Procedures for numerical operations. More...

Functions/Subroutines
elemental real(double) function	reldiff (x1, x2)
	Return the relative difference between two numbers: dx/<x> - double precision.

elemental real function	reldiff_sp (x1, x2)
	Return the relative difference between two numbers: dx/<x> - single precision version.

elemental logical function	deq (x1, x2, eps)
	Test whether two double-precision variables are equal to better than a given value (default: 2x machine precision)

elemental logical function	deq0 (x0, eps)
	Test whether a double-precision variable is equal to zero better than a given value (default: 2x machine precision)

elemental logical function	seq (x1, x2, eps)
	Test whether two single-precision variables are equal to better than a given value (default: 2x machine precision)

elemental logical function	seq0 (x0, eps)
	Test whether a single-precision variable ais equal to zero better than a given value (default: 2x machine precision)

elemental logical function	dne (x1, x2, eps)
	Test whether two double-precision variables are unequal to better than a given value (default: 2x machine precision)

elemental logical function	dne0 (x0, eps)
	Test whether a double-precision variable is unequal to zero better than a given value (default: 2x machine precision)

elemental logical function	sne (x1, x2, eps)
	Test whether two single-precision variables are unequal to better than a given value (default: 2x machine precision)

elemental logical function	sne0 (x0, eps)
	Test whether a single-precision variable is unequal to zero better than a given value (default: 2x machine precision)

elemental logical function	isinf (x0)
	Test whether a double-precision variable is (+/-) infinite.

elemental logical function	sisinf (x0)
	Test whether a single-precision variable is (+/-) infinite.

elemental logical function	isanan (x0)
	Test whether a double-precision variable is not a number (NaN)

elemental logical function	sisanan (x0)
	Test whether a single-precision variable is not a number (NaN)

elemental logical function	isnormal (x0)
	Test whether a double-precision variable is normal (not +/- Inf, not NaN)

elemental logical function	sisnormal (x0)
	Test whether a single-precision variable is normal (not +/- Inf, not NaN)

pure subroutine	plot_ranges (plx, ply, ddx, ddy, xmin, xmax, ymin, ymax, dx, dy)
	Determine plot ranges from data arrays in x and y, and relative margins.

elemental integer function	mod1 (number, period)
	A modulo function to wrap array indices properly in Fortran ([1,N], rather than [0,N-1])

integer function	gcd2 (a, b)
	Compute the greatest common divisor (GCD) of two positive integers using the Euclidean algoritm.

integer function	gcd (array)
	Computes the greatest common divisor (GCD) for an array of positive integers using the Euclidean algoritm.

integer function	lcm (array)
	Computes the least common multiplier (LCM) for an array of positive integers.

Detailed Description

Procedures for numerical operations.

Function/Subroutine Documentation

◆ deq()

elemental logical function sufr_numerics::deq	(	real(double), intent(in)	x1,
		real(double), intent(in)	x2,
		real(double), intent(in), optional	eps )

Test whether two double-precision variables are equal to better than a given value (default: 2x machine precision)

Parameters

x1	First number
x2	Second number
eps	Maximum absolute difference allowed (optional - default: twice the machine precision)

Return values

deq	The two numers are equal (true/false)

Definition at line 89 of file numerics.f90.

References deq(), and sufr_kinds::double.

Referenced by deq(), dne(), sufr_interpolate::locate_value_in_array(), sufr_solvers::minimum_solver(), plot_ranges(), sufr_statistics::prob_range(), and sufr_solvers::root_solver().

Here is the call graph for this function:

◆ deq0()

elemental logical function sufr_numerics::deq0	(	real(double), intent(in)	x0,
		real(double), intent(in), optional	eps )

Test whether a double-precision variable is equal to zero better than a given value (default: 2x machine precision)

Parameters

x0	Number to check
eps	Maximum absolute difference allowed (optional - default: twice the machine precision)

Return values

deq0	The number is equal to 0 (true/false)

Definition at line 117 of file numerics.f90.

References deq0(), and sufr_kinds::double.

Referenced by deq0(), dne0(), sufr_time2string::hdm(), sufr_time2string::hhms(), sufr_time2string::hm(), sufr_time2string::hmm(), sufr_time2string::hms(), sufr_time2string::hms_s(), sufr_time2string::hms_sss(), sufr_fitting::nonlin_fit_yerr(), sufr_time2string::um(), sufr_time2string::umm(), sufr_time2string::ums(), sufr_time2string::wum(), sufr_time2string::wumm(), sufr_time2string::wums(), and sufr_time2string::wums_s().

Here is the call graph for this function:

◆ dne()

elemental logical function sufr_numerics::dne	(	real(double), intent(in)	x1,
		real(double), intent(in)	x2,
		real(double), intent(in), optional	eps )

Test whether two double-precision variables are unequal to better than a given value (default: 2x machine precision)

Parameters

x1	First number
x2	Second number
eps	Maximum absolute difference allowed (optional - default: twice the machine precision)

Return values

dne	The two numbers are unequal (true/false)

Definition at line 201 of file numerics.f90.

