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#:include "common.fypp"
#:set RC_KINDS_TYPES = REAL_KINDS_TYPES + CMPLX_KINDS_TYPES
program test_distribution_normal
use stdlib_kinds, only : sp, dp, xdp, qp
use stdlib_error, only : check
use stdlib_random, only : random_seed
use stdlib_stats_distribution_uniform, only : uni => rvs_uniform
use stdlib_stats_distribution_normal, only : nor_rvs => rvs_normal, &
nor_pdf => pdf_normal, nor_cdf => cdf_normal
implicit none
#:for k1, t1 in REAL_KINDS_TYPES
${t1}$, parameter :: ${k1}$tol = 1000 * epsilon(1.0_${k1}$)
#:endfor
logical :: warn = .true.
integer :: put, get
put = 12345678
call random_seed(put, get)
call test_normal_random_generator
#:for k1, t1 in RC_KINDS_TYPES
call test_nor_rvs_${t1[0]}$${k1}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
call test_nor_rvs_default_${t1[0]}$${k1}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
call test_nor_pdf_${t1[0]}$${k1}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
call test_nor_cdf_${t1[0]}$${k1}$
#:endfor
contains
subroutine test_normal_random_generator
integer, parameter :: num = 10000000, array_size = 1000
integer :: i, j, freq(0:array_size)
real(dp) :: chisq, expct
print *, ""
print *, "Test normal random generator with chi-squared"
freq = 0
do i = 1, num
j = array_size * (1 + erf(nor_rvs(0.0, 1.0) / sqrt(2.0))) / 2.0
freq(j) = freq(j) + 1
end do
chisq = 0.0_dp
expct = num / array_size
do i = 0, array_size - 1
chisq = chisq + (freq(i) - expct) ** 2 / expct
end do
write(*,*) "The critical values for chi-squared with 1000 d. of f. is" &
//" 1143.92"
write(*,*) "Chi-squared for normal random generator is : ", chisq
call check((chisq < 1143.9), &
msg = "normal randomness failed chi-squared test", warn = warn)
end subroutine test_normal_random_generator
#:for k1, t1 in RC_KINDS_TYPES
subroutine test_nor_rvs_${t1[0]}$${k1}$
${t1}$ :: res(10), loc, scale
integer, parameter :: k = 5
integer :: i
integer :: seed, get
#:if t1[0] == "r"
#! for real type
${t1}$, parameter :: ans(10) = &
[2.66708039318040679432897377409972250_${k1}$, &
2.36030794936128329730706809641560540_${k1}$, &
1.27712218793084242296487218482070602_${k1}$, &
-2.39132544130814794769435138732660562_${k1}$, &
1.72566595106028652928387145948363468_${k1}$, &
-1.50621775537767632613395107910037041_${k1}$, &
2.13518835158352082714827702147886157_${k1}$, &
-0.636788253742142318358787633769679815_${k1}$, &
2.48600787778845799813609573902795091_${k1}$, &
-3.03711473837981227319460231228731573_${k1}$]
#:else
#! for complex type
${t1}$, parameter :: ans(10) = &
[(2.12531029488530509574673033057479188_${k1}$, &
1.46507698734032082432676702410390135_${k1}$), &
(1.08284164094813181722365413861552952_${k1}$, &
0.277168639672963013076412153168348595_${k1}$), &
(1.41924946329521489696290359461272601_${k1}$, &
0.498445561155580918466512230224907398_${k1}$), &
(1.72639126368764062036120776610914618_${k1}$, &
0.715802936564464420410303091557580046_${k1}$), &
(1.98950590834134349860207180427096318_${k1}$, &
0.115721315405046931701349421928171068_${k1}$), &
(-1.16929014824793620075382705181255005_${k1}$, &
0.250744737486995217246033007540972903_${k1}$), &
(1.57160542831869509683428987045772374_${k1}$, &
0.638282596371312238581197107123443857_${k1}$), &
(-1.36106107654239116833139178197598085_${k1}$, &
0.166259201494369124318950525776017457_${k1}$), &
