<p><b>dwj07@fsu.edu</b> 2013-03-28 13:10:52 -0600 (Thu, 28 Mar 2013)</p><p><br>
-- TRUNK COMMIT --<br>
COMMENTS AND WHITESPACE ONLY<br>
<br>
Adding doxygen comments to rbf_interpolation module.<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/mpas/src/operators/mpas_rbf_interpolation.F
===================================================================
--- trunk/mpas/src/operators/mpas_rbf_interpolation.F 2013-03-28 03:30:50 UTC (rev 2676)
+++ trunk/mpas/src/operators/mpas_rbf_interpolation.F 2013-03-28 19:10:52 UTC (rev 2677)
@@ -1,3 +1,16 @@
+!***********************************************************************
+!
+! mpas_rbf_interpolation
+!
+!> \brief MPAS Radial basis function interpolation module
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This module provides routines for performing interpolation with radial basis functions.
+!> It performs interpolation of scalar and vector functions in 2 and 3 dimensions.
+!
+!-----------------------------------------------------------------------
module mpas_rbf_interpolation
use mpas_dmpar
use mpas_grid_types
@@ -6,11 +19,6 @@
private
save
-!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-! Purpose: perform interpolation of scalar and vector functions in 2D
-! and 3D using Radial Basis Functions (RBFs).
-!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-
! Initialize the geometry that will be useful from interpolation
public :: mpas_rbf_interp_initialize
@@ -93,26 +101,32 @@
contains
- subroutine mpas_rbf_interp_initialize(grid)
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: compute geometric fields that will be potentially useful for calling
- ! the interpolation routines
- !
- ! Input: the grid
- !
- ! Output:
- ! edgeNormalVectors - the unit vector at the center of each edge tangent to the sphere
- ! cellTangentPlane - 2 orthogonal unit vectors in the tangent plane of each cell
- ! The first unit vector is chosen to point toward the center of the first
- ! edge on the cell.
- ! localVerticalUnitVectors - the unit normal vector of the tangent plane at the center
- ! of each cell
- !
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!***********************************************************************
+!
+! routine mpas_rbf_interp_initialize
+!
+!> \brief MPAS RBF interpolation initialization routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes geometric fields that will be potentially useful for calling
+!> the interpolation routines.
+!> Input: the grid
+!> Output:
+!> edgeNormalVectors - the unit vector at the center of each edge tangent to the sphere
+!> cellTangentPlane - 2 orthogonal unit vectors in the tangent plane of each cell
+!> The first unit vector is chosen to point toward the center of the first
+!> edge on the cell.
+!> localVerticalUnitVectors - the unit normal vector of the tangent plane at the center
+!> of each cell
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_initialize(grid)!{{{
+
implicit none
- type (mesh_type), intent(inout) :: grid
+ type (mesh_type), intent(inout) :: grid !< Input/Output: Grid information
integer :: nCells, nEdges
integer, dimension(:,:), pointer :: cellsOnEdge, edgesOnCell
@@ -185,34 +199,41 @@
cellTangentPlane(:,2,iCell) = yHatPlane
end do
- end subroutine mpas_rbf_interp_initialize
+ end subroutine mpas_rbf_interp_initialize!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 2D that can be used to
- ! reconstruct a given scalar function at varying locations. This is useful
- ! for finding the location on the the RBF reconstruction of a function
- ! (e.g., a height field) that minimizes the distance to a point in 3D space.
- ! The reconstruction is performed with basis functions that are RBFs and constant
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! coeffCount - the size of coefficients, must be at least pointCount + 1
- ! points - the location of the "source" points in the 2D space where the values of
- ! the function are known
- ! fieldValues - the values of the function of interest at the points
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! coefficients - the coefficients needed to perform interpolation of the funciton
- ! at destination points yet to be specified
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_loc_2D_sca_const_comp_coeffs(pointCount, coeffCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_loc_2D_sca_const_comp_coeffs
+!
+!> \brief MPAS 2D scalar constant interpolation coefficient routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 2D that can be used to reconstruct a given scalar function at varying locations.
+!> This is useful for finding the location on the RBF reconstruction of a function (e.g. a heigh field) that minimizes the distantce
+!> to a point in 3D space. The reconstruction is performed with basis functions that are RBFs and constant.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> coeffCount - the size of coefficients, must be at least pointCount + 1
+!> points - the location of the "source" points in the 2D space where the values of
+!> the function are known
+!> fieldValues - the values of the function of interest at the points
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> coefficients - the coefficients needed to perform interpolation of the funciton
+!> at destination points yet to be specified
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_loc_2D_sca_const_comp_coeffs(pointCount, coeffCount, &!{{{
points, fieldValues, alpha, coefficients)
- integer, intent(in) :: pointCount, coeffCount
- real(kind=RKIND), dimension(pointCount,2), intent(in) :: points
- real(kind=RKIND), dimension(pointCount), intent(in) :: fieldValues
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(coeffCount), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ integer, intent(in) :: coeffCount !< Input: Number of coefficients
+ real(kind=RKIND), dimension(pointCount,2), intent(in) :: points !< Input: List of points
+ real(kind=RKIND), dimension(pointCount), intent(in) :: fieldValues !< Input: Value at points
+ real(kind=RKIND), intent(in) :: alpha !< Input: Charachteristic length scale of RBFs
+ real(kind=RKIND), dimension(coeffCount), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j, matrixSize
real(kind=RKIND), dimension(pointCount+1,pointCount+1) :: matrix
@@ -242,35 +263,44 @@
call mpas_legs(matrix(1:matrixSize,1:matrixSize), matrixSize, rhs(1:matrixSize), &
coefficients(1:matrixSize), pivotIndices(1:matrixSize))
- end subroutine mpas_rbf_interp_loc_2D_sca_const_comp_coeffs
+ end subroutine mpas_rbf_interp_loc_2D_sca_const_comp_coeffs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 2D that can be used to
- ! reconstruct a given scalar function at varying locations. This is useful
- ! for finding the location on the the RBF reconstruction of a function
- ! (e.g., a height field) that minimizes the distance to a point in 3D space.
- ! The reconstruction is performed with basis functions that are RBFs plus constant
- ! and linear
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! coeffCount - the size of coefficients, must be at least pointCount + 3
- ! points - the location of the "source" points in the 2D space where the values of
- ! the function are known
- ! fieldValues - the values of the function of interest at the points
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! coefficients - the coefficients needed to perform interpolation of the funciton
- ! at destination points yet to be specified
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_loc_2D_sca_lin_comp_coeffs(pointCount, coeffCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_loc_2D_sca_lin_comp_coeffs
+!
+!> \brief MPAS 2D scalar linear interpolation coefficient routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 2D that can be used to
+!> reconstruct a given scalar function at varying locations. This is useful
+!> for finding the location on the the RBF reconstruction of a function
+!> (e.g., a height field) that minimizes the distance to a point in 3D space.
