clean up + add examples with NaN and concurrent call

Author: HugoMVale

example/stats_distribution_exponential/example_exponential_pdf.f90

@@ -1,39 +1,62 @@
 program example_exponential_pdf
   use stdlib_random, only: random_seed
   use stdlib_stats_distribution_exponential, only: exp_pdf => pdf_exp, &
-                                                   rexp => rvs_exp
+                                                    rexp => rvs_exp
 
   implicit none
-  real :: x(2, 3, 4), a(2, 3, 4)
+  real, dimension(2, 3, 4) :: x, lambda
+  real :: xsum
   complex :: scale
-  integer :: seed_put, seed_get
+  integer :: seed_put, seed_get, i
 
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  print *, exp_pdf(1.0, 1.0) !a probability density at 1.0 in standard expon
-
-! 0.367879450
-
-  print *, exp_pdf(2.0, 2.0) !a probability density at 2.0 with lambda=2.0
-
-! 3.66312787E-02
-
-  x = reshape(rexp(0.5, 24), [2, 3, 4]) ! standard expon random variates array
-  a(:, :, :) = 0.5
-  print *, exp_pdf(x, a)     ! a rank 3 standard expon probability density
-
-!  0.457115263  0.451488823  0.492391467  0.485233188  0.446215510
-!  0.401670188  0.485127628  0.316924453  0.418474048  0.483173639
-!  0.307366133  0.285812140  0.448017836  0.426440030  0.403896868
-!  0.334653258  0.410376132  0.485370994  0.333617479  0.263791025
-!  0.249779820  0.457159877  0.495636940  0.482243657
-
+  ! probability density at x=1.0 in standard exponential
+  print *, exp_pdf(1.0, 1.0)
+  ! 0.367879450
+
+  ! probability density at x=2.0 with lambda=2.0
+  print *, exp_pdf(2.0, 2.0) 
+  ! 3.66312787E-02
+
+  ! probability density at x=2.0 with lambda=-1.0 (out of range)
+  print *, exp_pdf(2.0, -1.0) 
+  ! NaN
+
+  ! standard exponential random variates array  
+  x = reshape(rexp(0.5, 24), [2, 3, 4])
+
+  ! a rank-3 exponential probability density
+  lambda(:, :, :) = 0.5
+  print *, exp_pdf(x, lambda)
+  ! 0.349295378      0.332413018     0.470253497     0.443498343      0.317152828
+  ! 0.208242029      0.443112582     8.07073265E-02  0.245337561      0.436016470
+  ! 7.14025944E-02   5.33841923E-02  0.322308093     0.264558554      0.212898195
+  ! 0.100339092      0.226891592     0.444002301     9.91026312E-02   3.87373678E-02
+  ! 3.11400592E-02   0.349431813     0.482774824     0.432669312     
+
+  ! probability density array where lambda<=0.0 for certain elements 
+  print *, exp_pdf([1.0, 1.0, 1.0], [1.0, 0.0, -1.0])
+  ! 0.367879450  NaN NaN
+
+  ! `pdf_exp` is pure and, thus, can be called concurrently 
+  xsum = 0.0
+  do concurrent (i=1:size(x,3))
+    xsum = xsum + sum(exp_pdf(x(:,:,i), lambda(:,:,i)))
+  end do
+  print *, xsum
+  ! 6.45566940
+
+  ! complex exponential probability density function at (1.5,1.0) with real part
+  ! of lambda=1.0 and imaginary part of lambda=2.0
   scale = (1.0, 2.)
   print *, exp_pdf((1.5, 1.0), scale)
-! a complex expon probability density function at (1.5,1.0) with real part
-!of lambda=1.0 and imaginary part of lambda=2.0
+  ! 6.03947677E-02
 
-! 6.03947677E-02
+  ! As above, but with lambda%re < 0 
+  scale = (-1.0, 2.)
+  print *, exp_pdf((1.5, 1.0), scale)
+  ! NaN
 
 end program example_exponential_pdf