(1.13403096805387920698038328737311531_${k1}$, &
1.04232618148691447146347854868508875_${k1}$), &
(-1.68220535920475811053620418533682823_${k1}$, &
1.63361446685040256898702182297711261_${k1}$)]
#:endif
print *, "Test normal_distribution_rvs_${t1[0]}$${k1}$"
seed = 25836914
call random_seed(seed, get)
#:if t1[0] == "r"
#! for real type
loc = 0.5_${k1}$; scale = 2.0_${k1}$
#:else
#! for complex type
loc = (0.5_${k1}$, 1.0_${k1}$); scale = (1.5_${k1}$, 0.5_${k1}$)
#:endif
do i = 1, k
res(i) = nor_rvs(loc, scale) ! 2 dummies
end do
res(6:10) = nor_rvs(loc, scale, k) ! 3 dummies
call check(all(abs(res - ans) < ${k1}$tol), &
msg="normal_distribution_rvs_${t1[0]}$${k1}$ failed", warn=warn)
end subroutine test_nor_rvs_${t1[0]}$${k1}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
subroutine test_nor_rvs_default_${t1[0]}$${k1}$
${t1}$ :: a1(10), a2(10), mold
integer :: i
integer :: seed, get
print *, "Test normal_distribution_rvs_default_${t1[0]}$${k1}$"
seed = 25836914
call random_seed(seed, get)
! explicit form with loc=0, scale=1
#:if t1[0] == "r"
a1 = nor_rvs(0.0_${k1}$, 1.0_${k1}$, 10)
#:else
a1 = nor_rvs((0.0_${k1}$, 0.0_${k1}$), (1.0_${k1}$, 1.0_${k1}$), 10)
#:endif
! reset seed to reproduce same random sequence
seed = 25836914
call random_seed(seed, get)
! default mold form: mold used only to disambiguate kind
! For real(dp), mold is optional; for other types (including complex), it's required
#:if t1[0] == "r" and k1 == "dp"
a2 = nor_rvs(10) ! mold optional for rdp only, defaults to real(dp)
#:else
#! mold required for all other types including complex and non-dp kinds
#:if t1[0] == "r"
mold = 0.0_${k1}$
#:else
mold = (0.0_${k1}$, 0.0_${k1}$)
#:endif
a2 = nor_rvs(10, mold)
#:endif
call check(all(a1 == a2), msg="normal_distribution_rvs_default_${t1[0]}$${k1}$ failed", warn=warn)
end subroutine test_nor_rvs_default_${t1[0]}$${k1}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
subroutine test_nor_pdf_${t1[0]}$${k1}$
${t1}$ :: x1, x2(3,4), loc, scale
integer, parameter :: k = 5
integer :: seed, get
real(${k1}$) :: res(3,5)
#:if t1[0] == "r"
#! for real type
real(${k1}$), parameter :: ans(15) = &
[0.215050766989949083210785218076278553_${k1}$, &
0.215050766989949083210785218076278553_${k1}$, &
0.215050766989949083210785218076278553_${k1}$, &
0.200537626692880596839299818454439236_${k1}$, &
5.66161527403268434368575024104022496E-0002_${k1}$, &
0.238986957612021514867582359518579138_${k1}$, &
0.265935969411942911029638292783132425_${k1}$, &
0.262147558654079961109031890374902943_${k1}$, &
0.249866408914952245533320687656894701_${k1}$, &
3.98721117498705317877792757313696510E-0002_${k1}$, &
0.265902369803533466897906694845094995_${k1}$, &
0.161311603170650092038944290133124635_${k1}$, &
0.249177740354276111998717092437037695_${k1}$, &
0.237427217242213206474603807278971527_${k1}$, &
0.155696086384122017518186260628090478_${k1}$]
#:else
#! for complex type
real(${k1}$), parameter :: ans(15) = &
[0.129377311291944176372137325120411497_${k1}$, &
0.129377311291944176372137325120411497_${k1}$, &
0.129377311291944176372137325120411497_${k1}$, &
4.05915662853246811934977653001971736E-0002_${k1}$, &
0.209143395418940756076861773161637924_${k1}$, &
2.98881041363874672676853084975547667E-0002_${k1}$, &
0.128679412679649127469385460133445161_${k1}$, &
0.177484732473055532384223611956177231_${k1}$, &
3.82205306942578982084957100753849738E-0002_${k1}$, &