+!> The reconstruction is performed with basis functions that are RBFs plus constant
+!> and linear
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> coeffCount - the size of coefficients, must be at least pointCount + 3
+!> points - the location of the "source" points in the 2D space where the values of
+!> the function are known
+!> fieldValues - the values of the function of interest at the points
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> coefficients - the coefficients needed to perform interpolation of the funciton
+!> at destination points yet to be specified
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_loc_2D_sca_lin_comp_coeffs(pointCount, coeffCount, &!{{{
points, fieldValues, alpha, coefficients)
- integer, intent(in) :: pointCount, coeffCount
- real(kind=RKIND), dimension(pointCount,2), intent(in) :: points
- real(kind=RKIND), dimension(pointCount), intent(in) :: fieldValues
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(coeffCount), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ integer, intent(in) :: coeffCount !< Input: Number of coefficients
+ real(kind=RKIND), dimension(pointCount,2), intent(in) :: points !< Input: List of points
+ real(kind=RKIND), dimension(pointCount), intent(in) :: fieldValues !< Input: List of values at points
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale for RBFs
+ real(kind=RKIND), dimension(coeffCount), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j, matrixSize
real(kind=RKIND), dimension(pointCount+3,pointCount+3) :: matrix
@@ -301,43 +331,53 @@
call mpas_legs(matrix(1:matrixSize,1:matrixSize), matrixSize, rhs(1:matrixSize), &
coefficients(1:matrixSize), pivotIndices(1:matrixSize))
- end subroutine mpas_rbf_interp_loc_2D_sca_lin_comp_coeffs
+ end subroutine mpas_rbf_interp_loc_2D_sca_lin_comp_coeffs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Evalute a scalar function in 2D using coefficients computed in
- ! rbfInterp_loc_2D_sca_const_compCoeffs. This
- ! function can be called repeatedly with different destination points
- ! to quickly evaluate the interpolating function using the same
- ! coefficients. This is useful for finding the location on the the
- ! RBF reconstruction of a function (e.g., a height field) that minimizes
- ! the distance to a point in 3D space. The reconstruction is performed
- ! with basis functions that are RBFs and constant
- ! Input:
- ! fieldCount - the number fields to be evaluated. This is useful for reconstructing,
- ! for example, the x-, y- and z-components of a vector field at the same
- ! point in 2D
- ! coeffCount - the size of coefficients, must be at least pointCount + 1
- ! pointCount - the number of "source" points and functionValues supplied
- ! coefficients - the coefficients needed to perform interpolation of the funciton
- ! at the evaluationPoint
- ! evaluationPoint - the point in 2D where the function is to be reconstructed
- ! points - the location of the "source" points in the 2D space where the values of
- ! the function are known
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! derivs - the value of the function, the 2 components of its Jacobian and
- ! the 3 unique components of its Hessian at the evaluationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_loc_2D_sca_const_eval_with_derivs(fieldCount, coeffCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_loc_2D_sca_const_eval_with_derivs
+!
+!> \brief MPAS 2D scalar constant evaulation routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine evalutes a scalar function in 2D using coefficients computed in
+!> rbfInterp_loc_2D_sca_const_compCoeffs. This
+!> function can be called repeatedly with different destination points
+!> to quickly evaluate the interpolating function using the same
+!> coefficients. This is useful for finding the location on the the
+!> RBF reconstruction of a function (e.g., a height field) that minimizes
+!> the distance to a point in 3D space. The reconstruction is performed
+!> with basis functions that are RBFs and constant
+!> Input:
+!> fieldCount - the number fields to be evaluated. This is useful for reconstructing,
+!> for example, the x-, y- and z-components of a vector field at the same
+!> point in 2D
+!> coeffCount - the size of coefficients, must be at least pointCount + 1
+!> pointCount - the number of "source" points and functionValues supplied
+!> coefficients - the coefficients needed to perform interpolation of the funciton
+!> at the evaluationPoint
+!> evaluationPoint - the point in 2D where the function is to be reconstructed
+!> points - the location of the "source" points in the 2D space where the values of
+!> the function are known
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> derivs - the value of the function, the 2 components of its Jacobian and
+!> the 3 unique components of its Hessian at the evaluationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_loc_2D_sca_const_eval_with_derivs(fieldCount, coeffCount, &!{{{
pointCount, coefficients, evaluationPoint, points, alpha, derivs)
- integer, intent(in) :: fieldCount, coeffCount, pointCount
- real(kind=RKIND), dimension(coeffCount, fieldCount), intent(in) :: coefficients
- real(kind=RKIND), dimension(2), intent(in) :: evaluationPoint
- real(kind=RKIND), dimension(pointCount,2), intent(in) :: points
- real(kind=RKIND), intent(in) :: alpha
+ integer, intent(in) :: fieldCount !< Input: Number of fields
+ integer, intent(in) :: coeffCount !< Input: Number of coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(coeffCount, fieldCount), intent(in) :: coefficients !< Input: List of coefficients
+ real(kind=RKIND), dimension(2), intent(in) :: evaluationPoint !< Input: Location for evaluation
+ real(kind=RKIND), dimension(pointCount,2), intent(in) :: points !< Input: List of points
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale for RBFs
- real(kind=RKIND), dimension(6,fieldCount), intent(out) :: derivs
+ real(kind=RKIND), dimension(6,fieldCount), intent(out) :: derivs !< Output: List of derivatives
integer :: pointIndex
real(kind=RKIND) :: x, y, rSquared, rbfValue, rbfDerivOverR, rbfSecondDeriv
@@ -369,43 +409,53 @@
end if
end do
derivs(1,:) = derivs(1,:) + coefficients(pointCount+1,:)
- end subroutine mpas_rbf_interp_loc_2D_sca_const_eval_with_derivs
+ end subroutine mpas_rbf_interp_loc_2D_sca_const_eval_with_derivs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Evalute a scalar function in 2D using coefficients computed in
- ! rbfInterp_loc_2D_sca_const_compCoeffs. This
- ! function can be called repeatedly with different destination points
- ! to quickly evaluate the interpolating function using the same
- ! coefficients. This is useful for finding the location on the the
- ! RBF reconstruction of a function (e.g., a height field) that minimizes
- ! the distance to a point in 3D space. The reconstruction is performed
- ! with basis functions that are RBFs, constant and linear
- ! Input:
- ! fieldCount - the number fields to be evaluated. This is useful for reconstructing,
- ! for example, the x-, y- and z-components of a vector field at the same
- ! point in 2D
- ! coeffCount - the size of coefficients, must be at least pointCount + 1
- ! pointCount - the number of "source" points and functionValues supplied
- ! coefficients - the coefficients needed to perform interpolation of the funciton
- ! at the evaluationPoint
- ! evaluationPoint - the point in 2D where the function is to be reconstructed
- ! points - the location of the "source" points in the 2D space where the values of
- ! the function are known
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! derivs - the value of the function, the 2 components of its Jacobian and
- ! the 3 unique components of its Hessian at the evaluationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_loc_2D_sca_lin_eval_with_derivs(fieldCount, coeffCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_loc_2D_sca_lin_eval_with_derivs
+!
+!> \brief MPAS 2D scalar linear evaluation routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine evalutes a scalar function in 2D using coefficients computed in
+!> rbfInterp_loc_2D_sca_const_compCoeffs. This
+!> function can be called repeatedly with different destination points
+!> to quickly evaluate the interpolating function using the same
+!> coefficients. This is useful for finding the location on the the
+!> RBF reconstruction of a function (e.g., a height field) that minimizes
+!> the distance to a point in 3D space. The reconstruction is performed
+!> with basis functions that are RBFs, constant and linear
+!> Input:
+!> fieldCount - the number fields to be evaluated. This is useful for reconstructing,
+!> for example, the x-, y- and z-components of a vector field at the same
+!> point in 2D
+!> coeffCount - the size of coefficients, must be at least pointCount + 1
+!> pointCount - the number of "source" points and functionValues supplied
+!> coefficients - the coefficients needed to perform interpolation of the funciton
+!> at the evaluationPoint
+!> evaluationPoint - the point in 2D where the function is to be reconstructed
+!> points - the location of the "source" points in the 2D space where the values of
+!> the function are known
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> derivs - the value of the function, the 2 components of its Jacobian and
+!> the 3 unique components of its Hessian at the evaluationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_loc_2D_sca_lin_eval_with_derivs(fieldCount, coeffCount, &!{{{
pointCount, coefficients, evaluationPoint, points, alpha, derivs)
- integer, intent(in) :: fieldCount, coeffCount, pointCount
- real(kind=RKIND), dimension(coeffCount, fieldCount), intent(in) :: coefficients
- real(kind=RKIND), dimension(2), intent(in) :: evaluationPoint
- real(kind=RKIND), dimension(pointCount,2), intent(in) :: points
- real(kind=RKIND), intent(in) :: alpha
+ integer, intent(in) :: fieldCount !< Input: Number of fields
+ integer, intent(in) :: coeffCount !< Input: Number of coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(coeffCount, fieldCount), intent(in) :: coefficients !< Input: List of coefficients
+ real(kind=RKIND), dimension(2), intent(in) :: evaluationPoint !< Input: Point for evaluation
+ real(kind=RKIND), dimension(pointCount,2), intent(in) :: points !< Input: List of points
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
- real(kind=RKIND), dimension(6,fieldCount), intent(out) :: derivs
+ real(kind=RKIND), dimension(6,fieldCount), intent(out) :: derivs !< Output: Derivatives
integer :: pointIndex
real(kind=RKIND) :: x, y, rSquared, rbfValue, rbfDerivOverR, rbfSecondDeriv
@@ -442,39 +492,47 @@
derivs(2,:) = derivs(2,:) + coefficients(pointCount+2,:)
derivs(3,:) = derivs(3,:) + coefficients(pointCount+3,:)
- end subroutine mpas_rbf_interp_loc_2D_sca_lin_eval_with_derivs
+ end subroutine mpas_rbf_interp_loc_2D_sca_lin_eval_with_derivs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 3D that can be used to
- ! interpolate a number of scalar functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling Dirichlet boundary
- ! conditions (or no boundaries). The interpolation is performed with basis functions
- ! that are RBFs plus a constant.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known
- ! destinationPoint - the point where the interpolation will be performed
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! coefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_sca_const_dir_comp_coeffs( &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_sca_const_dir_comp_coeffs
+!
