Probability Distribution and Statistical Functions -- Uniform Distribution Module

doc/specs/stdlib_stats_distribution_uniform.md

@@ -79,9 +79,9 @@ Without argument the function returns a scalar standard uniformly distributed va
 
 With single argument `scale` of `integer` type the function returns a scalar uniformly distributed variate of `integer` type on [0,scale]. This is the standard Rectangular distribution.
 
-With single argument `scale` of `real` or `complex` type the function returns a scalar uniformly distributed variate of `real` or `complex` type on [0, scale].
+With single argument `scale` of `real` or `complex` type the function returns a scalar uniformly distributed variate of `real` type on [0, scale] or `complex` type on [(0, 0i), (scale, i(scale))].
 
-With double arguments `loc` and `scale` the function returns a scalar uniformly distributed random variates of `integer`, `real` or `complex` type on [loc, loc + scale] dependent of input type.
+With double arguments `loc` and `scale` the function returns a scalar uniformly distributed random variates of `integer` or `real` type on [loc, loc + scale], or `complex` type on [(loc, i(loc)), ((loc + scale), i(loc + scale))], dependent of input type.
 
 With triple arguments `loc`, `scale` and `array_size` the function returns a rank one array of uniformly distributed variates of `integer`, `real` or `complex` type with an array size of `array_size`.
 
@@ -101,7 +101,7 @@ Elemental function (without the third argument).
 
 `scale`: optional argument has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
-`array_size`: optional argument has `intent(in)` and is a scalar of type `integer`.
+`array_size`: optional argument has `intent(in)` and is a scalar of type `integer` with default kind.
 
 `loc` and `scale` must have the same type and kind when both are present.
 

src/stdlib_stats_distribution_uniform.fypp

@@ -2,7 +2,7 @@
 #:set RC_KINDS_TYPES = REAL_KINDS_TYPES + CMPLX_KINDS_TYPES
 #:set ALL_KINDS_TYPES = INT_KINDS_TYPES + RC_KINDS_TYPES
 module stdlib_stats_distribution_uniform
- use stdlib_kinds
+ use stdlib_kinds, only : sp, dp, xdp, qp, int8, int16, int32, int64
  use stdlib_error, only : error_stop
  use stdlib_random, only : dist_rand
 
@@ -383,14 +383,15 @@ contains
  elemental function pdf_unif_${t1[0]}$${k1}$(x, loc, scale) result(res)
 
  ${t1}$, intent(in) :: x, loc, scale
- real :: res
+ ${t1}$ :: res
+ ${t1}$, parameter :: zero = 0.0_${k1}$, one = 1.0_${k1}$
 
- if(scale == 0.0_${k1}$) then
- res = 0.0
+ if(scale == zero) then
+ res = zero
  else if(x < loc .or. x > (loc + scale)) then
- res = 0.0
+ res = zero
  else
- res = 1.0 / scale
+ res = one / scale
  end if
  end function pdf_unif_${t1[0]}$${k1}$
 
@@ -402,17 +403,17 @@ contains
  elemental function pdf_unif_${t1[0]}$${k1}$(x, loc, scale) result(res)
 
  ${t1}$, intent(in) :: x, loc, scale
- real :: res
- real(${k1}$) :: tr, ti
+ real(${k1}$) :: res, tr, ti
+ real(${k1}$), parameter :: zero = 0.0_${k1}$, one = 1.0_${k1}$
 
  tr = loc % re + scale % re; ti = loc % im + scale % im
- if(scale == (0.0_${k1}$,0.0_${k1}$)) then
- res = 0.0
+ if(scale == (zero, zero)) then
+ res = zero
  else if((x % re >= loc % re .and. x % re <= tr) .and. &
  (x % im >= loc % im .and. x % im <= ti)) then
- res = 1.0 / (scale % re * scale % im)
+ res = one / (scale % re * scale % im)
  else
- res = 0.0
+ res = zero
  end if
  end function pdf_unif_${t1[0]}$${k1}$
 
@@ -445,16 +446,17 @@ contains
  elemental function cdf_unif_${t1[0]}$${k1}$(x, loc, scale) result(res)
 
  ${t1}$, intent(in) :: x, loc, scale
- real :: res
+ ${t1}$ :: res
+ ${t1}$, parameter :: zero = 0.0_${k1}$, one = 1.0_${k1}$
 
- if(scale == 0.0_${k1}$) then
- res = 0.0
+ if(scale == zero) then
+ res = zero
  else if(x < loc) then
- res = 0.0
+ res = zero
  else if(x >= loc .and. x <= (loc + scale)) then
  res = (x - loc) / scale
  else
- res = 1.0
+ res = one
  end if
  end function cdf_unif_${t1[0]}$${k1}$
 