References deq(), dne(), and sufr_kinds::double.

Referenced by dne().

Here is the call graph for this function:

◆ dne0()

elemental logical function sufr_numerics::dne0	(	real(double), intent(in)	x0,
		real(double), intent(in), optional	eps )

Test whether a double-precision variable is unequal to zero better than a given value (default: 2x machine precision)

Parameters

x0	Number to check
eps	Maximum absolute difference allowed (optional - default: twice the machine precision)

Return values

dne0	The number is unequal to 0 (true/false)

Definition at line 223 of file numerics.f90.

References deq0(), dne0(), and sufr_kinds::double.

Referenced by dne0().

Here is the call graph for this function:

◆ gcd()

integer function sufr_numerics::gcd ( integer, dimension(:), intent(in) array )

Computes the greatest common divisor (GCD) for an array of positive integers using the Euclidean algoritm.

Parameters

array The array of positive integers

Return values

gcd	The GCD of the integers

Note: This function uses gcd2() iteratively

See also: https://en.wikipedia.org/wiki/Euclidean_algorithm#Implementations

Definition at line 519 of file numerics.f90.

References gcd(), gcd2(), and sufr_system::quit_program_error().

Referenced by gcd().

Here is the call graph for this function:

◆ gcd2()

integer function sufr_numerics::gcd2	(	integer, intent(in)	a,
		integer, intent(in)	b )

Compute the greatest common divisor (GCD) of two positive integers using the Euclidean algoritm.

Parameters

a	Positive integer 1
b	Positive integer 2

Return values

gcd2	The GCD of the two integers

See also: https://en.wikipedia.org/wiki/Euclidean_algorithm#Implementations

Definition at line 479 of file numerics.f90.

References gcd2(), sufr_system::quit_program_error(), and sufr_system::swapint().

Referenced by gcd(), and gcd2().

Here is the call graph for this function:

◆ isanan()

elemental logical function sufr_numerics::isanan ( real(double), intent(in) x0 )

Test whether a double-precision variable is not a number (NaN)

Parameters

x0	Number to check

Return values

isanan The value is a NaN (true/false)

Definition at line 327 of file numerics.f90.

References sufr_kinds::double, and isanan().

Referenced by isanan(), and isnormal().

Here is the call graph for this function:

◆ isinf()

elemental logical function sufr_numerics::isinf ( real(double), intent(in) x0 )

Test whether a double-precision variable is (+/-) infinite.

Parameters

x0	Number to check

Return values

isinf The number is infinite (true/false)

Definition at line 295 of file numerics.f90.

References sufr_kinds::double, and isinf().

Referenced by isinf(), and isnormal().

Here is the call graph for this function:

◆ isnormal()

elemental logical function sufr_numerics::isnormal ( real(double), intent(in) x0 )

Test whether a double-precision variable is normal (not +/- Inf, not NaN)

Parameters

x0	Number to check

Return values

isnormal This is a normal value (true/false)

Definition at line 359 of file numerics.f90.

References sufr_kinds::double, isanan(), isinf(), and isnormal().

Referenced by isnormal().

Here is the call graph for this function:

◆ lcm()

integer function sufr_numerics::lcm ( integer, dimension(:), intent(in) array )

Computes the least common multiplier (LCM) for an array of positive integers.

Parameters

array The array of positive integers

Return values

lcm	The LCM of the integers

See also: https://en.wikipedia.org/wiki/Least_common_multiple#A_simple_algorithm

Definition at line 544 of file numerics.f90.

References lcm(), and sufr_system::quit_program_error().

Referenced by lcm().

Here is the call graph for this function:

◆ mod1()

elemental integer function sufr_numerics::mod1	(	integer, intent(in)	number,
		integer, intent(in)	period )

A modulo function to wrap array indices properly in Fortran ([1,N], rather than [0,N-1])

   Since array indices in Fortran run from 1 to N, and the mod() function returns 0 to N-1 which can be used as an array
   index directly in e.g. C, mod1() provides that service in Fortran.

Parameters

number	Number to take the modulo of
period	Period to wrap around

Return values

mod1	Modulo of the given number with the given period

Definition at line 457 of file numerics.f90.

References mod1().

Referenced by mod1().

Here is the call graph for this function:

◆ plot_ranges()

pure subroutine sufr_numerics::plot_ranges	(	real(double), dimension(:), intent(in)	plx,
		real(double), dimension(:), intent(in)	ply,
		real(double), intent(in)	ddx,
		real(double), intent(in)	ddy,
		real(double), intent(out)	xmin,
		real(double), intent(out)	xmax,
		real(double), intent(out)	ymin,
		real(double), intent(out)	ymax,
		real(double), intent(out), optional	dx,
		real(double), intent(out), optional	dy )

Determine plot ranges from data arrays in x and y, and relative margins.