+!> \brief MPAS 3D scalar constant coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 3D that can be used to
+!> interpolate a number of scalar functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling Dirichlet boundary
+!> conditions (or no boundaries). The interpolation is performed with basis functions
+!> that are RBFs plus a constant.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known
+!> destinationPoint - the point where the interpolation will be performed
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> coefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_sca_const_dir_comp_coeffs( &!{{{
pointCount, sourcePoints, destinationPoint, alpha, coefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of source points
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: List of destination points
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(pointCount), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j
integer :: matrixSize
@@ -513,46 +571,54 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_sca_const_dir_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_sca_const_dir_comp_coeffs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in a plane in 3D that can be used to
- ! interpolate a number of scalar functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling both Dirichlet (or no)
- ! boundary conditions. The interpolation is performed with basis functions that are
- ! RBFs plus constant and linear. All points are projected into the plane given by the
- ! planeBasisVectors.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known. The points will be projected into the plane given by
- ! planeBasisVectors
- ! destinationPoint - the point in 3D where the interpolation will be performed. The
- ! destinationPoint will be projected into the plane given by planeBasisVectors.
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! planeBasisVectors - the basis fectors for the plane where interpolation is performed.
- ! All points are projected into this plane.
- ! Output:
- ! coefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_plane_sca_lin_dir_comp_coeffs( &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_plane_sca_lin_dir_comp_coeffs
+!
+!> \brief MPAS 3D planar scalar linear coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in a plane in 3D that can be used to
+!> interpolate a number of scalar functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling both Dirichlet (or no)
+!> boundary conditions. The interpolation is performed with basis functions that are
+!> RBFs plus constant and linear. All points are projected into the plane given by the
+!> planeBasisVectors.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known. The points will be projected into the plane given by
+!> planeBasisVectors
+!> destinationPoint - the point in 3D where the interpolation will be performed. The
+!> destinationPoint will be projected into the plane given by planeBasisVectors.
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> planeBasisVectors - the basis fectors for the plane where interpolation is performed.
+!> All points are projected into this plane.
+!> Output:
+!> coefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_plane_sca_lin_dir_comp_coeffs( &!{{{
pointCount, sourcePoints, destinationPoint, &
alpha, planeBasisVectors, coefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(2,3) :: planeBasisVectors
- real(kind=RKIND), dimension(pointCount), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of source points
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(2,3) :: planeBasisVectors !< Input: Basis vectors for the interpolation plane
+ real(kind=RKIND), dimension(pointCount), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j
integer :: matrixSize
@@ -596,39 +662,47 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_plane_sca_lin_dir_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_plane_sca_lin_dir_comp_coeffs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 3D that can be used to
- ! interpolate a number of scalar functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling both Dirichlet (or no)
- ! boundary conditions. The interpolation is performed with basis functions that are
- ! RBFs plus constant and linear.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known
- ! destinationPoint - the point where the interpolation will be performed
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! coefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_sca_lin_dir_comp_coeffs(pointCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_sca_lin_dir_comp_coeffs
+!
+!> \brief MPAS 3D scalar linear coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 3D that can be used to
+!> interpolate a number of scalar functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling both Dirichlet (or no)
+!> boundary conditions. The interpolation is performed with basis functions that are
+!> RBFs plus constant and linear.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known
+!> destinationPoint - the point where the interpolation will be performed
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> coefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_sca_lin_dir_comp_coeffs(pointCount, &!{{{
sourcePoints, destinationPoint, alpha, coefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of source points
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale for RBFs
+ real(kind=RKIND), dimension(pointCount), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j
integer :: matrixSize
@@ -670,52 +744,60 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_sca_lin_dir_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_sca_lin_dir_comp_coeffs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 3D that can be used to
- ! interpolate a number of scalar functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling both Dirichlet and Neumann
- ! boundary conditions. The interpolation is performed with basis functions that are
- ! RBFs plus a constant.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known
- ! isInterface - a logical array indicating which of the source points (if any) are at
- ! at the domain interface. These points and their normals will be used to compute the
- ! neumannCoefficients below
- ! interfaceNormals - a 3D normal vector for each sourcePoint. These vectors are only used
- ! at points where isInterface == .true., and can take arbitrary values elsewehere. The
- ! normal vector is used to compute coefficients for the normal derivative of the
- ! interpolating function in order to impose the Neumann Boundary condition
- ! destinationPoint - the point where the interpolation will be performed
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! dirichletCoefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- ! neumannCoefficients - the coefficients used to interpolate a function with Neumann
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_sca_const_dir_neu_comp_coeffs( &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_sca_const_dir_neu_comp_coeffs
+!
+!> \brief MPAS 3D scalar constant Dirichlet and Neumann coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 3D that can be used to
+!> interpolate a number of scalar functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling both Dirichlet and Neumann
+!> boundary conditions. The interpolation is performed with basis functions that are
+!> RBFs plus a constant.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known
+!> isInterface - a logical array indicating which of the source points (if any) are at
+!> at the domain interface. These points and their normals will be used to compute the
+!> neumannCoefficients below
+!> interfaceNormals - a 3D normal vector for each sourcePoint. These vectors are only used
+!> at points where isInterface == .true., and can take arbitrary values elsewehere. The
+!> normal vector is used to compute coefficients for the normal derivative of the
+!> interpolating function in order to impose the Neumann Boundary condition
+!> destinationPoint - the point where the interpolation will be performed
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> dirichletCoefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!> neumannCoefficients - the coefficients used to interpolate a function with Neumann
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_sca_const_dir_neu_comp_coeffs( &!{{{
pointCount, sourcePoints, isInterface, interfaceNormals, destinationPoint, &
alpha, dirichletCoefficients, neumannCoefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- logical, dimension(pointCount), intent(in) :: isInterface
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: interfaceNormals
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount), intent(out) :: &
- dirichletCoefficients, neumannCoefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of source points
+ logical, dimension(pointCount), intent(in) :: isInterface !< Input: Logicals determining if a source point is at an interface
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: interfaceNormals !< Input: Normal vector at interface for each source point
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(pointCount), intent(out) :: dirichletCoefficients !< Output: Coefficients with Dirichlet BCs
+ real(kind=RKIND), dimension(pointCount), intent(out) :: neumannCoefficients !< Output: Coefficients with Neumann BCs
integer :: i, j
integer :: matrixSize
@@ -772,58 +854,66 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_sca_const_dir_neu_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_sca_const_dir_neu_comp_coeffs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in a plane in 3D that can be used to
- ! interpolate a number of scalar functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling both Dirichlet and Neumann
- ! boundary conditions. The interpolation is performed with basis functions that are
- ! RBFs plus constant and linear. All points are projected into the plane given by the
- ! planeBasisVectors.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known. The sourcePoints will be projected into the plane given by
- ! planeBasisVectors
- ! isInterface - a logical array indicating which of the source points (if any) are at
- ! at the domain interface. These points and their normals will be used to compute the
- ! neumannCoefficients below
- ! interfaceNormals - a 3D normal vector for each sourcePoint. These vectors are only used
- ! at points where isInterface == .true., and can take arbitrary values elsewehere. The
- ! normal vector is used to compute coefficients for the normal derivative of the
- ! interpolating function in order to impose the Neumann Boundary condition
- ! destinationPoint - the point in 3D where the interpolation will be performed. The
- ! destinationPoint will be projected into the plane given by planeBasisVectors.