@@ -466,29 +468,30 @@ contains
  elemental function cdf_unif_${t1[0]}$${k1}$(x, loc, scale) result(res)
 
  ${t1}$, intent(in) :: x, loc, scale
- real :: res
+ real(${k1}$) :: res
+ real(${k1}$), parameter :: zero = 0.0_${k1}$, one = 1.0_${k1}$
  logical :: r1, r2, i1, i2
 
- if(scale == (0.0_${k1}$,0.0_${k1}$)) then
- res = 0.0
+ if(scale == (zero, zero)) then
+ res = zero
  return
  end if
  r1 = x % re < loc % re
  r2 = x % re > (loc % re + scale % re)
  i1 = x % im < loc % im
  i2 = x % im > (loc % im + scale % im)
  if(r1 .or. i1) then
- res = 0.0
+ res = zero
  else if((.not. r1) .and. (.not. r2) .and. i2) then
  res = (x % re - loc % re) / scale % re
  else if((.not. i1) .and. (.not. i2) .and. r2) then
  res = (x % im - loc % im) / scale % im
  else if((.not. r1) .and. (.not. r2) .and. (.not. i1) .and. (.not. i2)) &
  then
- res = (x % re - loc % re) * (x % im - loc % im) /  &
-  (scale % re * scale % im)
+ res = ((x % re - loc % re) / scale % re) * ((x % im - loc % im) / &
+ scale % im)
  else if(r2 .and. i2)then
- res = 1.0
+ res = one
  end if
  end function cdf_unif_${t1[0]}$${k1}$
 

src/tests/stats/test_distribution_uniform.fypp

@@ -207,16 +207,18 @@ contains
  subroutine test_uni_pdf_${t1[0]}$${k1}$
  ${t1}$ :: x1, x2(3,4), loc, scale
  integer :: seed, get, i
- real :: res(3,5)
  #:if t1[0] == "i"
  #! for integer type
+ real :: res(3, 5)
  real, parameter :: ans(15) = [(1.96078438E-02, i=1,15)]
  #:elif t1[0] == "r"
  #! for real type
- real, parameter :: ans(15) = [(0.5, i=1,15)]
+ ${t1}$ :: res(3, 5)
+ ${t1}$, parameter :: ans(15) = [(0.5_${k1}$, i=1,15)]
  #:else
  #! for complex type
- real, parameter :: ans(15) = [(1.0, i=1,15)]
+ real(${k1}$) :: res(3, 5)
+ real(${k1}$), parameter :: ans(15) = [(1.0_${k1}$, i=1,15)]
  #:endif
 
  print *, "Test pdf_uniform_${t1[0]}$${k1}$"
@@ -236,8 +238,15 @@ contains
  x2 = reshape(uni_rvs(loc, scale, 12), [3,4])
  res(:,1) = uni_pdf(x1, loc, scale)
  res(:, 2:5) = uni_pdf(x2, loc, scale)
+ #:if t1[0] == "i"
+ #! for integer type
  call check(all(abs(res - reshape(ans,[3,5])) < sptol), &
  msg = "pdf_uniform_${t1[0]}$${k1}$ failed", warn=warn)
+ #:else
+ #! for real and complex types
+ call check(all(abs(res - reshape(ans,[3,5])) < ${k1}$tol), &
+ msg = "pdf_uniform_${t1[0]}$${k1}$ failed", warn=warn)
+ #:endif
  end subroutine test_uni_pdf_${t1[0]}$${k1}$
 
