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Commit 01b3fb9

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[stdlib_math] add arg/argd/argpi (#498)
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‎CHANGELOG.md

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@@ -16,6 +16,11 @@ Features available from the latest git source
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- new module `stdlib_io_npy`
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[#581](https://github.com/fortran-lang/stdlib/pull/581)
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- new procedures `save_npy`, `load_npy`
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- update module `stdlib_math`
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- new procedures `is_close` and `all_close`
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[#488](https://github.com/fortran-lang/stdlib/pull/488)
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- new procedures `arg`, `argd` and `argpi`
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[#498](https://github.com/fortran-lang/stdlib/pull/498)
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Changes to existing modules
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‎doc/specs/stdlib_math.md

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@@ -389,6 +389,129 @@ program demo_math_arange
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end program demo_math_arange
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```
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### `arg` - Computes the phase angle in radian of a complex scalar
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#### Status
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Experimental
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#### Class
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Elemental function.
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#### Description
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`arg` computes the phase angle (radian version) of `complex` scalar in the interval (-π,π].
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The angles in `θ` are such that `z = abs(z)*exp((0.0, θ))`.
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#### Syntax
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`result = [[stdlib_math(module):arg(interface)]](z)`
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#### Arguments
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`z`: Shall be a `complex` scalar/array.
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This is an `intent(in)` argument.
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#### Return value
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Returns the `real` type phase angle (radian version) of the `complex` argument `z`.
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Notes: Although the angle of the complex number `0` is undefined, `arg((0,0))` returns the value `0`.
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#### Example
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```fortran
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program demo_math_arg
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use stdlib_math, only: arg
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print *, arg((0.0, 0.0)) !! 0.0
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print *, arg((3.0, 4.0)) !! 0.927
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print *, arg(2.0*exp((0.0, 0.5))) !! 0.5
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end program demo_math_arg
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```
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### `argd` - Computes the phase angle in degree of a complex scalar
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#### Status
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Experimental
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#### Class
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Elemental function.
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#### Description
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`argd` computes the phase angle (degree version) of `complex` scalar in the interval (-180.0,180.0].
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The angles in `θ` are such that `z = abs(z)*exp((0.0, θ*π/180.0))`.
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#### Syntax
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`result = [[stdlib_math(module):argd(interface)]](z)`
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#### Arguments
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`z`: Shall be a `complex` scalar/array.
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This is an `intent(in)` argument.
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#### Return value
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Returns the `real` type phase angle (degree version) of the `complex` argument `z`.
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Notes: Although the angle of the complex number `0` is undefined, `argd((0,0))` returns the value `0`.
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#### Example
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```fortran
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program demo_math_argd
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use stdlib_math, only: argd
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print *, argd((0.0, 0.0)) !! 0.0
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print *, argd((3.0, 4.0)) !! 53.1°
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print *, argd(2.0*exp((0.0, 0.5))) !! 28.64°
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end program demo_math_argd
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```
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### `argpi` - Computes the phase angle in circular of a complex scalar
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#### Status
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Experimental
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#### Class
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Elemental function.
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#### Description
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`argpi` computes the phase angle (IEEE circular version) of `complex` scalar in the interval (-1.0,1.0].
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The angles in `θ` are such that `z = abs(z)*exp((0.0, θ*π))`.
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#### Syntax
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`result = [[stdlib_math(module):argpi(interface)]](z)`
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#### Arguments
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`z`: Shall be a `complex` scalar/array.
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This is an `intent(in)` argument.
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#### Return value
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Returns the `real` type phase angle (circular version) of the `complex` argument `z`.
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Notes: Although the angle of the complex number `0` is undefined, `argpi((0,0))` returns the value `0`.
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#### Example
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```fortran
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program demo_math_argpi
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use stdlib_math, only: argpi
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print *, argpi((0.0, 0.0)) !! 0.0
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print *, argpi((3.0, 4.0)) !! 0.295
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print *, argpi(2.0*exp((0.0, 0.5))) !! 0.159
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end program demo_math_argpi
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```
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### `is_close`
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#### Description
@@ -449,7 +572,6 @@ Returns a `logical` scalar/array.
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program demo_math_is_close
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use stdlib_math, only: is_close
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use stdlib_error, only: check
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real :: x(2) = [1, 2], y, NAN
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y = -3
@@ -514,7 +636,6 @@ Returns a `logical` scalar.
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program demo_math_all_close
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use stdlib_math, only: all_close
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use stdlib_error, only: check
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real :: x(2) = [1, 2], y, NAN
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complex :: z(4, 4)
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‎src/stdlib_math.fypp