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! planeBasisVectors - the basis fectors for the plane where interpolation is performed.
- ! All points are projected into this plane.
- ! Output:
- ! dirichletCoefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- ! neumannCoefficients - the coefficients used to interpolate a function with Neumann
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_plane_sca_lin_dir_neu_comp_coeffs( &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_plane_sca_lin_dir_neu_comp_coeffs
+!
+!> \brief MPAS 3D scalar planar linear Dirichlet and Neumann coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in a plane in 3D that can be used to
+!> interpolate a number of scalar functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling both Dirichlet and Neumann
+!> boundary conditions. The interpolation is performed with basis functions that are
+!> RBFs plus constant and linear. All points are projected into the plane given by the
+!> planeBasisVectors.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known. The sourcePoints will be projected into the plane given by
+!> planeBasisVectors
+!> isInterface - a logical array indicating which of the source points (if any) are at
+!> at the domain interface. These points and their normals will be used to compute the
+!> neumannCoefficients below
+!> interfaceNormals - a 3D normal vector for each sourcePoint. These vectors are only used
+!> at points where isInterface == .true., and can take arbitrary values elsewehere. The
+!> normal vector is used to compute coefficients for the normal derivative of the
+!> interpolating function in order to impose the Neumann Boundary condition
+!> destinationPoint - the point in 3D where the interpolation will be performed. The
+!> destinationPoint will be projected into the plane given by planeBasisVectors.
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> planeBasisVectors - the basis fectors for the plane where interpolation is performed.
+!> All points are projected into this plane.
+!> Output:
+!> dirichletCoefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!> neumannCoefficients - the coefficients used to interpolate a function with Neumann
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_plane_sca_lin_dir_neu_comp_coeffs( &!{{{
pointCount, sourcePoints, isInterface, interfaceNormals, destinationPoint, &
alpha, planeBasisVectors, dirichletCoefficients, neumannCoefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- logical, dimension(pointCount), intent(in) :: isInterface
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: interfaceNormals
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(2,3) :: planeBasisVectors
- real(kind=RKIND), dimension(pointCount), intent(out) :: &
- dirichletCoefficients, neumannCoefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of points
+ logical, dimension(pointCount), intent(in) :: isInterface !< Input: List of logicals determining if point is at an interface
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: interfaceNormals !< Input: List of interface normals
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(2,3) :: planeBasisVectors !< Input: Basis vectors for interpolation plane
+ real(kind=RKIND), dimension(pointCount), intent(out) :: dirichletCoefficients !< Output: List of Dirichlet coefficients
+ real(kind=RKIND), dimension(pointCount), intent(out) :: neumannCoefficients !< Output: List of Neumann coefficients
integer :: i, j
integer :: matrixSize
@@ -889,52 +979,60 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_plane_sca_lin_dir_neu_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_plane_sca_lin_dir_neu_comp_coeffs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 3D that can be used to
- ! interpolate a number of scalar functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling both Dirichlet and Neumann
- ! boundary conditions. The interpolation is performed with basis functions that are
- ! RBFs plus constant and linear.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known
- ! isInterface - a logical array indicating which of the source points (if any) are at
- ! at the domain interface. These points and their normals will be used to compute the
- ! neumannCoefficients below
- ! interfaceNormals - a 3D normal vector for each sourcePoint. These vectors are only used
- ! at points where isInterface == .true., and can take arbitrary values elsewehere. The
- ! normal vector is used to compute coefficients for the normal derivative of the
- ! interpolating function in order to impose the Neumann Boundary condition
- ! destinationPoint - the point where the interpolation will be performed
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! dirichletCoefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- ! neumannCoefficients - the coefficients used to interpolate a function with Neumann
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_sca_lin_dir_neu_comp_coeffs(pointCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_sca_lin_dir_neu_comp_coeffs
+!
+!> \brief MPAS 3D scalar linear Dirichlet and Neumann coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 3D that can be used to
+!> interpolate a number of scalar functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling both Dirichlet and Neumann
+!> boundary conditions. The interpolation is performed with basis functions that are
+!> RBFs plus constant and linear.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known
+!> isInterface - a logical array indicating which of the source points (if any) are at
+!> at the domain interface. These points and their normals will be used to compute the
+!> neumannCoefficients below
+!> interfaceNormals - a 3D normal vector for each sourcePoint. These vectors are only used
+!> at points where isInterface == .true., and can take arbitrary values elsewehere. The
+!> normal vector is used to compute coefficients for the normal derivative of the
+!> interpolating function in order to impose the Neumann Boundary condition
+!> destinationPoint - the point where the interpolation will be performed
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> dirichletCoefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!> neumannCoefficients - the coefficients used to interpolate a function with Neumann
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_sca_lin_dir_neu_comp_coeffs(pointCount, &!{{{
sourcePoints, isInterface, interfaceNormals, destinationPoint, &
alpha, dirichletCoefficients, neumannCoefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- logical, dimension(pointCount), intent(in) :: isInterface
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: interfaceNormals
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount), intent(out) :: &
- dirichletCoefficients, neumannCoefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of points
+ logical, dimension(pointCount), intent(in) :: isInterface !< Input: List of logicals determining if point as at an interface
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: interfaceNormals !< Input: List of interface normals
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(pointCount), intent(out) :: dirichletCoefficients !< Output: List of Dirichlet coefficients
+ real(kind=RKIND), dimension(pointCount), intent(out) :: neumannCoefficients !< Outut: List of Neumann coefficients
integer :: i, j
integer :: matrixSize
@@ -997,45 +1095,53 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_sca_lin_dir_neu_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_sca_lin_dir_neu_comp_coeffs!}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 3D that can be used to
- ! interpolate a number of vector functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the vector fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling Dirichlet boundary
- ! conditions (or no boundaries). The interpolation is performed with basis functions
- ! that are RBFs plus a constant.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known
- ! unitVectors - the unit vectors associated with each of the sourcePoints. Interpolation
- ! is performed by supplying the value of the vector function dotted into each of these unit
- ! vectors. If multiple unit vectors are supplied at the same sourcePoint, they *must* be
- ! orthogonal for the interpolation to succeed.
- ! destinationPoint - the point where the interpolation will be performed
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! coefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_vec_const_dir_comp_coeffs(pointCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_vec_const_dir_comp_coeffs
+!
+!> \brief MPAS 3D vector constant Dirichlet coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 3D that can be used to
+!> interpolate a number of vector functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the vector fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling Dirichlet boundary
+!> conditions (or no boundaries). The interpolation is performed with basis functions
+!> that are RBFs plus a constant.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known
+!> unitVectors - the unit vectors associated with each of the sourcePoints. Interpolation
+!> is performed by supplying the value of the vector function dotted into each of these unit
+!> vectors. If multiple unit vectors are supplied at the same sourcePoint, they *must* be
+!> orthogonal for the interpolation to succeed.
