.0000000, -72.0000000)
549getPolyStr(diff)
550(4.,9.)x^0 + (-10.,0.)x^1 + (-9.,3.)x^2 + (0.,-12.)x^3 + (-15.,-30.)x^4 + (54.,24.)x^5 + (14.,7.)x^6 + (-56.,-72.)x^7
551
552degree = getUnifRand(0, 9_IK)
553degree
554+8
555coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
556coef
557(-9.00000000, +5.00000000), (-5.00000000, +4.00000000), (+3.00000000, +2.00000000), (-7.00000000, -1.00000000), (-2.00000000, +9.00000000), (+5.00000000, -2.00000000), (-1.00000000, +8.00000000), (+6.00000000, +9.00000000)
558getPolyStr(coef)
559(-9.,5.)x^0 + (-5.,4.)x^1 + (3.,2.)x^2 + (-7.,-1.)x^3 + (-2.,9.)x^4 + (5.,-2.)x^5 + (-1.,8.)x^6 + (6.,9.)x^7
560order = getUnifRand(0, size(coef) + 1)
561order
562+2
563
564call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
565call setPolyDiff(diff, coef, order)
566diff ! derivative coefficients.
567(+6.00000000, +4.00000000), (-21.0000000, -3.00000000), (-8.00000000, +36.0000000), (+25.0000000, -10.0000000), (-6.00000000, +48.0000000), (+42.0000000, +63.0000000)
568getPolyStr(diff)
569(6.,4.)x^0 + (-21.,-3.)x^1 + (-8.,36.)x^2 + (25.,-10.)x^3 + (-6.,48.)x^4 + (42.,63.)x^5
570
571degree = getUnifRand(0, 9_IK)
572degree
573+7
574coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
575coef
576(-9.00000000, +2.00000000), (+3.00000000, +5.00000000), (-6.00000000, -2.00000000), (+3.00000000, +7.00000000), (+5.00000000, +7.00000000), (+5.00000000, +8.00000000), (+5.00000000, -5.00000000)
577getPolyStr(coef)
578(-9.,2.)x^0 + (3.,5.)x^1 + (-6.,-2.)x^2 + (3.,7.)x^3 + (5.,7.)x^4 + (5.,8.)x^5 + (5.,-5.)x^6
579order = getUnifRand(0, size(coef) + 1)
580order
581+1
582
583call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
584call setPolyDiff(diff, coef, order)
585diff ! derivative coefficients.
586(+3.00000000, +5.00000000), (-12.0000000, -4.00000000), (+9.00000000, +21.0000000), (+20.0000000, +28.0000000), (+25.0000000, +40.0000000), (+30.0000000, -30.0000000)
587getPolyStr(diff)
588(3.,5.)x^0 + (-12.,-4.)x^1 + (9.,21.)x^2 + (20.,28.)x^3 + (25.,40.)x^4 + (30.,-30.)x^5
589
590degree = getUnifRand(0, 9_IK)
591degree
592+8
593coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
594coef
595(+7.00000000, +4.00000000), (-1.00000000, -6.00000000), (-4.00000000, +3.00000000), (+6.00000000, +7.00000000), (-4.00000000, +9.00000000), (+9.00000000, +0.00000000), (+1.00000000, +5.00000000), (-2.00000000, -7.00000000)
596getPolyStr(coef)
597(7.,4.)x^0 + (-1.,-6.)x^1 + (-4.,3.)x^2 + (6.,7.)x^3 + (-4.,9.)x^4 + (9.,0.)x^5 + (1.,5.)x^6 + (-2.,-7.)x^7
598order = getUnifRand(0, size(coef) + 1)
599order
600+4
601
602call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
603call setPolyDiff(diff, coef, order)
604diff ! derivative coefficients.
