carlson_elliptic_module – carlson-elliptic-integrals

Carlson symmetric forms of elliptic integrals.

These routines are refactored versions of the ones from SLATEC. They have been converted into modern Fortran, and the documentation has been converted to FORD syntax.

Uses

- iso_fortran_env
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Variables

Type	Visibility	Attributes		Name		Initial
integer,	public,	parameter	::	carlson_elliptic_module_wp	=	wp
real(kind=wp),	private,	parameter, dimension(5)	::	d1mach	=	[tiny(1.0_wp), huge(1.0_wp), real(radix(1.0_wp), wp)**(-digits(1.0_wp)), epsilon(1.0_wp), log10(real(radix(1.0_wp), wp))]	Machine constants (replaces the old SLATEC D1MACH function) The traditional D1MACH constants are: * `D1MACH( 1) = B*(EMIN-1)`, the smallest positive magnitude. `D1MACH( 2) = B*EMAX(1 - B*(-T))`, the largest magnitude. `D1MACH( 3) = B*(-T)`, the smallest relative spacing. `D1MACH( 4) = B*(1-T)`, the largest relative spacing. `D1MACH( 5) = LOG10(B)`

Functions

public function drc(x, y, ier)

Compute an approximation of the Carlson elliptic integral: $R_C(x,y) = \frac{1}{2} \int_{0}^{\infty} (t+x)^{-1/2}(t+y)^{-1} dt$ where $x\ge0$ and $y>0$ .

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x	nonnegative variable
real(kind=wp),	intent(in)	::	y	positive variable
integer,	intent(out)	::	ier	indicates normal or abnormal termination: `IER = 0`: Normal and reliable termination of the routine. It is assumed that the requested accuracy has been achieved. `IER > 0`: Abnormal termination of the routine: `IER = 1`: `x<0 or y<=0` `IER = 2`: `x+y<LOLIM` `IER = 3`: `max(x,y) > UPLIM`

Return Value real(kind=wp)

public function drd(x, y, z, ier)

Compute an approximation for the incomplete or complete elliptic integral of the 2nd kind: $R_D(x,y,z) = \frac{3}{2} \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1/2} (t+z)^{-3/2} dt$ Where $x\ge0$ , $y\ge0$ , $x+y>0$ , and $z>0$ .

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x	nonnegative variable ( $x+y>0$ )
real(kind=wp),	intent(in)	::	y	nonnegative variable ( $x+y>0$ )
real(kind=wp),	intent(in)	::	z	positive variable
integer,	intent(out)	::	ier	indicates normal or abnormal termination: `IER = 0`: Normal and reliable termination of the routine. It is assumed that the requested accuracy has been achieved. `IER > 0`: Abnormal termination of the routine: `IER = 1`: `min(x,y) < 0` `IER = 2`: `min(x + y, z ) < LOLIM` `IER = 3`: `max(x,y,z) > UPLIM`

Return Value real(kind=wp)

public function drf(x, y, z, ier)

Compute an approximation for the incomplete or complete elliptic integral of the 1st kind: $R_F(x,y,z) = \frac{1}{2} \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1/2} (t+z)^{-1/2} dt$ Where $x\ge0$ , $y\ge0$ , $z\ge0$ , and at most one of them is $=0$ .

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x	nonnegative variable
real(kind=wp),	intent(in)	::	y	nonnegative variable
real(kind=wp),	intent(in)	::	z	nonnegative variable
integer,	intent(out)	::	ier	indicates normal or abnormal termination: `IER = 0`: Normal and reliable termination of the routine. It is assumed that the requested accuracy has been achieved. `IER > 0`: Abnormal termination of the routine: `IER = 1`: `min(x,y,z) < 0` `IER = 2`:`min(x+y,x+z,y+z) < LOLIM` `IER = 3`: `max(x,y,z) > UPLIM`

Return Value real(kind=wp)

public function drj(x, y, z, p, ier)

Compute an approximation for the incomplete or complete elliptic integral of the 3rd kind: $R_J(x,y,z,p) = \frac{3}{2} \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1/2} (t+z)^{-1/2} (t+p)^{-1} dt$ where $x\ge0$ , $y\ge0$ , and $z\ge0$ , and at most one of them $=0$ , and $p>0$ .

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x	nonnegative variable
real(kind=wp),	intent(in)	::	y	nonnegative variable
real(kind=wp),	intent(in)	::	z	nonnegative variable
real(kind=wp),	intent(in)	::	p	positive variable
integer,	intent(out)	::	ier	indicates normal or abnormal termination: `IER = 0`: Normal and reliable termination of the routine. It is assumed that the requested accuracy has been achieved. `IER = 1`: `min(x,y,z) < 0.0_wp` `IER = 2`: `min(x+y,x+z,y+z,p) < LOLIM` `IER = 3`: `max(x,y,z,p) > UPLIM`

carlson_elliptic_module Module

Contents

Variables

Functions

Uses

Contents

Variables

Functions

Variables

Functions

public function drc(x, y, ier)

Arguments

Return Value real(kind=wp)

public function drd(x, y, z, ier)

Arguments

Return Value real(kind=wp)

public function drf(x, y, z, ier)

Arguments

Return Value real(kind=wp)

public function drj(x, y, z, p, ier)

Arguments

Return Value real(kind=wp)