  #:endfor
@@ -247,47 +256,73 @@ contains
  #:for k1, t1 in ALL_KINDS_TYPES
  subroutine test_uni_cdf_${t1[0]}$${k1}$
  ${t1}$ :: x1, x2(3,4), loc, scale
- real :: res(3,5)
  integer :: seed, get
  #:if k1 == "int8"
+ real :: res(3,5)
  real, parameter :: ans(15) = [0.435643554, 0.435643554, 0.435643554, &
  0.702970326, 0.653465331, 0.485148519, &
  0.386138618, 0.386138618, 0.336633652, &
  0.277227730, 0.237623766, 0.524752498, &
  0.732673287, 0.534653485, 0.415841579]
  #:elif k1 == "int16"
+ real :: res(3,5)
  real, parameter :: ans(15) = [0.178217828, 0.178217828, 0.178217828, &
  0.465346545, 0.673267305, 0.247524753, &
  0.158415839, 0.792079210, 0.742574275, &
  0.574257433, 0.881188095, 0.663366318, &
  0.524752498, 0.623762369, 0.178217828]
  #:elif k1 == "int32"
+ real :: res(3,5)
  real, parameter :: ans(15) = [0.732673287, 0.732673287, 0.732673287, &
  0.722772300, 0.792079210, 5.94059415E-02,&
  0.841584146, 0.405940592, 0.960396051, &
  0.534653485, 0.782178223, 0.861386120, &
  0.564356446, 0.613861382, 0.306930691]
  #:elif k1 == "int64"
+ real :: res(3,5)
  real, parameter :: ans(15) = [0.455445558, 0.455445558, 0.455445558, &
  0.277227730, 0.455445558, 0.930693090, &
  0.851485133, 0.623762369, 5.94059415E-02,&
  0.693069279, 0.544554472, 0.207920790, &
  0.306930691, 0.356435657, 0.128712878]
  #:elif t1[0] == "r"
  #! for real type
- real, parameter :: ans(15) = [0.170192942, 0.170192942, 0.170192942, &
- 0.276106149, 0.754930079, 0.406620681, &
- 0.187742814, 0.651605546, 0.934733927, &
- 0.151271492, 0.987674534, 0.130533904, &
- 0.106271908, 9.27578658E-02, 0.203399420]
+ ${t1}$ :: res(3,5)
+ ${t1}$, parameter :: ans(15) = &
+ [0.170192944297557408050991512027394492_${k1}$, &
+ 0.170192944297557408050991512027394492_${k1}$, &
+ 0.170192944297557408050991512027394492_${k1}$, &
+ 0.276106146274646191418611351764411665_${k1}$, &
+ 0.754930097473875072466853453079238534_${k1}$, &
+ 0.406620682573118008562573777453508228_${k1}$, &
+ 0.187742819191801080247472555129206739_${k1}$, &
+ 0.651605526090507591874256831943057477_${k1}$, &
+ 0.934733949732104885121941606485052034_${k1}$, &
+ 0.151271491851613287815681019310432021_${k1}$, &
+ 0.987674522797719611766353864368284121_${k1}$, &
+ 0.130533899463404684526679488953959662_${k1}$, &
+ 0.106271905921876880229959283497009892_${k1}$, &
+ 9.27578652240113182836367400341259781E-0002_${k1}$, &
+ 0.203399426853420439709196898547816090_${k1}$]
  #:else
  #! for complex type
- real, parameter :: ans(15) = [4.69913185E-02, 4.69913185E-02, &
- 4.69913185E-02, 0.306970179, 0.122334257,&
- 0.141398594, 0.128925011, 9.85755492E-03,&
- 8.16527531E-02, 0.163921610, &
- 7.81712309E-02, 0.446415812, &
- 5.31753292E-04, 0.101455867, 0.155276477]
+ real(${k1}$) :: res(3,5)
+ real(${k1}$), parameter :: ans(15) = &
+ [4.69913179731340971083526490627998168E-0002_${k1}$, &
+ 4.69913179731340971083526490627998168E-0002_${k1}$, &
+ 4.69913179731340971083526490627998168E-0002_${k1}$, &
+ 0.306970191529817593217448363707416739_${k1}$, &
+ 0.122334258469188588238756489506609443_${k1}$, &
+ 0.141398599060326408705075175176932616_${k1}$, &
+ 0.128925006861443729884744412460848140_${k1}$, &
+ 9.85755512660026594506599410104817938E-0003_${k1}$, &
+ 8.16527497645585445208592050401597260E-0002_${k1}$, &
+ 0.163921605454974749736935624944263178_${k1}$, &
+ 7.81712317416218284294000447064256003E-0002_${k1}$, &
+ 0.446415807686727375005224206895756087_${k1}$, &
+ 5.31753272901435018841591264266743165E-0004_${k1}$, &
+ 0.101455865191097416942685556683943046_${k1}$, &
+ 0.155276470981788516449112374966730510_${k1}$]
  #:endif
 
  print *, "Test cdf_uniform_${t1[0]}$${k1}$"
@@ -307,8 +342,15 @@ contains
  x2 = reshape(uni_rvs(loc, scale, 12), [3,4])
  res(:,1) = uni_cdf(x1, loc, scale)
  res(:, 2:5) = uni_cdf(x2, loc, scale)
+ #:if t1[0] == "i"
+ #! for integer type
  call check(all(abs(res - reshape(ans,[3,5])) < sptol), &
  msg = "cdf_uniform_${t1[0]}$${k1}$ failed", warn=warn)
+ #:else
+ #! for real and complex types
+ call check(all(abs(res - reshape(ans,[3,5])) < ${k1}$tol), &
+ msg = "cdf_uniform_${t1[0]}$${k1}$ failed", warn=warn)
+ #:endif
  end subroutine test_uni_cdf_${t1[0]}$${k1}$
 
  #:endfor