tensor Module Reference

Tensor operations.

Data Types
interface	transpose
interface	triple_tensor_product

Functions/Subroutines
subroutine, public	tensr3 (v, nv, u, nu, a, bt, ct, w)
	Tensor product \( v =(C \otimes B \otimes A) u \).
subroutine, public	trsp (a, lda, b, ldb)
	Transpose of a rectangular tensor \( A = B^T \).
subroutine, public	trsp1 (a, n)
	In-place transpose of a square tensor.
subroutine, public	tnsr2d_el (v, nv, u, nu, a, bt)
	Computes \( v = A u B^T \).
subroutine, public	tnsr3d_el (v, nv, u, nu, a, bt, ct)
	Tensor product \( v =(C \otimes B \otimes A) u \) performed on a single element.
subroutine, public	tnsr3d_el_list (v, nv, u, nu, a, bt, ct, el_list, n_pt)
	Tensor product \( v =(C \otimes B \otimes A) u \) performed on a subset of the elements.
subroutine, public	tnsr3d (v, nv, u, nu, a, bt, ct, nelv)
	Tensor product \( v =(C \otimes B \otimes A) u \) performed on nelv elements.
subroutine, public	tnsr1_3d (v, nv, nu, a, bt, ct, nelv)
	In place tensor product \( v =(C \otimes B \otimes A) v \).
subroutine, public	addtnsr (s, h1, h2, h3, nx, ny, nz)
	Maps and adds to S a tensor product form of the three functions H1,H2,H3. This is a single element routine used for deforming geometry.
subroutine	triple_tensor_product_scalar (v, u, nu, hr, hs, ht)
	Computes the tensor product \( v =(H_t \otimes H_s \otimes H_r) u \). This operation is usually performed for spectral interpolation of a scalar field as defined by.
subroutine	triple_tensor_product_vector (v, u1, u2, u3, nu, hr, hs, ht)
	Computes the tensor product on a vector field \( \mathbf{v} =(H_t \otimes H_s \otimes H_r) \mathbf{u} \). This operation is usually performed for spectral interpolation on a 3D vector field \( \mathbf{u} = (u_1,u_2,u_3) \) as defined by.

Function/Subroutine Documentation

addtnsr()

subroutine, public tensor::addtnsr	(	real(kind=rp), dimension(nx, ny, nz), intent(inout)	s,
		real(kind=rp), dimension(nx), intent(in)	h1,
		real(kind=rp), dimension(ny), intent(in)	h2,
		real(kind=rp), dimension(nz), intent(in)	h3,
		integer, intent(in)	nx,
		integer, intent(in)	ny,
		integer, intent(in)	nz
	)

Definition at line 265 of file tensor.f90.

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tensr3()

subroutine, public tensor::tensr3	(	real(kind=rp), dimension(nv, nv, nv), intent(inout)	v,
		integer	nv,
		real(kind=rp), dimension(nu, nu, nu), intent(inout)	u,
		integer	nu,
		real(kind=rp), dimension(nv, nu), intent(inout)	a,
		real(kind=rp), dimension(nu, nv), intent(inout)	bt,
		real(kind=rp), dimension(nu, nv), intent(inout)	ct,
		real(kind=rp), dimension(nu*nu*nv), intent(inout)	w
	)

Todo:

Add 2d case

Definition at line 90 of file tensor.f90.

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tnsr1_3d()

subroutine, public tensor::tnsr1_3d	(	real(kind=rp), dimension(nv*nv*nv*nelv), intent(inout)	v,
		integer, intent(inout)	nv,
		integer, intent(inout)	nu,
		real(kind=rp), dimension(nv,nu), intent(inout)	a,
		real(kind=rp), dimension(nu, nv), intent(inout)	bt,
		real(kind=rp), dimension(nu,nv), intent(inout)	ct,
		integer, intent(inout)	nelv
	)

Definition at line 248 of file tensor.f90.

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tnsr2d_el()

subroutine, public tensor::tnsr2d_el	(	real(kind=rp), dimension(nv*nv), intent(inout)	v,
		integer, intent(in)	nv,
		real(kind=rp), dimension(nu*nu), intent(inout)	u,
		integer, intent(in)	nu,
		real(kind=rp), dimension(nv,nu), intent(inout)	a,
		real(kind=rp), dimension(nu,nv), intent(inout)	bt
	)

Definition at line 153 of file tensor.f90.