+!> destinationPoint - the point where the interpolation will be performed
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> coefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_vec_const_dir_comp_coeffs(pointCount, &!{{{
sourcePoints, unitVectors, destinationPoint, &
alpha, coefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: unitVectors
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount, 3), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: unitVectors !< Input: List of unit vectors
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(pointCount, 3), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j
integer :: matrixSize
@@ -1082,51 +1188,59 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_vec_const_dir_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_vec_const_dir_comp_coeffs !}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 3D that can be used to
- ! interpolate a number of vector functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the vector fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling Dirichlet boundary
- ! conditions (or no boundaries). The interpolation is performed with basis functions
- ! that are RBFs plus a constant.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known. The sourcePoints are projected into the plane given by
- ! planeBasisVectors
- ! unitVectors - the unit vectors associated with each of the sourcePoints. Interpolation
- ! is performed by supplying the value of the vector function dotted into each of these unit
- ! vectors. If multiple unit vectors are supplied at the same sourcePoint, they *must* be
- ! orthogonal for the interpolation to succeed. The unitVectors are projected into the
- ! plane given by planeBasisVectors
- ! destinationPoint - the point where the interpolation will be performed. The destinationPoint
- ! is projected into the plane given by planeBasisVectors
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! planeBasisVectors - the basis fectors for the plane where interpolation is performed.
- ! All points are projected into this plane.
- ! Output:
- ! coefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_plane_vec_const_dir_comp_coeffs(pointCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_plane_vec_const_dir_comp_coeffs
+!
+!> \brief MPAS 3D vector planar constant Dirichlet coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 3D that can be used to
+!> interpolate a number of vector functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the vector fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling Dirichlet boundary
+!> conditions (or no boundaries). The interpolation is performed with basis functions
+!> that are RBFs plus a constant.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known. The sourcePoints are projected into the plane given by
+!> planeBasisVectors
+!> unitVectors - the unit vectors associated with each of the sourcePoints. Interpolation
+!> is performed by supplying the value of the vector function dotted into each of these unit
+!> vectors. If multiple unit vectors are supplied at the same sourcePoint, they *must* be
+!> orthogonal for the interpolation to succeed. The unitVectors are projected into the
+!> plane given by planeBasisVectors
+!> destinationPoint - the point where the interpolation will be performed. The destinationPoint
+!> is projected into the plane given by planeBasisVectors
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> planeBasisVectors - the basis fectors for the plane where interpolation is performed.
+!> All points are projected into this plane.
+!> Output:
+!> coefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_plane_vec_const_dir_comp_coeffs(pointCount, &!{{{
sourcePoints, unitVectors, destinationPoint, &
alpha, planeBasisVectors, coefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: unitVectors
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(2,3) :: planeBasisVectors
- real(kind=RKIND), dimension(pointCount, 3), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: unitVectors !< Input: List of unit vectors
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(2,3) :: planeBasisVectors !< Input: Basis vectors for interpolation plane
+ real(kind=RKIND), dimension(pointCount, 3), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j
integer :: matrixSize
@@ -1191,55 +1305,63 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_plane_vec_const_dir_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_plane_vec_const_dir_comp_coeffs !}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 3D that can be used to
- ! interpolate a number of vector functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the vector fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling Dirichlet normal /
- ! Neumann tangential boundary conditions (such as free slip). The interpolation is
- ! performed with basis functions that are RBFs plus a constant.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known
- ! isTangentToInterface - a logical array indicating which sourcePoints/unitVectors are
- ! tangent to the interface where the boundary condition will be applied. A Neumann
- ! boundary condition will be applied at these points in these directions.
- ! normalVectorIndex - where isTangentToInterface == .true., the index into unitVectors that
- ! gives the normal vector at the same sourcePoint. This information is needed to compute
- ! the Neumann boundary condition at this point.
- ! unitVectors - the unit vectors associated with each of the sourcePoints. Interpolation
- ! is performed by supplying the value of the vector function dotted into each of these unit
- ! vectors. If multiple unit vectors are supplied at the same sourcePoint, they *must* be
- ! orthogonal for the interpolation to succeed. A normal vector and two tangential vectors
- ! are needed at each interface point in order to satisfy the Dirichlet normal boundary
- ! condition and the Neumann tangential boundary conditions at these points.
- ! destinationPoint - the point where the interpolation will be performed
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! Output:
- ! coefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_vec_const_tan_neu_comp_coeffs(pointCount, &
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_vec_const_tan_neu_comp_coeffs
+!
+!> \brief MPAS 3D vector constant tangent Neumann coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 3D that can be used to
+!> interpolate a number of vector functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the vector fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling Dirichlet normal /
+!> Neumann tangential boundary conditions (such as free slip). The interpolation is
+!> performed with basis functions that are RBFs plus a constant.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known
+!> isTangentToInterface - a logical array indicating which sourcePoints/unitVectors are
+!> tangent to the interface where the boundary condition will be applied. A Neumann
+!> boundary condition will be applied at these points in these directions.
+!> normalVectorIndex - where isTangentToInterface == .true., the index into unitVectors that
+!> gives the normal vector at the same sourcePoint. This information is needed to compute
+!> the Neumann boundary condition at this point.
+!> unitVectors - the unit vectors associated with each of the sourcePoints. Interpolation
+!> is performed by supplying the value of the vector function dotted into each of these unit
+!> vectors. If multiple unit vectors are supplied at the same sourcePoint, they *must* be
+!> orthogonal for the interpolation to succeed. A normal vector and two tangential vectors
+!> are needed at each interface point in order to satisfy the Dirichlet normal boundary
+!> condition and the Neumann tangential boundary conditions at these points.
+!> destinationPoint - the point where the interpolation will be performed
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> Output:
+!> coefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+ subroutine mpas_rbf_interp_func_3D_vec_const_tan_neu_comp_coeffs(pointCount, &!{{{
sourcePoints, isTangentToInterface, normalVectorIndex, unitVectors, destinationPoint, &
alpha, coefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- logical, dimension(pointCount), intent(in) :: isTangentToInterface
- integer, dimension(pointCount), intent(in) :: normalVectorIndex
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: unitVectors
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount, 3), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of points
+ logical, dimension(pointCount), intent(in) :: isTangentToInterface !< Input: List of logicals determining if point is tangent to interface
+ integer, dimension(pointCount), intent(in) :: normalVectorIndex !< Input: Index of for normal vectors
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: unitVectors !< Input: List of unit vectors
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(pointCount, 3), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j
integer :: matrixSize
@@ -1287,61 +1409,70 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_vec_const_tan_neu_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_vec_const_tan_neu_comp_coeffs !}}}
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- ! Purpose: Compute interpolation coefficients in 3D that can be used to
- ! interpolate a number of vector functions at a given locations. This is useful
- ! if the interpolation location does not change with time, or if several
- ! fields are to be interpolated at a given time step. (If both the vector fields
- ! and the interpolation locations vary with time, there is no clear advantage in
- ! using either this method or the method for 2D interpoaltion above; for simplicity
- ! and because we foresee more uses for the method of this subroutine, we have not
- ! implemented a 3D version of the fixed field, variable interpolation location method
- ! as we have in 2D.) Coefficients are produced for handling Dirichlet normal /
- ! Neumann tangential boundary conditions (such as free slip). The interpolation is
- ! performed with basis functions that are RBFs plus a constant.
- ! Input:
- ! pointCount - the number of "source" points and functionValues supplied
- ! sourcePoints - the location of the "source" points in the 3D space where the values of
- ! the function are known. The sourcePoints are projected into the plane given by
- ! planeBasisVectors
- ! isTangentToInterface - a logical array indicating which sourcePoints/unitVectors are
- ! tangent to the interface where the boundary condition will be applied. A Neumann
- ! boundary condition will be applied at these points in these directions.
- ! normalVectorIndex - where isTangentToInterface == .true., the index into unitVectors that
- ! gives the normal vector at the same sourcePoint. This information is needed to compute
- ! the Neumann boundary condition at this point.
