mathutil Module Reference

Math functions. More...

Functions/Subroutines
subroutine	computequadraturepoints (x1, x2, points, weights, nbq, method)
subroutine	computematrixtransform_mapping21 (mat, tl, tr, ni, nj, side)
subroutine	zspecialmatrixtransform (mat, coeffs, nx, ny, leftside)
subroutine	computevectortransform_mapping21 (vec, t, ni, nj, side)
subroutine	zcomputevectortransform_mapping21 (vec, t, ni, nj, side)
subroutine	computevelocityspacediscretization (dx, nqw, nqa, lw, nw, na)
real(kind=r8) function	uniform ()
real(kind=r8) function	gaussian_number ()
real(kind=r8) function	plusminus ()

Variables
complex(kind=r8), parameter	cpone =cmplx(1e0_r8, 0e0_r8)
complex(kind=r8), parameter	cpzero =cmplx(0e0_r8, 0e0_r8)
integer, parameter	quad_gauss =1
integer, parameter	quad_equid =2
real(kind=r8), dimension(2), save	coeffsq = (/1e0_r8,-1e0_r8/)
real(kind=r8), dimension(2, 2), save	tlq = reshape( (/ 2e0_r8, -1e0_r8, 0e0_r8, 1e0_r8 /), (/2, 2/) )
real(kind=r8), dimension(2, 2), save	tlq_inv = reshape( (/ 0.5_r8, 0.5_r8, 0e0_r8, 1e0_r8 /), (/2, 2/) )
real(kind=r8), dimension(2, 2), save	tlq_tr = reshape( (/ 2e0_r8, 0e0_r8,-1e0_r8,1e0_r8 /), (/2, 2/) )
real(kind=r8), dimension(2, 2), save	trq = reshape( (/ 1e0_r8, 0e0_r8, -1e0_r8, 2e0_r8 /), (/2, 2/) )
real(kind=r8), dimension(2, 2), save	trq_inv = reshape( (/ 1e0_r8, 0e0_r8, 0.5_r8,0.5_r8 /), (/2, 2/) )
real(kind=r8), dimension(2, 2), save	trq_tr = reshape( (/ 1e0_r8, -1e0_r8,0e0_r8, 2e0_r8 /), (/2, 2/) )
real(kind=r8), dimension(3), save	coeffsc = (/5e0_r8,-4e0_r8,-1e0_r8/)
real(kind=r8), dimension(3, 3), save	tlc = reshape( (/ 6e0_r8, -4e0_r8, -1e0_r8, 0e0_r8, 1e0_r8, 0e0_r8, 0e0_r8, 0e0_r8, 1e0_r8 /), (/3, 3/) )
real(kind=r8), dimension(3, 3), save	tlc_inv = reshape( (/ 1e0_r8/6e0_r8, 2e0_r8/3e0_r8, 1e0_r8/6e0_r8, 0e0_r8, 1e0_r8, 0e0_r8, 0e0_r8, 0e0_r8, 1e0_r8 /), (/3, 3/) )
real(kind=r8), dimension(3, 3), save	tlc_tr = reshape( (/ 6e0_r8, 0e0_r8, 0e0_r8, -4e0_r8, 1e0_r8, 0e0_r8, -1e0_r8, 0e0_r8, 1e0_r8 /), (/3, 3/) )
real(kind=r8), dimension(3, 3), save	trc = reshape( (/ 1e0_r8, 0e0_r8, 0e0_r8, 0e0_r8, 1e0_r8, 0e0_r8, -1e0_r8, -4e0_r8, 6e0_r8 /), (/3, 3/) )
real(kind=r8), dimension(3, 3), save	trc_inv = reshape( (/ 1e0_r8, 0e0_r8, 0e0_r8, 0e0_r8, 1e0_r8, 0e0_r8, 1e0_r8/6e0_r8, 2e0_r8/3e0_r8, 1e0_r8/6e0_r8 /), (/3, 3/) )
real(kind=r8), dimension(3, 3), save	trc_tr = reshape( (/ 1e0_r8, 0e0_r8, -1e0_r8, 0e0_r8, 1e0_r8, -4e0_r8, 0e0_r8, 0e0_r8, 6e0_r8 /), (/3, 3/) )
real(kind=r8), dimension(3, 3), save	trc_deboor = reshape( (/ 1.0_r8, 0.0_r8, 0.0_r8, 1.0_r8/3.0_r8, 2.0_r8/3.0_r8, 0.0_r8, 1.0_r8/6.0_r8, 2.0_r8/3.0_r8, 1.0_r8/6.0_r8 /), (/3, 3/) )
real(kind=r8), dimension(3, 3), save	tlc_deboor = reshape( (/ 1.0_r8/6.0_r8, 2.0_r8/3.0_r8, 1.0_r8/6.0_r8, 0.0_r8, 2.0_r8/3.0_r8, 1.0_r8/3.0_r8, 0.0_r8, 0.0_r8, 1.0_r8 /), (/3, 3/) )