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tnsr3d()

subroutine, public tensor::tnsr3d	(	real(kind=rp), dimension(nv*nv*nv,nelv), intent(inout)	v,
		integer, intent(in)	nv,
		real(kind=rp), dimension(nu*nu*nu,nelv), intent(in)	u,
		integer, intent(in)	nu,
		real(kind=rp), dimension(nv,nu), intent(in)	a,
		real(kind=rp), dimension(nu, nv), intent(in)	bt,
		real(kind=rp), dimension(nu,nv), intent(in)	ct,
		integer, intent(in)	nelv
	)

Definition at line 222 of file tensor.f90.

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tnsr3d_el()

subroutine, public tensor::tnsr3d_el	(	real(kind=rp), dimension(nv*nv*nv), intent(inout)	v,
		integer, intent(in)	nv,
		real(kind=rp), dimension(nu*nu*nu), intent(inout)	u,
		integer, intent(in)	nu,
		real(kind=rp), dimension(nv,nu), intent(inout)	a,
		real(kind=rp), dimension(nu, nv), intent(inout)	bt,
		real(kind=rp), dimension(nu,nv), intent(inout)	ct
	)

Definition at line 170 of file tensor.f90.

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tnsr3d_el_list()

subroutine, public tensor::tnsr3d_el_list	(	real(kind=rp), dimension(nv*nv*nv, n_pt), intent(inout)	v,
		integer, intent(in)	nv,
		real(kind=rp), dimension(nu*nu*nu,1), intent(inout)	u,
		integer, intent(in)	nu,
		real(kind=rp), dimension(nv,nu,n_pt), intent(inout)	a,
		real(kind=rp), dimension(nu, nv,n_pt), intent(inout)	bt,
		real(kind=rp), dimension(nu,nv,n_pt), intent(inout)	ct,
		integer, dimension(n_pt), intent(in)	el_list,
		integer, intent(in)	n_pt
	)

Definition at line 187 of file tensor.f90.

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triple_tensor_product_scalar()

subroutine tensor::triple_tensor_product_scalar ( real(kind=rp), intent(inout)  v, real(kind=rp), dimension(nu,nu,nu), intent(inout)  u, integer, intent(in)  nu, real(kind=rp), dimension(nu), intent(inout)  hr, real(kind=rp), dimension(nu), intent(inout)  hs, real(kind=rp), dimension(nu), intent(inout)  ht  )

private

\begin{eqnarray*} v(r,s,t) = \sum_{i=0}^{N}{\sum_{j=0}^{N}{ \sum_{k=0}^{N}{u_{ijk}h_i(r)h_j(s)h_k(t)}}} \end{eqnarray*}

Parameters

v	Interpolated value (scalar).
u	Field values at the GLL points (e.g. velocity in x-direction).
nu	Size of the interpolation weights (usually lx).
Hr	Interpolation weights in the r-direction.
Hs	Interpolation weights in the s-direction.
Ht	Interpolation weights in the t-direction.

Definition at line 298 of file tensor.f90.

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triple_tensor_product_vector()

subroutine tensor::triple_tensor_product_vector ( real(kind=rp), dimension(3), intent(inout)  v, real(kind=rp), dimension(nu,nu,nu), intent(inout)  u1, real(kind=rp), dimension(nu,nu,nu), intent(inout)  u2, real(kind=rp), dimension(nu,nu,nu), intent(inout)  u3, integer, intent(in)  nu, real(kind=rp), dimension(nu), intent(inout)  hr, real(kind=rp), dimension(nu), intent(inout)  hs, real(kind=rp), dimension(nu), intent(inout)  ht  )

private

\begin{eqnarray*} \mathbf{v}(r,s,t) = \sum_{i=0}^{N}{\sum_{j=0}^{N}{ \sum_{k=0}^{N}{\mathbf{u}_{ijk}h_i(r)h_j(s)h_k(t)}}} \end{eqnarray*}

Parameters

v	Interpolated value (scalar).
u1	3D-array containing values at the GLL points (e.g. velocity).
u2	3D-array containing values at the GLL points (e.g. velocity).
u3	3D-array containing values at the GLL points (e.g. velocity).
nu	Size of the interpolation weights (usually lx).
Hr	Interpolation weights in the r-direction.
Hs	Interpolation weights in the s-direction.
Ht	Interpolation weights in the t-direction.

Definition at line 334 of file tensor.f90.

trsp()

subroutine, public tensor::trsp	(	real(kind=rp), dimension(lda, ldb), intent(inout)	a,
		integer, intent(in)	lda,
		real(kind=rp), dimension(ldb, lda), intent(in)	b,
		integer, intent(in)	ldb
	)

Definition at line 120 of file tensor.f90.

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trsp1()

subroutine, public tensor::trsp1	(	real(kind=rp), dimension(n, n), intent(inout)	a,
		integer, intent(in)	n
	)

Definition at line 136 of file tensor.f90.

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