- ! unitVectors - the unit vectors associated with each of the sourcePoints. Interpolation
- ! is performed by supplying the value of the vector function dotted into each of these unit
- ! vectors. If multiple unit vectors are supplied at the same sourcePoint, they *must* be
- ! orthogonal for the interpolation to succeed. A normal vector and two tangential vectors
- ! are needed at each interface point in order to satisfy the Dirichlet normal boundary
- ! condition and the Neumann tangential boundary conditions at these points. The unitVectors
- ! are projected into the plane given by planeBasisVectors
- ! destinationPoint - the point where the interpolation will be performed. The destinationPoint
- ! is projected into the plane given by planeBasisVectors
- ! alpha - a constant that give the characteristic length scale of the RBFs,
- ! should be on the order of the distance between points
- ! planeBasisVectors - the basis fectors for the plane where interpolation is performed.
- ! All points are projected into this plane.
- ! Output:
- ! coefficients - the coefficients used to interpolate a function with Dirichlet
- ! boundary conditions to the specified destinationPoint
- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- subroutine mpas_rbf_interp_func_3D_plane_vec_const_tan_neu_comp_coeffs(&
+!***********************************************************************
+!
+! routine mpas_rbf_interp_func_3D_plane_vec_const_tan_neu_comp_coeffs
+!
+!> \brief MPAS 3D vector planar constant tangent Neumann coefficients routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes interpolation coefficients in 3D that can be used to
+!> interpolate a number of vector functions at a given locations. This is useful
+!> if the interpolation location does not change with time, or if several
+!> fields are to be interpolated at a given time step. (If both the vector fields
+!> and the interpolation locations vary with time, there is no clear advantage in
+!> using either this method or the method for 2D interpoaltion above; for simplicity
+!> and because we foresee more uses for the method of this subroutine, we have not
+!> implemented a 3D version of the fixed field, variable interpolation location method
+!> as we have in 2D.) Coefficients are produced for handling Dirichlet normal /
+!> Neumann tangential boundary conditions (such as free slip). The interpolation is
+!> performed with basis functions that are RBFs plus a constant.
+!> Input:
+!> pointCount - the number of "source" points and functionValues supplied
+!> sourcePoints - the location of the "source" points in the 3D space where the values of
+!> the function are known. The sourcePoints are projected into the plane given by
+!> planeBasisVectors
+!> isTangentToInterface - a logical array indicating which sourcePoints/unitVectors are
+!> tangent to the interface where the boundary condition will be applied. A Neumann
+!> boundary condition will be applied at these points in these directions.
+!> normalVectorIndex - where isTangentToInterface == .true., the index into unitVectors that
+!> gives the normal vector at the same sourcePoint. This information is needed to compute
+!> the Neumann boundary condition at this point.
+!> unitVectors - the unit vectors associated with each of the sourcePoints. Interpolation
+!> is performed by supplying the value of the vector function dotted into each of these unit
+!> vectors. If multiple unit vectors are supplied at the same sourcePoint, they *must* be
+!> orthogonal for the interpolation to succeed. A normal vector and two tangential vectors
+!> are needed at each interface point in order to satisfy the Dirichlet normal boundary
+!> condition and the Neumann tangential boundary conditions at these points. The unitVectors
+!> are projected into the plane given by planeBasisVectors
+!> destinationPoint - the point where the interpolation will be performed. The destinationPoint
+!> is projected into the plane given by planeBasisVectors
+!> alpha - a constant that give the characteristic length scale of the RBFs,
+!> should be on the order of the distance between points
+!> planeBasisVectors - the basis fectors for the plane where interpolation is performed.
+!> All points are projected into this plane.
+!> Output:
+!> coefficients - the coefficients used to interpolate a function with Dirichlet
+!> boundary conditions to the specified destinationPoint
+!-----------------------------------------------------------------------
+
+ subroutine mpas_rbf_interp_func_3D_plane_vec_const_tan_neu_comp_coeffs(&!{{{
pointCount, sourcePoints, isTangentToInterface, normalVectorIndex, unitVectors, &
destinationPoint, alpha, planeBasisVectors, coefficients)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- logical, dimension(pointCount), intent(in) :: isTangentToInterface
- integer, dimension(pointCount), intent(in) :: normalVectorIndex
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: unitVectors
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(2,3), intent(in) :: planeBasisVectors
- real(kind=RKIND), dimension(pointCount, 3), intent(out) :: coefficients
+ integer, intent(in) :: pointCount !< input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of points
+ logical, dimension(pointCount), intent(in) :: isTangentToInterface !< Input: List of logicals determining if point is tangent to interface
+ integer, dimension(pointCount), intent(in) :: normalVectorIndex !< Input: Index for normal vectors
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: unitVectors !< Input: List of unit vectors
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(2,3), intent(in) :: planeBasisVectors !< Input: Basis vectors for interpolation plane
+ real(kind=RKIND), dimension(pointCount, 3), intent(out) :: coefficients !< Output: List of coefficients
integer :: i, j
integer :: matrixSize
@@ -1407,52 +1538,99 @@
deallocate(coeffs)
deallocate(pivotIndices)
- end subroutine mpas_rbf_interp_func_3D_plane_vec_const_tan_neu_comp_coeffs
+ end subroutine mpas_rbf_interp_func_3D_plane_vec_const_tan_neu_comp_coeffs !}}}
!!!!!!!!!!!!!!!!!!!!!
! private subroutines
!!!!!!!!!!!!!!!!!!!!!
- function evaluate_rbf(rSquared) result(rbfValue)
- real(kind=RKIND), intent(in) :: rSquared
+!***********************************************************************
+!
+! function evaluate_rbf
+!
+!> \brief MPAS RBF Evaluation function
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This function evaluates an RBF and returns the value.
+!-----------------------------------------------------------------------
+ function evaluate_rbf(rSquared) result(rbfValue)!{{{
+ real(kind=RKIND), intent(in) :: rSquared !< Input: Squared value of r
real(kind=RKIND) :: rbfValue
! inverse multiquadratic
rbfValue = 1/sqrt(1 + rSquared)
- end function evaluate_rbf
+ end function evaluate_rbf!}}}
- subroutine mpas_evaluate_rbf_and_deriv(rSquared, rbfValue, rbfDerivOverR)
- real(kind=RKIND), intent(in) :: rSquared
- real(kind=RKIND), intent(out) :: rbfValue, rbfDerivOverR
+!***********************************************************************
+!
+! routine mpas_evaluate_rbf_and_deriv
+!
+!> \brief MPAS RBF Evaluation and derivative routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes the value and derivative of a RBF.
+!-----------------------------------------------------------------------
+ subroutine mpas_evaluate_rbf_and_deriv(rSquared, rbfValue, rbfDerivOverR)!{{{
+ real(kind=RKIND), intent(in) :: rSquared !< Input: Squared value of R
+ real(kind=RKIND), intent(out) :: rbfValue !< Output: Value of RBF
+ real(kind=RKIND), intent(out) :: rbfDerivOverR !< Outut: Derivative of RBF over R
! inverse multiquadratic
rbfValue = 1/sqrt(1 + rSquared)
rbfDerivOverR = -rbfValue**3
- end subroutine mpas_evaluate_rbf_and_deriv
+ end subroutine mpas_evaluate_rbf_and_deriv!}}}
- subroutine mpas_evaluate_rbf_and_derivs(rSquared, rbfValue, rbfDerivOverR, rbfSecondDeriv)
- real(kind=RKIND), intent(in) :: rSquared
- real(kind=RKIND), intent(out) :: rbfValue, rbfDerivOverR, rbfSecondDeriv
+!***********************************************************************
+!
+! routine mpas_evaluate_rbf_and_derivs
+!
+!> \brief MPAS RBF Evaluation and first and second derivative routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes the value and the first two derivatives of a RBF.
