array_utils Module Reference

This module provides convenience routines to operate or get information on arrays. More...

Data Types
interface	save_array
	save_array Stores an 1D or 2D array to file or stdout More...

Functions/Subroutines
logical function, public	allclose (a, b, rtol, atol)
	allclose returns True if two arrays are element-wise equal within a tolerance.
real(dp) function, dimension(:), allocatable, public	merge_sorted (x1, x2, tolerance)
	This function creates a sorted array with values from two input sorted arrays.
real(dp) function, public	std (x)
	std Computes the standard deviation of the array.
real(dp) function, public	mean (x)
	mean Computes the arithmetic mean of the array.

Detailed Description

This module provides convenience routines to operate or get information on arrays.

Function/Subroutine Documentation

allclose()

logical function, public allclose	(	real(dp), dimension(:), intent(in)	a,
		real(dp), dimension(size(a)), intent(in)	b,
		real(dp), intent(in), optional	rtol,
		real(dp), intent(in), optional	atol )

allclose returns True if two arrays are element-wise equal within a tolerance.

Very similar to Numpy allclose

The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.
If the following equation
abs(a - b) <= (atol + rtol * absolute(b))
is element-wise True, then allclose returns .True.

The above equation is not symmetric in a and b, so that allclose(a, b) might be different from allclose(b, a) in some rare cases.

Examples:

allclose([1e10,1e-7], [1.00001e10,1e-8])
! .False.
allclose([1e10,1e-8], [1.00001e10,1e-9])
! .True.
allclose([1e10,1e-8], [1.0001e10,1e-9])
! .False.
!

Returns

True if the two arrays are equal within the given tolerance; False otherwise.

Parameters

[in]	a	Array
[in]	b	Array
[in]	rtol	The relative tolerance parameter. Default = 1.e-5
[in]	atol	The absolute tolerance parameter. Default = 1.e-8

mean()

real(dp) function, public mean

(

real(dp), dimension(:), intent(in)

x

)

mean Computes the arithmetic mean of the array.

Note

the mean is basically: sum(x)/size(x)

Returns

Mean value

Parameters

[in]

x

Input array of real values

Referenced by histograms::histogram(), and std().

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merge_sorted()

real(dp) function, dimension(:), allocatable, public merge_sorted	(	real(dp), dimension(:), intent(in), target	x1,
		real(dp), dimension(:), intent(in), target	x2,
		real(dp), intent(in), optional	tolerance )

This function creates a sorted array with values from two input sorted arrays.

Equal values (within tolerance) are only included once

Examples:

real(dp), dimension(:), allocatable :: a
real(dp), dimension(:), allocatable :: b
real(dp), dimension(:), allocatable :: c
integer :: j
a = [1.9999999999_dp, 2._dp, 2._dp, 3._dp]
b = [-1._dp, 2._dp, 3._dp, 4._dp]
print *, ""
print '(A)', repeat('-', 30)//' a '//repeat('-', 30)
print "(4(g0.12,1x))", a
print '(A)', repeat('-', 30)//' b '//repeat('-', 30)
print "(4(g0.12,1x))", b
c = merge_sorted(a, b)
j = 30 - int(len("merge_sorted(a,b)") / 2._dp)
print '(A)', repeat('-', 60)
print '(A)', repeat('-', j)//' merge_sorted(a,b) '//repeat('-', j)
print "(4(g0.12,1x))", c
c = merge_sorted(a, b, 1.e-6_dp)
j = 30 - int(len("merge_sorted(a,b,1.e-6)") / 2._dp)
print '(A)', repeat('-', j)//' merge_sorted(a,b,1.e-6) '//repeat('-', j)
print "(4(g0.12,1x))", c
c = merge_sorted(a, b, -1.e-6_dp)
j = 30 - int(len("merge_sorted(a,b,-1.e-6)") / 2._dp)
print '(A)', repeat('-', j)//' merge_sorted(a,b,-1.e-6) '//repeat('-', j)
print "(4(g0.12,1x))", c
!
! Outputs:
!
!  ------------------------------ a ------------------------------
!  1.99999999990 2.00000000000 2.00000000000 3.00000000000
!  ------------------------------ b ------------------------------
!  -1.00000000000 2.00000000000 3.00000000000 4.00000000000
!  ------------------------------------------------------------
!  ---------------------- merge_sorted(a,b) ----------------------
!  -1.00000000000 1.99999999990 2.00000000000 3.00000000000
!  4.00000000000
!  ------------------- merge_sorted(a,b,1.e-6) -------------------
!  -1.00000000000 1.99999999990 3.00000000000 4.00000000000
!  ------------------ merge_sorted(a,b,-1.e-6) ------------------
!  -1.00000000000 1.99999999990 2.00000000000 2.00000000000
!  2.00000000000 3.00000000000 3.00000000000 4.00000000000
!

Parameters

[in]	x1	First array
[in]	x2	Second array
[in]	tolerance	Defines the minimum value by which two numbers are considered different

Returns

Output array with values from both x1 and x2

References basic::small.

std()

real(dp) function, public std

(

real(dp), dimension(:), intent(in)

x

)

std Computes the standard deviation of the array.

Note

: Basically: sqrt(mean(x - mean(x))* alfa ) with alfa= (N/(N-1))

Returns

Standard deviation

Parameters

[in]

x

Input array of real values

References mean().

Referenced by histograms::histogram().

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