605(-16.0000000, +36.0000000), (+45.0000000, +0.00000000), (+6.00000000, +30.0000000), (-14.0000000, -49.0000000)
606getPolyStr(diff)
607(-16.,36.)x^0 + (45.,0.)x^1 + (6.,30.)x^2 + (-14.,-49.)x^3
608
609degree = getUnifRand(0, 9_IK)
610degree
611+8
612coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
613coef
614(+2.00000000, +5.00000000), (-1.00000000, -6.00000000), (+8.00000000, -8.00000000), (-7.00000000, -9.00000000), (+8.00000000, -5.00000000), (-7.00000000, -4.00000000), (+7.00000000, -2.00000000), (-8.00000000, -3.00000000)
615getPolyStr(coef)
616(2.,5.)x^0 + (-1.,-6.)x^1 + (8.,-8.)x^2 + (-7.,-9.)x^3 + (8.,-5.)x^4 + (-7.,-4.)x^5 + (7.,-2.)x^6 + (-8.,-3.)x^7
617order = getUnifRand(0, size(coef) + 1)
618order
619+9
620
621call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
622call setPolyDiff(diff, coef, order)
623diff ! derivative coefficients.
624
625getPolyStr(diff)
626
627
628degree = getUnifRand(0, 9_IK)
629degree
630+8
631coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
632coef
633(-4.00000000, -3.00000000), (+1.00000000, -8.00000000), (+1.00000000, -7.00000000), (+2.00000000, +9.00000000), (-1.00000000, +9.00000000), (-3.00000000, -4.00000000), (-1.00000000, +2.00000000), (+0.00000000, -7.00000000)
634getPolyStr(coef)
635(-4.,-3.)x^0 + (1.,-8.)x^1 + (1.,-7.)x^2 + (2.,9.)x^3 + (-1.,9.)x^4 + (-3.,-4.)x^5 + (-1.,2.)x^6 + (0.,-7.)x^7
636order = getUnifRand(0, size(coef) + 1)
637order
638+5
639
640call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
641call setPolyDiff(diff, coef, order)
642diff ! derivative coefficients.
643(-15.0000000, -20.0000000), (-6.00000000, +12.0000000), (+0.00000000, -49.0000000)
644getPolyStr(diff)
645(-15.,-20.)x^0 + (-6.,12.)x^1 + (0.,-49.)x^2
646
647degree = getUnifRand(0, 9_IK)
648degree
649+3
650coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
651coef
652(-5.00000000, +6.00000000), (+5.00000000, -3.00000000), (-6.00000000, -5.00000000)
653getPolyStr(coef)
654(-5.,6.)x^0 + (5.,-3.)x^1 + (-6.,-5.)x^2
655order = getUnifRand(0, size(coef) + 1)
656order
657+0
658
659call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
660call setPolyDiff(diff, coef, order)
661diff ! derivative coefficients.
662(-5.00000000, +6.00000000), (+5.00000000, -3.00000000), (-6.00000000, -5.00000000)
663getPolyStr(diff)
664(-5.,6.)x^0 + (5.,-3.)x^1 + (-6.,-5.)x^2
665
666degree = getUnifRand(0, 9_IK)
667degree
668+7
669coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
670coef
671(+1.00000000, +8.00000000), (+9.00000000, +8.00000000), (-8.00000000, +6.00000000), (-6.00000000, +3.00000000), (+1.00000000, -1.00000000), (-4.00000000, -9.00000000), (-8.00000000, +1.00000000)
672getPolyStr(coef)
673(1.,8.)x^0 + (9.,8.)x^1 + (-8.,6.)x^2 + (-6.,3.)x^3 + (1.,-1.)x^4 + (-4.,-9.)x^5 + (-8.,1.)x^6
674order = getUnifRand(0, size(coef) + 1)
675order
676+4
677
678call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
679call setPolyDiff(diff, coef, order)
680diff ! derivative coefficients.
