m_maths – Fortran Program

Math routines

Used By

Interfaces

crossproduct cumprod cumsum fastTwoDiff fastTwoSum geometricMean mean median norm1 normI project trimmedmean twoDiff twoSum std variance

Interfaces

public interface crossproduct

Compute the cross product between two arrays of length 2 or 3

public function crossproduct_r1D(a, b) result(res)

Interfaced with crossproduct()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: a(3)
1D Array

real(kind=r32), intent(in) :: b(3)
1D Array

Return Value real(kind=r32) (3)

cross product
public function crossproduct_d1D(a, b) result(res)

Interfaced with crossproduct()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: a(3)
1D Array

real(kind=r64), intent(in) :: b(3)
1D Array

Return Value real(kind=r64) (3)

cross product

Type	Intent	Optional	Attributes		Name
real(kind=r32),	intent(in)			::	a(3)	1D Array
real(kind=r32),	intent(in)			::	b(3)	1D Array

Type	Intent	Optional	Attributes		Name
real(kind=r64),	intent(in)			::	a(3)	1D Array
real(kind=r64),	intent(in)			::	b(3)	1D Array

public interface cumprod

Compute the variance of an array

public function cumprod_r1D(this) result(res)

Interfaced with cumprod()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)
1D array

Return Value real(kind=r32) (size(this))

Cumulative product
public function cumprod_d1D(this) result(res)

Interfaced with cumprod()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)
1D array

Return Value real(kind=r64) (size(this))

Cumulative product
public function cumprod_i1D(this) result(res)

Interfaced with cumprod()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)
1D array

Return Value integer(kind=i32) (size(this))

Cumulative product
public function cumprod_id1D(this) result(res)

Interfaced with cumprod()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)
1D array

Return Value integer(kind=i64) (size(this))

Cumulative product

public interface cumsum

Compute the variance of an array

public function cumsum_r1D(this) result(res)

Interfaced with cumsum()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)
1D array

Return Value real(kind=r32) (size(this))

Cumulative sum
public function cumsum_d1D(this) result(res)

Interfaced with cumsum()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)
1D array

Return Value real(kind=r64) (size(this))

Cumulative sum
public function cumsum_i1D(this) result(res)

Interfaced with cumsum()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)
1D array

Return Value integer(kind=i32) (size(this))

Cumulative sum
public function cumsum_id1D(this) result(res)

Interfaced with cumsum()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)
1D array

Return Value integer(kind=i64) (size(this))

Cumulative sum

public interface fastTwoDiff

Compute the difference two numbers and compute the numerical round-off error. See Shewchuk 1997 Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates This should only be used if you know that the magnitude of a is greater than or equal to b, otherwise, you should use the slower twoDiff routine

public function fastTwoDiff_r(a, b) result(res)

Interfaced with fastTwoDiff()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r32),	intent(in)			::	a	First number
real(kind=r32),	intent(in)			::	b	Second number

Return Value real(kind=r32) (2)

Result and its error

public function fastTwoDiff_d(a, b) result(res)

Interfaced with fastTwoDiff()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r64),	intent(in)			::	a	First number
real(kind=r64),	intent(in)			::	b	Second number

Return Value real(kind=r64) (2)

Result and its error

public interface fastTwoSum

Compute the sum of two numbers and compute the numerical round-off error. See Shewchuk 1997 Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates This should only be used if you know that the magnitude of a is greater than or equal to b, otherwise, you should use the slower twoSum routine

public function fastTwoSum_r(a, b) result(res)

Interfaced with fastTwoSum()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r32),	intent(in)			::	a	First number
real(kind=r32),	intent(in)			::	b	Second number

Return Value real(kind=r32) (2)

Result and its error

public function fastTwoSum_d(a, b) result(res)

Interfaced with fastTwoSum()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r64),	intent(in)			::	a	First number
real(kind=r64),	intent(in)			::	b	Second number

Return Value real(kind=r64) (2)

Result and its error

public interface geometricMean

Compute the geometric mean of a vector

public function geometricMean_r1D(this) result(res)

Interfaced with geometricMean()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)

Return Value real(kind=r64)
public function geometricMean_d1D(this) result(res)

Interfaced with geometricMean()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)

Return Value real(kind=r64)
public function geometricMean_i1D(this) result(res)

Interfaced with geometricMean()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)

Return Value real(kind=r64)
public function geometricMean_id1D(this) result(res)