+!-----------------------------------------------------------------------
+ subroutine mpas_evaluate_rbf_and_derivs(rSquared, rbfValue, rbfDerivOverR, rbfSecondDeriv)!{{{
+ real(kind=RKIND), intent(in) :: rSquared !< Input: Squared value of R
+ real(kind=RKIND), intent(out) :: rbfValue !< Output: Value of RBF
+ real(kind=RKIND), intent(out) :: rbfDerivOverR !< Output: Value of first derivative of RBF
+ real(kind=RKIND), intent(out) :: rbfSecondDeriv !< Output: Value of second derivative of RBF
! inverse multiquadratic
rbfValue = 1/sqrt(1 + rSquared)
rbfDerivOverR = -rbfValue**3
rbfSecondDeriv = (2*rSquared-1)*rbfValue**5
- end subroutine mpas_evaluate_rbf_and_derivs
+ end subroutine mpas_evaluate_rbf_and_derivs!}}}
- subroutine mpas_set_up_scalar_rbf_dirichlet_matrix_and_rhs(pointCount, sourcePoints, destinationPoint, &
+!***********************************************************************
+!
+! routine mpas_set_up_scalar_rbf_dirichlet_matrix_and_rhs
+!
+!> \brief MPAS RBF Scalar Matrix and RHS setup routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine sets up the matrix and RHS for scalar Dirichlet RBF interpolation.
+!-----------------------------------------------------------------------
+ subroutine mpas_set_up_scalar_rbf_dirichlet_matrix_and_rhs(pointCount, sourcePoints, destinationPoint, &!{{{
alpha, dirichletMatrix, rhs)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: dirichletMatrix
- real(kind=RKIND), dimension(pointCount), intent(out) :: rhs
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of points
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBF
+ real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: dirichletMatrix !< Output: Matrix
+ real(kind=RKIND), dimension(pointCount), intent(out) :: rhs !< Output: Right hand side
integer :: i, j
@@ -1471,21 +1649,32 @@
rhs(j) = evaluate_rbf(rSquared)
end do
- end subroutine mpas_set_up_scalar_rbf_dirichlet_matrix_and_rhs
+ end subroutine mpas_set_up_scalar_rbf_dirichlet_matrix_and_rhs!}}}
- subroutine mpas_set_up_scalar_rbf_matrix_and_rhs(pointCount, &
+!***********************************************************************
+!
+! routine mpas_set_up_scalar_rbf_matrix_and_rhs
+!
+!> \brief MPAS RBF Scalar Matrix and RHS setup routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine sets up the matrix and RHS for scalar Dirichlet and Neumann RBF interpolation.
+!-----------------------------------------------------------------------
+ subroutine mpas_set_up_scalar_rbf_matrix_and_rhs(pointCount, &!{{{
sourcePoints, isInterface, interfaceNormals, destinationPoint, &
alpha, dirichletMatrix, neumannMatrix, rhs)
- integer, intent(in) :: pointCount
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints
- logical, dimension(pointCount), intent(in) :: isInterface
- real(kind=RKIND), dimension(pointCount,3), intent(in) :: interfaceNormals
- real(kind=RKIND), dimension(3), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: &
- dirichletMatrix, neumannMatrix
- real(kind=RKIND), dimension(pointCount), intent(out) :: rhs
+ integer, intent(in) :: pointCount !< Input: Number of points
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: sourcePoints !< Input: List of points
+ logical, dimension(pointCount), intent(in) :: isInterface !< Input: Logicals determining if point is an interface
+ real(kind=RKIND), dimension(pointCount,3), intent(in) :: interfaceNormals !< Input: Normals at interfaces
+ real(kind=RKIND), dimension(3), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBF
+ real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: dirichletMatrix !< Output: Dirichlet Matrix
+ real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: neumannMatrix !< Output: Neumann Matrix
+ real(kind=RKIND), dimension(pointCount), intent(out) :: rhs !< Output: Right hand side
integer :: i, j
@@ -1517,19 +1706,31 @@
rhs(j) = evaluate_rbf(rSquared)
end do
- end subroutine mpas_set_up_scalar_rbf_matrix_and_rhs
+ end subroutine mpas_set_up_scalar_rbf_matrix_and_rhs!}}}
- subroutine mpas_set_up_vector_dirichlet_rbf_matrix_and_rhs(pointCount, dimensions, &
+!***********************************************************************
+!
+! routine mpas_set_up_vector_dirichlet_rbf_matrix_and_rhs
+!
+!> \brief MPAS RBF Vector Matrix and RHS setup routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine sets up the matrix and RHS for vector Dirichlet RBF interpolation.
+!-----------------------------------------------------------------------
+ subroutine mpas_set_up_vector_dirichlet_rbf_matrix_and_rhs(pointCount, dimensions, &!{{{
sourcePoints, unitVectors, destinationPoint, &
alpha, matrix, rhs)
- integer, intent(in) :: pointCount, dimensions
- real(kind=RKIND), dimension(pointCount,dimensions), intent(in) :: sourcePoints
- real(kind=RKIND), dimension(pointCount,dimensions), intent(in) :: unitVectors
- real(kind=RKIND), dimension(dimensions), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: matrix
- real(kind=RKIND), dimension(pointCount,dimensions), intent(out) :: rhs
+ integer, intent(in) :: pointCount !< Input: Number of points
+ integer, intent(in) :: dimensions !< Input: Number of dimensions
+ real(kind=RKIND), dimension(pointCount,dimensions), intent(in) :: sourcePoints !< Input: List of points
+ real(kind=RKIND), dimension(pointCount,dimensions), intent(in) :: unitVectors !< Input: List of unit vectors
+ real(kind=RKIND), dimension(dimensions), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBFs
+ real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: matrix !< Output: Matrix
+ real(kind=RKIND), dimension(pointCount,dimensions), intent(out) :: rhs !< Output: Right hand side
integer :: i, j
@@ -1550,21 +1751,33 @@
rhs(j,:) = evaluate_rbf(rSquared)*unitVectors(j,:)
end do
- end subroutine mpas_set_up_vector_dirichlet_rbf_matrix_and_rhs
+ end subroutine mpas_set_up_vector_dirichlet_rbf_matrix_and_rhs!}}}
- subroutine mpas_set_up_vector_free_slip_rbf_matrix_and_rhs(pointCount, dimensions, &
+!***********************************************************************
+!
+! routine mpas_set_up_vector_free_slip_rbf_matrix_and_rhs
+!
+!> \brief MPAS RBF Vector Matrix and RHS setup routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine sets up the matrix and RHS for vector Free Slip RBF interpolation.
+!-----------------------------------------------------------------------
+ subroutine mpas_set_up_vector_free_slip_rbf_matrix_and_rhs(pointCount, dimensions, &!{{{
sourcePoints, isTangentToInterface, normalVectorIndex, unitVectors, destinationPoint, &
alpha, matrix, rhs)
- integer, intent(in) :: pointCount, dimensions
- real(kind=RKIND), dimension(pointCount,dimensions), intent(in) :: sourcePoints
- logical, dimension(pointCount), intent(in) :: isTangentToInterface
- integer, dimension(pointCount), intent(in) :: normalVectorIndex
- real(kind=RKIND), dimension(pointCount,dimensions), intent(in) :: unitVectors
- real(kind=RKIND), dimension(dimensions), intent(in) :: destinationPoint
- real(kind=RKIND), intent(in) :: alpha
- real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: matrix
- real(kind=RKIND), dimension(pointCount,dimensions), intent(out) :: rhs
+ integer, intent(in) :: pointCount !< Input: Number of points
+ integer, intent(in) :: dimensions !< Input: Number of dimensions
+ real(kind=RKIND), dimension(pointCount,dimensions), intent(in) :: sourcePoints !< Input: List of points
+ logical, dimension(pointCount), intent(in) :: isTangentToInterface !< Input: Logical to determine if point is tangent to interface
+ integer, dimension(pointCount), intent(in) :: normalVectorIndex !< Input: Index to normal vector
+ real(kind=RKIND), dimension(pointCount,dimensions), intent(in) :: unitVectors !< Input: List of unit vectors
+ real(kind=RKIND), dimension(dimensions), intent(in) :: destinationPoint !< Input: Destination point
+ real(kind=RKIND), intent(in) :: alpha !< Input: Characteristic length scale of RBF
+ real(kind=RKIND), dimension(pointCount,pointCount), intent(out) :: matrix !< Output: Matrix
+ real(kind=RKIND), dimension(pointCount,dimensions), intent(out) :: rhs !< Output: Right hand side
integer :: i, j
@@ -1597,24 +1810,47 @@
rhs(j,:) = evaluate_rbf(rSquared)*unitVectors(j,:)
end do
- end subroutine mpas_set_up_vector_free_slip_rbf_matrix_and_rhs
+ end subroutine mpas_set_up_vector_free_slip_rbf_matrix_and_rhs!}}}
- subroutine mpas_unit_vec_in_r3(xin)
+!***********************************************************************
+!