7.09915714309796034515515428785324918E-0002_${k1}$, &
4.56126582912124629544443072483362352E-0002_${k1}$, &
6.57454133967021123696499056531595921E-0002_${k1}$, &
0.165161039915667041643464172210282279_${k1}$, &
3.86104822953520989775015755966798359E-0002_${k1}$, &
0.196922947431391188040943672442575686_${k1}$]
#:endif
print *, "Test normal_distribution_pdf_${t1[0]}$${k1}$"
seed = 741852963
call random_seed(seed, get)
#:if t1[0] == "r"
#! for real type
loc = -0.5_${k1}$; scale = 1.5_${k1}$
#:else
#! for complex type
loc = (-0.5_${k1}$, 0.5_${k1}$); scale = (0.5_${k1}$, 1.5_${k1}$)
#:endif
x1 = nor_rvs(loc, scale)
x2 = reshape(nor_rvs(loc, scale, 12), [3,4])
res(:,1) = nor_pdf(x1, loc, scale)
res(:, 2:5) = nor_pdf(x2, loc, scale)
call check(all(abs(res - reshape(ans, [3,5])) < ${k1}$tol), &
msg="normal_distribution_pdf_${t1[0]}$${k1}$ failed", warn=warn)
end subroutine test_nor_pdf_${t1[0]}$${k1}$
#:endfor
#:for k1, t1 in RC_KINDS_TYPES
subroutine test_nor_cdf_${t1[0]}$${k1}$
${t1}$ :: x1, x2(3,4), loc, scale
integer :: seed, get
real(${k1}$) :: res(3,5)
#:if t1[0] == "r"
#!for real type
real(${k1}$), parameter :: ans(15) = &
[7.50826305038441048487991102776953948E-0002_${k1}$, &
7.50826305038441048487991102776953948E-0002_${k1}$, &
7.50826305038441048487991102776953948E-0002_${k1}$, &
0.143119834108717983250834016885129863_${k1}$, &
0.241425421525703182028420560765471735_${k1}$, &
0.284345878626039240974266199229875972_${k1}$, &
0.233239836366015928845367994433532757_${k1}$, &
0.341059506137219171082517155967522896_${k1}$, &
0.353156850199835111081038166086606192_${k1}$, &
6.81066766396638231790017005897813244E-0002_${k1}$, &
4.38792331441682923984716366123285346E-0002_${k1}$, &
0.763679637882860826030745070304416929_${k1}$, &
0.363722187587355040667876190724308059_${k1}$, &
0.868187114884980488672309198087692444_${k1}$, &
0.626506799809652872401992867475200722_${k1}$]
#:else
#! for complex type
real(${k1}$), parameter :: ans(15) = &
[1.07458136221563368133842063954746170E-0002_${k1}$, &
1.07458136221563368133842063954746170E-0002_${k1}$, &
1.07458136221563368133842063954746170E-0002_${k1}$, &
6.86483236063879585051085536740820057E-0002_${k1}$, &
7.95486634025192048896990048539218724E-0002_${k1}$, &
2.40523393996423661445007940057223384E-0002_${k1}$, &
3.35096768781160662250307446207445131E-0002_${k1}$, &
0.315778916661119434962814841317323376_${k1}$, &
0.446311293878359175362094845206410428_${k1}$, &
0.102010220821382542292905161748120877_${k1}$, &
7.66919007012121545175655727052974512E-0002_${k1}$, &
0.564690968410069125818268877247699603_${k1}$, &
0.708769523556518785240723539383512333_${k1}$, &
6.40553790808161720088070925562830659E-0002_${k1}$, &
5.39999153072107729358158443133850711E-0002_${k1}$]
#:endif
print *, "Test normal_distribution_cdf_${t1[0]}$${k1}$"
seed = 369147582
call random_seed(seed, get)
#:if t1[0] == "r"
#! for real type
loc = -1.0_${k1}$; scale = 2.0_${k1}$
#:else
#! for complex type
loc = (-1.0_${k1}$, 1.0_${k1}$); scale = (1.7_${k1}$, 2.4_${k1}$)
#:endif
x1 = nor_rvs(loc, scale)
x2 = reshape(nor_rvs(loc, scale, 12), [3,4])
res(:,1) = nor_cdf(x1, loc, scale)
res(:, 2:5) = nor_cdf(x2, loc, scale)
call check(all(abs(res - reshape(ans,[3,5])) < ${k1}$tol), &
msg="normal_distribution_cdf_${t1[0]}$${k1}$ failed", warn=warn)
end subroutine test_nor_cdf_${t1[0]}$${k1}$
#:endfor
end program test_distribution_normal
|