681(+4.00000000, -4.00000000), (-20.0000000, -45.0000000), (-48.0000000, +6.00000000)
682getPolyStr(diff)
683(4.,-4.)x^0 + (-20.,-45.)x^1 + (-48.,6.)x^2
684
685degree = getUnifRand(0, 9_IK)
686degree
687+0
688coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
689coef
690
691getPolyStr(coef)
692
693order = getUnifRand(0, size(coef) + 1)
694order
695+1
696
697call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
698call setPolyDiff(diff, coef, order)
699diff ! derivative coefficients.
700
701getPolyStr(diff)
702
703
704degree = getUnifRand(0, 9_IK)
705degree
706+8
707coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
708coef
709(+8.00000000, -5.00000000), (-9.00000000, +6.00000000), (+8.00000000, +6.00000000), (+1.00000000, +2.00000000), (-2.00000000, -6.00000000), (-1.00000000, -5.00000000), (-4.00000000, -6.00000000), (-9.00000000, -4.00000000)
710getPolyStr(coef)
711(8.,-5.)x^0 + (-9.,6.)x^1 + (8.,6.)x^2 + (1.,2.)x^3 + (-2.,-6.)x^4 + (-1.,-5.)x^5 + (-4.,-6.)x^6 + (-9.,-4.)x^7
712order = getUnifRand(0, size(coef) + 1)
713order
714+6
715
716call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
717call setPolyDiff(diff, coef, order)
718diff ! derivative coefficients.
719(-24.0000000, -36.0000000), (-63.0000000, -28.0000000)
720getPolyStr(diff)
721(-24.,-36.)x^0 + (-63.,-28.)x^1
722
723degree = getUnifRand(0, 9_IK)
724degree
725+2
726coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
727coef
728(-2.00000000, +7.00000000), (+9.00000000, +4.00000000)
729getPolyStr(coef)
730(-2.,7.)x^0 + (9.,4.)x^1
731order = getUnifRand(0, size(coef) + 1)
732order
733+3
734
735call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
736call setPolyDiff(diff, coef, order)
737diff ! derivative coefficients.
738
739getPolyStr(diff)
740
741
742degree = getUnifRand(0, 9_IK)
743degree
744+9
745coef = cmplx(getUnifRand(-9, 9, degree), getUnifRand(-9, 9, degree), TKG)
746coef
747(-2.00000000, -1.00000000), (+0.00000000, +9.00000000), (+8.00000000, +2.00000000), (+6.00000000, +4.00000000), (+6.00000000, -3.00000000), (+3.00000000, +0.00000000), (-6.00000000, -4.00000000), (+1.00000000, -4.00000000), (-5.00000000, +9.00000000)
748getPolyStr(coef)
749(-2.,-1.)x^0 + (0.,9.)x^1 + (8.,2.)x^2 + (6.,4.)x^3 + (6.,-3.)x^4 + (3.,0.)x^5 + (-6.,-4.)x^6 + (1.,-4.)x^7 + (-5.,9.)x^8
750order = getUnifRand(0, size(coef) + 1)
751order
752+0
753
754call setResized(diff, max(0_IK, size(coef, 1, IK) - order))
755call setPolyDiff(diff, coef, order)
756diff ! derivative coefficients.
757(-2.00000000, -1.00000000), (+0.00000000, +9.00000000), (+8.00000000, +2.00000000), (+6.00000000, +4.00000000), (+6.00000000, -3.00000000), (+3.00000000, +0.00000000), (-6.00000000, -4.00000000), (+1.00000000, -4.00000000), (-5.00000000, +9.00000000)
758getPolyStr(diff)
759(-2.,-1.)x^0 + (0.,9.)x^1 + (8.,2.)x^2 + (6.,4.)x^3 + (6.,-3.)x^4 + (3.,0.)x^5 + (-6.,-4.)x^6 + (1.,-4.)x^7 + (-5.,9.)x^8
760
761
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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  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.
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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 2730 of file pm_polynomial.F90.

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