Detailed Description

Math functions.

Author

Julien Dominski

Date

January 2013

Function/Subroutine Documentation

computematrixtransform_mapping21()

subroutine mathutil::computematrixtransform_mapping21	(	type(gemat), intent(inout)	mat,
		real(kind=r8), dimension(:,:), intent(in)	tl,
		real(kind=r8), dimension(:,:), intent(in)	tr,
		integer, intent(in)	ni,
		integer, intent(in)	nj,
		integer, intent(in)	side )

computequadraturepoints()

subroutine mathutil::computequadraturepoints	(	real(kind=r8), intent(in)	x1,
		real(kind=r8), intent(in)	x2,
		real(kind=r8), dimension(:), intent(inout)	points,
		real(kind=r8), dimension(:), intent(inout)	weights,
		integer, intent(in)	nbq,
		integer, intent(in)	method )

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computevectortransform_mapping21()

subroutine mathutil::computevectortransform_mapping21	(	real(kind=r8), dimension(:), intent(inout)	vec,
		real(kind=r8), dimension(:,:), intent(in)	t,
		integer, intent(in)	ni,
		integer, intent(in)	nj,
		integer, intent(in)	side )

computevelocityspacediscretization()

subroutine mathutil::computevelocityspacediscretization	(	real(kind=r8), intent(in)	dx,
		integer, intent(in)	nqw,
		integer, intent(in)	nqa,
		real(kind=r8), intent(in)	lw,
		integer, intent(out)	nw,
		integer, intent(out)	na )

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gaussian_number()

real(kind=r8) function mathutil::gaussian_number

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plusminus()

real(kind=r8) function mathutil::plusminus

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uniform()

real(kind=r8) function mathutil::uniform

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zcomputevectortransform_mapping21()

subroutine mathutil::zcomputevectortransform_mapping21	(	complex(kind=r8), dimension(:), intent(inout)	vec,
		real(kind=r8), dimension(:,:), intent(in)	t,
		integer, intent(in)	ni,
		integer, intent(in)	nj,
		integer, intent(in)	side )

zspecialmatrixtransform()

subroutine mathutil::zspecialmatrixtransform	(	type(zpbmat), intent(inout)	mat,
		real(kind=r8), dimension(:), intent(in)	coeffs,
		integer, intent(in)	nx,
		integer, intent(in)	ny,
		logical, intent(in)	leftside )

Variable Documentation

coeffsc

real(kind=r8), dimension(3), save mathutil::coeffsc = (/5e0_r8,-4e0_r8,-1e0_r8/)

coeffsq

real(kind=r8), dimension(2), save mathutil::coeffsq = (/1e0_r8,-1e0_r8/)

cpone

complex(kind=r8), parameter mathutil::cpone =cmplx(1e0_r8, 0e0_r8)

cpzero

complex(kind=r8), parameter mathutil::cpzero =cmplx(0e0_r8, 0e0_r8)