Interfaced with geometricMean()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)

Return Value real(kind=r64)

Type	Intent	Optional	Attributes		Name
real(kind=r32),	intent(in)			::	this(:)

Type	Intent	Optional	Attributes		Name
real(kind=r64),	intent(in)			::	this(:)

Type	Intent	Optional	Attributes		Name
integer(kind=i32),	intent(in)			::	this(:)

Type	Intent	Optional	Attributes		Name
integer(kind=i64),	intent(in)			::	this(:)

public interface mean

Compute the mean

public function mean_r1D(this) result(res)

Interfaced with mean()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

mean
public function mean_d1D(this) result(res)

Interfaced with mean()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

mean
public function mean_i1D(this) result(res)

Interfaced with mean()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

mean
public function mean_id1D(this) result(res)

Interfaced with mean()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

mean

public interface median

Compute the median of a set of numbers

public function median_r1D(this) result(res)

Interfaced with median()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)
1D array

Return Value real(kind=r32)

median
public function median_d1D(this) result(res)

Interfaced with median()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

median
public function median_i1D(this) result(res)

Interfaced with median()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

median
public function median_id1D(this) result(res)

Interfaced with median()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

median

public interface norm1

Compute the L1 norm of a set of numbers

public function norm1_r1D(this) result(res)

Interfaced with norm1()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)
1D array

Return Value real(kind=r32)

L1 norm
public function norm1_d1D(this) result(res)

Interfaced with norm1()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

L1 norm
public function norm1_i1D(this) result(res)

Interfaced with norm1()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

L1 norm
public function norm1_id1D(this) result(res)

Interfaced with norm1()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

L1 norm

public interface normI

Compute the Linfinity norm of a set of numbers

public function normI_r1D(this) result(res)

Interfaced with normI()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)
1D array

Return Value real(kind=r32)

Linfinity norm
public function normI_d1D(this) result(res)

Interfaced with normI()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

Linfinity norm
public function normI_i1D(this) result(res)

Interfaced with normI()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)
1D array

Return Value integer(kind=i32)

Linfinity norm
public function normI_id1D(this) result(res)

Interfaced with normI()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)
1D array

Return Value integer(kind=i64)

Linfinity norm

public interface project

Project a vector a onto vector b

public function project_r1D(a, b) result(c)

Interfaced with project()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r32),	intent(in)			::	a(:)	1D array
real(kind=r32),	intent(in)			::	b(size(a))	1D array

Return Value real(kind=r32) (size(a))

1D array

public function project_d1D(a, b) result(c)

Interfaced with project()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r64),	intent(in)			::	a(:)	1D array
real(kind=r64),	intent(in)			::	b(size(a))	1D array

Return Value real(kind=r64) (size(a))

1D array

public interface trimmedmean

Compute the Trimmed mean of an array, alpha is a percent value to trim from either end

public function trimmedmean_r1D(this, alpha) result(res)

Interfaced with trimmedmean()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r32),	intent(in)			::	this(:)	1D array
real(kind=r32),	intent(in)			::	alpha	Percentage to trim off each end

Return Value real(kind=r64)

trimmedmean

public function trimmedmean_d1D(this, alpha) result(res)

Interfaced with trimmedmean()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r64),	intent(in)			::	this(:)	1D array
real(kind=r64),	intent(in)			::	alpha	Percentage to trim off each end

Return Value real(kind=r64)

trimmedmean

public function trimmedmean_i1D(this, alpha) result(res)

Interfaced with trimmedmean()

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=i32),	intent(in)			::	this(:)	1D array
real(kind=r64),	intent(in)			::	alpha	Percentage to trim off each end

Return Value real(kind=r64)

trimmedmean

public function trimmedmean_id1D(this, alpha) result(res)

Interfaced with trimmedmean()

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=i64),	intent(in)			::	this(:)	1D array
real(kind=r64),	intent(in)			::	alpha	Percentage to trim off each end

Return Value real(kind=r64)

trimmedmean

public interface twoDiff

Compute the difference between two numbers and compute the numerical round-off error. See Shewchuk 1997 Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates If you know that the magnitude of a is greater than or equal to b, use fastTwoDiff

public function twoDiff_r(a, b) result(res)

Interfaced with twoDiff()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r32),	intent(in)			::	a	First number
real(kind=r32),	intent(in)			::	b	Second number

Return Value real(kind=r32) (2)

Result and its error

public function twoDiff_d(a, b) result(res)