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@@ -14,7 +14,7 @@ module stdlib_math
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public :: EULERS_NUMBER_QP
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#:endif
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public :: DEFAULT_LINSPACE_LENGTH, DEFAULT_LOGSPACE_BASE, DEFAULT_LOGSPACE_LENGTH
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public :: arange, is_close, all_close
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public :: arange, arg, argd, argpi, is_close, all_close
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integer, parameter :: DEFAULT_LINSPACE_LENGTH = 100
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integer, parameter :: DEFAULT_LOGSPACE_LENGTH = 50
@@ -27,6 +27,11 @@ module stdlib_math
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real(qp), parameter :: EULERS_NUMBER_QP = exp(1.0_qp)
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#:endif
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!> Useful constants `PI` for `argd/argpi`
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#:for k1 in REAL_KINDS
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real(kind=${k1}$), parameter :: PI_${k1}$ = acos(-1.0_${k1}$)
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#:endfor
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interface clip
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#:for k1, t1 in IR_KINDS_TYPES
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module procedure clip_${k1}$
@@ -296,6 +301,34 @@ module stdlib_math
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!> Version: experimental
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!>
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!> `arg` computes the phase angle in the interval (-π,π].
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!> ([Specification](../page/specs/stdlib_math.html#arg))
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interface arg
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#:for k1 in CMPLX_KINDS
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procedure :: arg_${k1}$
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#:endfor
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end interface arg
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!> Version: experimental
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!>
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!> `argd` computes the phase angle of degree version in the interval (-180.0,180.0].
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!> ([Specification](../page/specs/stdlib_math.html#argd))
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interface argd
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#:for k1 in CMPLX_KINDS
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procedure :: argd_${k1}$
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#:endfor
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end interface argd
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!> Version: experimental
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!>
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!> `argpi` computes the phase angle of circular version in the interval (-1.0,1.0].
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!> ([Specification](../page/specs/stdlib_math.html#argpi))
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interface argpi
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#:for k1 in CMPLX_KINDS
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procedure :: argpi_${k1}$
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#:endfor
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end interface argpi
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!> Returns a boolean scalar/array where two scalar/arrays are element-wise equal within a tolerance.
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!> ([Specification](../page/specs/stdlib_math.html#is_close))
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interface is_close
@@ -341,6 +374,34 @@ contains
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#:endfor
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#:for k1, t1 in CMPLX_KINDS_TYPES
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elemental function arg_${k1}$(z) result(result)
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${t1},ドル intent(in) :: z
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real(${k1}$) :: result
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result = merge(0.0_${k1},ドル atan2(z%im, z%re), z == (0.0_${k1},ドル 0.0_${k1}$))
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end function arg_${k1}$
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elemental function argd_${k1}$(z) result(result)
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${t1},ドル intent(in) :: z
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real(${k1}$) :: result
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result = merge(0.0_${k1},ドル atan2(z%im, z%re), z == (0.0_${k1},ドル 0.0_${k1}$)) &
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*180.0_${k1}$/PI_${k1}$
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end function argd_${k1}$
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elemental function argpi_${k1}$(z) result(result)
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${t1},ドル intent(in) :: z
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real(${k1}$) :: result
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result = merge(0.0_${k1},ドル atan2(z%im, z%re), z == (0.0_${k1},ドル 0.0_${k1}$)) &
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/PI_${k1}$
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end function argpi_${k1}$
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#:endfor
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#:for k1, t1 in INT_KINDS_TYPES
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!> Returns the greatest common divisor of two integers of kind ${k1}$
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!> using the Euclidean algorithm.
@@ -361,4 +422,5 @@ contains
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end function gcd_${k1}$
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#:endfor
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end module stdlib_math

‎src/tests/math/Makefile.manual

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@@ -9,5 +9,4 @@ PROGS_SRC = test_linspace.f90 test_logspace.f90 \
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$(SRCGEN): %.f90: %.fypp ../../common.fypp
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fypp -I../.. $(FYPPFLAGS) $< $@
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include ../Makefile.manual.test.mk