Parameters

plx	Array contaiting x values
ply	Array contaiting y values
ddx	Relative margin in x
ddy	Relative margin in y
xmin	Minimum of plot range in x (output)
xmax	Maximum of plot range in x (output)
ymin	Minimum of plot range in y (output)
ymax	Maximum of plot range in y (output)
dx	Range width of x (xmax-xmin; output, optional)
dy	Range wifth of y (ymax-ymin; output, optional)

Definition at line 404 of file numerics.f90.

References deq(), and sufr_kinds::double.

Here is the call graph for this function:

◆ reldiff()

elemental real(double) function sufr_numerics::reldiff	(	real(double), intent(in)	x1,
		real(double), intent(in)	x2 )

Return the relative difference between two numbers: dx/<x> - double precision.

Parameters

x1	First number
x2	Second number

Return values

reldiff The relative difference

Definition at line 37 of file numerics.f90.

References sufr_kinds::dbl, sufr_kinds::double, and reldiff().

Referenced by reldiff(), and reldiff_sp().

Here is the call graph for this function:

◆ reldiff_sp()

elemental real function sufr_numerics::reldiff_sp	(	real, intent(in)	x1,
		real, intent(in)	x2 )

Return the relative difference between two numbers: dx/<x> - single precision version.

Parameters

x1	First number
x2	Second number

Return values

reldiff_sp The relative difference

Definition at line 67 of file numerics.f90.

References reldiff(), and reldiff_sp().

Referenced by reldiff_sp().

Here is the call graph for this function:

◆ seq()

elemental logical function sufr_numerics::seq	(	real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(in), optional	eps )

Test whether two single-precision variables are equal to better than a given value (default: 2x machine precision)

Parameters

x1	First number
x2	Second number
eps	Maximum absolute difference allowed (optional - default: twice the machine precision)

Return values

seq	The two numers are equal (true/false)

Definition at line 147 of file numerics.f90.

References seq().

Referenced by seq(), and sne().

Here is the call graph for this function:

◆ seq0()

elemental logical function sufr_numerics::seq0	(	real, intent(in)	x0,
		real, intent(in), optional	eps )

Test whether a single-precision variable ais equal to zero better than a given value (default: 2x machine precision)

Parameters

x0	Number to check
eps	Maximum absolute difference allowed (optional - default: twice the machine precision)

Return values

seq0	The number is equal to 0 (true/false)

Definition at line 173 of file numerics.f90.

References seq0().

Referenced by seq0(), and sne0().

Here is the call graph for this function:

◆ sisanan()

elemental logical function sufr_numerics::sisanan ( real, intent(in) x0 )

Test whether a single-precision variable is not a number (NaN)

Parameters

x0	Number to check

Return values

sisanan The value is a NaN (true/false)

Definition at line 343 of file numerics.f90.

References sisanan().

Referenced by sisanan(), and sisnormal().

Here is the call graph for this function:

◆ sisinf()

elemental logical function sufr_numerics::sisinf ( real, intent(in) x0 )

Test whether a single-precision variable is (+/-) infinite.

Parameters

x0	Number to check

Return values

sisinf The number is infinite (true/false)

Definition at line 311 of file numerics.f90.

References sisinf().

Referenced by sisinf(), and sisnormal().

Here is the call graph for this function:

◆ sisnormal()

elemental logical function sufr_numerics::sisnormal ( real, intent(in) x0 )

Test whether a single-precision variable is normal (not +/- Inf, not NaN)

Parameters

x0	Number to check

Return values

sisnormal This is a normal value (true/false)

Definition at line 375 of file numerics.f90.

References sisanan(), sisinf(), and sisnormal().

Referenced by sisnormal().

Here is the call graph for this function:

◆ sne()

elemental logical function sufr_numerics::sne	(	real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(in), optional	eps )

Test whether two single-precision variables are unequal to better than a given value (default: 2x machine precision)

Parameters

x1	First number
x2	Second number
eps	Maximum absolute difference allowed (optional - default: twice the machine precision)

Return values

sne	The two numers are unequal (true/false)

Definition at line 248 of file numerics.f90.

References seq(), and sne().

Referenced by sne().

Here is the call graph for this function:

◆ sne0()

elemental logical function sufr_numerics::sne0	(	real, intent(in)	x0,
		real, intent(in), optional	eps )

Test whether a single-precision variable is unequal to zero better than a given value (default: 2x machine precision)

Parameters

x0	Number to check
eps	Maximum absolute difference allowed (optional - default: twice the machine precision)

Return values

sne0	The number is unequal to 0 (true/false)

Definition at line 270 of file numerics.f90.

References seq0(), and sne0().

Referenced by sne0().

Here is the call graph for this function:

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ deq()

◆ deq0()

◆ dne()

◆ dne0()

◆ gcd()

◆ gcd2()

◆ isanan()

◆ isinf()

◆ isnormal()

◆ lcm()

◆ mod1()

◆ plot_ranges()

◆ reldiff()

◆ reldiff_sp()

◆ seq()

◆ seq0()

◆ sisanan()

◆ sisinf()

◆ sisnormal()

◆ sne()

◆ sne0()