+! routine mpas_unit_vec_in_r3
+!
+!> \brief MPAS 3D unit vector routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine creates a unit vector out of an input point.
+!-----------------------------------------------------------------------
+ subroutine mpas_unit_vec_in_r3(xin)!{{{
implicit none
- real (kind=RKIND), intent(inout) :: xin(3)
+ real (kind=RKIND), intent(inout) :: xin(3) !< Input/Output: Vector and unit vector
real (kind=RKIND) :: mag
mag = sqrt(xin(1)**2+xin(2)**2+xin(3)**2)
xin(:) = xin(:) / mag
- end subroutine mpas_unit_vec_in_r3
+ end subroutine mpas_unit_vec_in_r3!}}}
- subroutine mpas_cross_product_in_r3(p_1,p_2,p_out)
- real (kind=RKIND), intent(in) :: p_1 (3), p_2 (3)
- real (kind=RKIND), intent(out) :: p_out (3)
+!***********************************************************************
+!
+! routine mpas_cross_product_in_r3
+!
+!> \brief MPAS 3D cross product routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine computes the cross product of two input vectors.
+!-----------------------------------------------------------------------
+ subroutine mpas_cross_product_in_r3(p_1,p_2,p_out)!{{{
+ real (kind=RKIND), intent(in) :: p_1 (3) !< Input: Vector 1
+ real (kind=RKIND), intent(in) :: p_2 (3) !< Input: Vector 2
+ real (kind=RKIND), intent(out) :: p_out (3) !< Output: Cross product of vector 1 and vector 2
p_out(1) = p_1(2)*p_2(3)-p_1(3)*p_2(2)
p_out(2) = p_1(3)*p_2(1)-p_1(1)*p_2(3)
p_out(3) = p_1(1)*p_2(2)-p_1(2)*p_2(1)
- end subroutine mpas_cross_product_in_r3
+ end subroutine mpas_cross_product_in_r3!}}}
! Updated 10/24/2001.
!
@@ -1656,20 +1892,28 @@
! WRITE (6, "(F16.8)") (X(I), I=1,N)
!END PROGRAM EX43
-
-subroutine mpas_legs (A,N,B,X,INDX)
+!***********************************************************************
!
-! subroutine to solve the equation A(N,N)*X(N) = B(N) with the
-! partial-pivoting Gaussian elimination scheme.
-! Copyright (c) Tao Pang 2001.
+! routine mpas_legs
!
+!> \brief MPAS Gaussian elimination solver routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine solves the equation A(N,N)*X(N) = B(N) with the partial-pivoting
+!> Gaussian Elimination scheme. Copyright (c) Tao Pang 2001.
+!-----------------------------------------------------------------------
+subroutine mpas_legs (A,N,B,X,INDX)!{{{
+
IMPLICIT NONE
- integer, INTENT (IN) :: N
- integer :: I,J
- integer, INTENT (OUT), DIMENSION (N) :: INDX
- real(kind=RKIND), INTENT (INOUT), DIMENSION (N,N) :: A
- real(kind=RKIND), INTENT (INOUT), DIMENSION (N) :: B
- real(kind=RKIND), INTENT (OUT), DIMENSION (N) :: X
+ integer, INTENT (IN) :: N !< Input: Size of matrix and vectors
+ integer, INTENT (OUT), DIMENSION (N) :: INDX !< Output: Pivot vector
+ real(kind=RKIND), INTENT (INOUT), DIMENSION (N,N) :: A !< Input/Output: Matrix
+ real(kind=RKIND), INTENT (INOUT), DIMENSION (N) :: B !< Input/Output: Right hand side vector
+ real(kind=RKIND), INTENT (OUT), DIMENSION (N) :: X !< Output: Solution
+
+ integer :: I,J
!
CALL elgs (A,N,INDX)
!
@@ -1688,7 +1932,7 @@
X(I) = X(I)/A(INDX(I),I)
END DO
!
-END subroutine mpas_legs
+END subroutine mpas_legs!}}}
!
@@ -1709,18 +1953,26 @@
! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
-subroutine migs (A,N,X,INDX)
+!***********************************************************************
!
-! subroutine to invert matrix A(N,N) with the inverse stored
-! in X(N,N) in the output. Copyright (c) Tao Pang 2001.
+! routine migs
!
+!> \brief Matrix inversion routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine inverts the matrix A(N,N) and stores it in X(N,B)
+!> Copyright (c) Tao Pang 2001.
+!-----------------------------------------------------------------------
+subroutine migs (A,N,X,INDX)!{{{
IMPLICIT NONE
- integer, INTENT (IN) :: N
+ integer, INTENT (IN) :: N !< Input: Size of matrix and inverse
+ integer, INTENT (OUT), DIMENSION (N) :: INDX !< Output: Pivot vector
+ real(kind=RKIND), INTENT (INOUT), DIMENSION (N,N):: A !< Input/Output: Matrix to invert
+ real(kind=RKIND), INTENT (OUT), DIMENSION (N,N):: X !< Output: Inverse of Matrix
+ real(kind=RKIND), DIMENSION (N,N) :: B
integer :: I,J,K
- integer, INTENT (OUT), DIMENSION (N) :: INDX
- real(kind=RKIND), INTENT (INOUT), DIMENSION (N,N):: A
- real(kind=RKIND), INTENT (OUT), DIMENSION (N,N):: X
- real(kind=RKIND), DIMENSION (N,N) :: B
!
DO I = 1, N
DO J = 1, N
@@ -1751,10 +2003,22 @@
X(J,I) = X(J,I)/A(INDX(J),J)
END DO
END DO
-END subroutine migs
+END subroutine migs!}}}
+!***********************************************************************
+!
+! routine elgs
+!
+!> \brief Partial-pivoting Gaussian elimination routine
+!> \author Xylar Asay-Davis
+!> \date 03/28/13
+!> \version SVN:$Id$
+!> \details
+!> This routine performs the partial-pivoting Gaussian elimination.
+!> Copyright (c) Tao Pang 2001.
+!-----------------------------------------------------------------------
-subroutine elgs (A,N,INDX)
+subroutine elgs (A,N,INDX)!{{{
!
! subroutine to perform the partial-pivoting Gaussian elimination.
! A(N,N) is the original matrix in the input and transformed matrix
@@ -1762,11 +2026,11 @@
! INDX(N) records the pivoting order. Copyright (c) Tao Pang 2001.
!
IMPLICIT NONE
- integer, INTENT (IN) :: N
+ integer, INTENT (IN) :: N !< Input: Size of matrix
+ integer, INTENT (OUT), DIMENSION (N) :: INDX !< Output: Pivot vector
+ real(kind=RKIND), INTENT (INOUT), DIMENSION (N,N) :: A !< Input/Output: Matrix and solution
integer :: I,J,K,ITMP
- integer, INTENT (OUT), DIMENSION (N) :: INDX
real(kind=RKIND) :: C1,PI,PI1,PJ
- real(kind=RKIND), INTENT (INOUT), DIMENSION (N,N) :: A
real(kind=RKIND), DIMENSION (N) :: C
!
! Initialize the index
@@ -1818,7 +2082,7 @@
END DO
END DO
!
-END subroutine elgs
+END subroutine elgs!}}}
end module mpas_rbf_interpolation
</font>
</pre>