‎src/tests/math/test_stdlib_math.fypp

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@@ -4,11 +4,15 @@
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module test_stdlib_math
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use testdrive, only : new_unittest, unittest_type, error_type, check, skip_test
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use stdlib_math, only: clip, is_close, all_close
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use stdlib_math, only: clip, arg, argd, argpi, arange, is_close, all_close
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use stdlib_kinds, only: int8, int16, int32, int64, sp, dp, xdp, qp
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implicit none
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1111
public :: collect_stdlib_math
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#:for k1 in REAL_KINDS
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real(kind=${k1}$), parameter :: PI_${k1}$ = acos(-1.0_${k1}$)
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#:endfor
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contains
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@@ -33,6 +37,13 @@ contains
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new_unittest("clip-real-quad", test_clip_rqp), &
3438
new_unittest("clip-real-quad-bounds", test_clip_rqp_bounds) &
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!> Tests for arg/argd/argpi
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#:for k1 in CMPLX_KINDS
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, new_unittest("arg-cmplx-${k1}$", test_arg_${k1}$) &
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, new_unittest("argd-cmplx-${k1}$", test_argd_${k1}$) &
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, new_unittest("argpi-cmplx-${k1}$", test_argpi_${k1}$) &
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#:endfor
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!> Tests for `is_close` and `all_close`
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#:for k1 in REAL_KINDS
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, new_unittest("is_close-real-${k1}$", test_is_close_real_${k1}$) &
@@ -211,7 +222,66 @@ contains
211222
#:endif
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end subroutine test_clip_rqp_bounds
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#:for k1 in CMPLX_KINDS
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subroutine test_arg_${k1}$(error)
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type(error_type), allocatable, intent(out) :: error
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real(${k1}$), parameter :: tol = sqrt(epsilon(1.0_${k1}$))
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real(${k1}$), allocatable :: theta(:)
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#! For scalar
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call check(error, abs(arg(2*exp((0.0_${k1},ドル 0.5_${k1}$))) - 0.5_${k1}$) < tol, &
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"test_nonzero_scalar")
235+
if (allocated(error)) return
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call check(error, abs(arg((0.0_${k1},ドル 0.0_${k1}$)) - 0.0_${k1}$) < tol, &
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"test_zero_scalar")
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#! and for array (180.0° see scalar version)
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theta = arange(-179.0_${k1},ドル 179.0_${k1},ドル 3.58_${k1}$)
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call check(error, all(abs(arg(exp(cmplx(0.0_${k1},ドル theta/180*PI_${k1},ドル ${k1}$))) - theta/180*PI_${k1}$) < tol), &
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"test_array")
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end subroutine test_arg_${k1}$
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subroutine test_argd_${k1}$(error)
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type(error_type), allocatable, intent(out) :: error
248+
real(${k1}$), parameter :: tol = sqrt(epsilon(1.0_${k1}$))
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real(${k1}$), allocatable :: theta(:)
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#! For scalar
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call check(error, abs(argd((-1.0_${k1},ドル 0.0_${k1}$)) - 180.0_${k1}$) < tol, &
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"test_nonzero_scalar")
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if (allocated(error)) return
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call check(error, abs(argd((0.0_${k1},ドル 0.0_${k1}$)) - 0.0_${k1}$) < tol, &
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"test_zero_scalar")
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#! and for array (180.0° see scalar version)
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theta = arange(-179.0_${k1},ドル 179.0_${k1},ドル 3.58_${k1}$)
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call check(error, all(abs(argd(exp(cmplx(0.0_${k1},ドル theta/180*PI_${k1},ドル ${k1}$))) - theta) < tol), &
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"test_array")
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end subroutine test_argd_${k1}$
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subroutine test_argpi_${k1}$(error)
266+
type(error_type), allocatable, intent(out) :: error
267+
real(${k1}$), parameter :: tol = sqrt(epsilon(1.0_${k1}$))
268+
real(${k1}$), allocatable :: theta(:)
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#! For scalar
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call check(error, abs(argpi((-1.0_${k1},ドル 0.0_${k1}$)) - 1.0_${k1}$) < tol, &
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"test_nonzero_scalar")
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if (allocated(error)) return
274+
call check(error, abs(argpi((0.0_${k1},ドル 0.0_${k1}$)) - 0.0_${k1}$) < tol, &
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"test_zero_scalar")
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#! and for array (180.0° see scalar version)
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theta = arange(-179.0_${k1},ドル 179.0_${k1},ドル 3.58_${k1}$)
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call check(error, all(abs(argpi(exp(cmplx(0.0_${k1},ドル theta/180*PI_${k1},ドル ${k1}$))) - theta/180) < tol), &
280+
"test_array")
281+
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end subroutine test_argpi_${k1}$
283+
#:endfor
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#:for k1 in REAL_KINDS
216286
subroutine test_is_close_real_${k1}$(error)
217287
type(error_type), allocatable, intent(out) :: error

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