quad_equid

integer, parameter mathutil::quad_equid =2

quad_gauss

integer, parameter mathutil::quad_gauss =1

tlc

real(kind=r8), dimension(3,3), save mathutil::tlc = reshape( (/ 6e0_r8, -4e0_r8, -1e0_r8, 0e0_r8, 1e0_r8, 0e0_r8, 0e0_r8, 0e0_r8, 1e0_r8 /), (/3, 3/) )

tlc_deboor

real(kind=r8), dimension(3,3), save mathutil::tlc_deboor = reshape( (/ 1.0_r8/6.0_r8, 2.0_r8/3.0_r8, 1.0_r8/6.0_r8, 0.0_r8, 2.0_r8/3.0_r8, 1.0_r8/3.0_r8, 0.0_r8, 0.0_r8, 1.0_r8 /), (/3, 3/) )

tlc_inv

real(kind=r8), dimension(3,3), save mathutil::tlc_inv = reshape( (/ 1e0_r8/6e0_r8, 2e0_r8/3e0_r8, 1e0_r8/6e0_r8, 0e0_r8, 1e0_r8, 0e0_r8, 0e0_r8, 0e0_r8, 1e0_r8 /), (/3, 3/) )

tlc_tr

real(kind=r8), dimension(3,3), save mathutil::tlc_tr = reshape( (/ 6e0_r8, 0e0_r8, 0e0_r8, -4e0_r8, 1e0_r8, 0e0_r8, -1e0_r8, 0e0_r8, 1e0_r8 /), (/3, 3/) )

tlq

real(kind=r8), dimension(2,2), save mathutil::tlq = reshape( (/ 2e0_r8, -1e0_r8, 0e0_r8, 1e0_r8 /), (/2, 2/) )

tlq_inv

real(kind=r8), dimension(2,2), save mathutil::tlq_inv = reshape( (/ 0.5_r8, 0.5_r8, 0e0_r8, 1e0_r8 /), (/2, 2/) )

tlq_tr

real(kind=r8), dimension(2,2), save mathutil::tlq_tr = reshape( (/ 2e0_r8, 0e0_r8,-1e0_r8,1e0_r8 /), (/2, 2/) )

trc

real(kind=r8), dimension(3,3), save mathutil::trc = reshape( (/ 1e0_r8, 0e0_r8, 0e0_r8, 0e0_r8, 1e0_r8, 0e0_r8, -1e0_r8, -4e0_r8, 6e0_r8 /), (/3, 3/) )

trc_deboor

real(kind=r8), dimension(3,3), save mathutil::trc_deboor = reshape( (/ 1.0_r8, 0.0_r8, 0.0_r8, 1.0_r8/3.0_r8, 2.0_r8/3.0_r8, 0.0_r8, 1.0_r8/6.0_r8, 2.0_r8/3.0_r8, 1.0_r8/6.0_r8 /), (/3, 3/) )

trc_inv

real(kind=r8), dimension(3,3), save mathutil::trc_inv = reshape( (/ 1e0_r8, 0e0_r8, 0e0_r8, 0e0_r8, 1e0_r8, 0e0_r8, 1e0_r8/6e0_r8, 2e0_r8/3e0_r8, 1e0_r8/6e0_r8 /), (/3, 3/) )

trc_tr

real(kind=r8), dimension(3,3), save mathutil::trc_tr = reshape( (/ 1e0_r8, 0e0_r8, -1e0_r8, 0e0_r8, 1e0_r8, -4e0_r8, 0e0_r8, 0e0_r8, 6e0_r8 /), (/3, 3/) )

trq

real(kind=r8), dimension(2,2), save mathutil::trq = reshape( (/ 1e0_r8, 0e0_r8, -1e0_r8, 2e0_r8 /), (/2, 2/) )

trq_inv

real(kind=r8), dimension(2,2), save mathutil::trq_inv = reshape( (/ 1e0_r8, 0e0_r8, 0.5_r8,0.5_r8 /), (/2, 2/) )

trq_tr

real(kind=r8), dimension(2,2), save mathutil::trq_tr = reshape( (/ 1e0_r8, -1e0_r8,0e0_r8, 2e0_r8 /), (/2, 2/) )