Interfaced with twoDiff()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r64),	intent(in)			::	a	First number
real(kind=r64),	intent(in)			::	b	Second number

Return Value real(kind=r64) (2)

Result and its error

public interface twoSum

Compute the sum of two numbers and compute the numerical round-off error. See Shewchuk 1997 Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates If you know that the magnitude of a is greater than or equal to b, use fastTwoSum

public function twoSum_r(a, b) result(res)

Interfaced with twoSum()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r32),	intent(in)			::	a	First number in sum
real(kind=r32),	intent(in)			::	b	Second number in sum

Return Value real(kind=r32) (2)

The sum and its error

public function twoSum_d(a, b) result(res)

Interfaced with twoSum()

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=r64),	intent(in)			::	a	First number in sum
real(kind=r64),	intent(in)			::	b	Second number in sum

Return Value real(kind=r64) (2)

The sum and its error

public interface std

Compute the standard deviation of an array

public function std_r1D(this) result(res)

Interfaced with std()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

standard deviation
public function std_d1D(this) result(res)

Interfaced with std()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

standard deviation
public function std_i1D(this) result(res)

Interfaced with std()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

standard deviation
public function std_id1D(this) result(res)

Interfaced with std()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

standard deviation

public interface variance

Compute the variance of an array

public function variance_r1D(this) result(res)

Interfaced with variance()

Arguments

Type Intent Optional Attributes Name

real(kind=r32), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

variance
public function variance_d1D(this) result(res)

Interfaced with variance()

Arguments

Type Intent Optional Attributes Name

real(kind=r64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

variance
public function variance_i1D(this) result(res)

Interfaced with variance()

Arguments

Type Intent Optional Attributes Name

integer(kind=i32), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

variance
public function variance_id1D(this) result(res)

Interfaced with variance()

Arguments

Type Intent Optional Attributes Name

integer(kind=i64), intent(in) :: this(:)
1D array

Return Value real(kind=r64)

variance

m_maths Module

Interfaces

All Modules

Uses:

Used By

Interfaces

Interfaces

public interface crossproduct

public function crossproduct_r1D(a, b) result(res)

Arguments

Return Value real(kind=r32) (3)

public function crossproduct_d1D(a, b) result(res)

Arguments

Return Value real(kind=r64) (3)

public interface cumprod

public function cumprod_r1D(this) result(res)

Arguments

Return Value real(kind=r32) (size(this))

public function cumprod_d1D(this) result(res)

Arguments

Return Value real(kind=r64) (size(this))

public function cumprod_i1D(this) result(res)

Arguments

Return Value integer(kind=i32) (size(this))

public function cumprod_id1D(this) result(res)

Arguments

Return Value integer(kind=i64) (size(this))

public interface cumsum

public function cumsum_r1D(this) result(res)

Arguments

Return Value real(kind=r32) (size(this))

public function cumsum_d1D(this) result(res)

Arguments

Return Value real(kind=r64) (size(this))

public function cumsum_i1D(this) result(res)

Arguments

Return Value integer(kind=i32) (size(this))

public function cumsum_id1D(this) result(res)

Arguments

Return Value integer(kind=i64) (size(this))

public interface fastTwoDiff

public function fastTwoDiff_r(a, b) result(res)

Arguments

Return Value real(kind=r32) (2)

public function fastTwoDiff_d(a, b) result(res)

Arguments

Return Value real(kind=r64) (2)

public interface fastTwoSum

public function fastTwoSum_r(a, b) result(res)

Arguments

Return Value real(kind=r32) (2)

public function fastTwoSum_d(a, b) result(res)

Arguments

Return Value real(kind=r64) (2)

public interface geometricMean

public function geometricMean_r1D(this) result(res)

Arguments

Return Value real(kind=r64)

public function geometricMean_d1D(this) result(res)

Arguments

Return Value real(kind=r64)

public function geometricMean_i1D(this) result(res)

Arguments

Return Value real(kind=r64)

public function geometricMean_id1D(this) result(res)

Arguments

Return Value real(kind=r64)

public interface mean

public function mean_r1D(this) result(res)

Arguments

Return Value real(kind=r64)

public function mean_d1D(this) result(res)

Arguments

Return Value real(kind=r64)

public function mean_i1D(this) result(res)

Arguments

Return Value real(kind=r64)

public function mean_id1D(this) result(res)

Arguments

Return Value real(kind=r64)