\hypertarget{namespaceregrid__interp}{}\section{regrid\+\_\+interp Module Reference} \label{namespaceregrid__interp}\index{regrid\+\_\+interp@{regrid\+\_\+interp}} \subsection{Detailed Description} Vertical interpolation for regridding. \subsection*{Data Types} \begin{DoxyCompactItemize} \item type \hyperlink{structregrid__interp_1_1interp__cs__type}{interp\+\_\+cs\+\_\+type} \begin{DoxyCompactList}\small\item\em Control structure for \hyperlink{namespaceregrid__interp}{regrid\+\_\+interp} module. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine, public \hyperlink{namespaceregrid__interp_a3d1406836d089b4553421776277e1339}{regridding\+\_\+set\+\_\+ppolys} (CS, densities, n0, h0, ppoly0\+\_\+E, ppoly0\+\_\+S, ppoly0\+\_\+coefs, degree, h\+\_\+neglect, h\+\_\+neglect\+\_\+edge) \begin{DoxyCompactList}\small\item\em Builds an interpolated profile for the densities within each grid cell. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespaceregrid__interp_a52b8ce5b52f9d45f8180c6fd75388174}{interpolate\+\_\+grid} (n0, h0, x0, ppoly0\+\_\+E, ppoly0\+\_\+coefs, target\+\_\+values, degree, n1, h1, x1, answers\+\_\+2018) \begin{DoxyCompactList}\small\item\em Given target values (e.\+g., density), build new grid based on polynomial. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespaceregrid__interp_abaef8cc7e1258b61710adbd6fb742122}{build\+\_\+and\+\_\+interpolate\+\_\+grid} (CS, densities, n0, h0, x0, target\+\_\+values, n1, h1, x1, h\+\_\+neglect, h\+\_\+neglect\+\_\+edge) \begin{DoxyCompactList}\small\item\em Build a grid by interpolating for target values. \end{DoxyCompactList}\item real function \hyperlink{namespaceregrid__interp_a30dfad0833745d069498db25c1538238}{get\+\_\+polynomial\+\_\+coordinate} (N, h, x\+\_\+g, edge\+\_\+values, ppoly\+\_\+coefs, target\+\_\+value, degree, answers\+\_\+2018) \begin{DoxyCompactList}\small\item\em Given a target value, find corresponding coordinate for given polynomial. \end{DoxyCompactList}\item integer function \hyperlink{namespaceregrid__interp_ab4d21d91c26022a3e79268be4fe14d44}{interpolation\+\_\+scheme} (interp\+\_\+scheme) \begin{DoxyCompactList}\small\item\em Numeric value of interpolation\+\_\+scheme corresponding to scheme name. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespaceregrid__interp_ae77f3027ed51829db5d4ed6dbc744550}{set\+\_\+interp\+\_\+scheme} (CS, interp\+\_\+scheme) \begin{DoxyCompactList}\small\item\em Store the interpolation\+\_\+scheme value in the interp\+\_\+\+CS based on the input string. \end{DoxyCompactList}\item subroutine, public \hyperlink{namespaceregrid__interp_a9ed8b5720d74090e95ca0074240a0d8a}{set\+\_\+interp\+\_\+extrap} (CS, extrap) \begin{DoxyCompactList}\small\item\em Store the boundary\+\_\+extrapolation value in the interp\+\_\+\+CS. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Variables} \begin{DoxyCompactItemize} \item \mbox{\Hypertarget{namespaceregrid__interp_a0ec76d7fa1b5308e54bc44a25dca551c}\label{namespaceregrid__interp_a0ec76d7fa1b5308e54bc44a25dca551c}} integer, parameter \hyperlink{namespaceregrid__interp_a0ec76d7fa1b5308e54bc44a25dca551c}{interpolation\+\_\+p1m\+\_\+h2} = 0 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$2) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_a490ec10b45d4eb0055fd09d5bc787570}\label{namespaceregrid__interp_a490ec10b45d4eb0055fd09d5bc787570}} integer, parameter \hyperlink{namespaceregrid__interp_a490ec10b45d4eb0055fd09d5bc787570}{interpolation\+\_\+p1m\+\_\+h4} = 1 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$2) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_ad0e6beb11f02b409e4c203c4847a949e}\label{namespaceregrid__interp_ad0e6beb11f02b409e4c203c4847a949e}} integer, parameter \hyperlink{namespaceregrid__interp_ad0e6beb11f02b409e4c203c4847a949e}{interpolation\+\_\+p1m\+\_\+ih4} = 2 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$2) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_a5854f2a813d5b963987d298ca770a7e7}\label{namespaceregrid__interp_a5854f2a813d5b963987d298ca770a7e7}} integer, parameter \hyperlink{namespaceregrid__interp_a5854f2a813d5b963987d298ca770a7e7}{interpolation\+\_\+plm} = 3 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$2) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_a06cc3d7cc7ce4321646cc5599a83544d}\label{namespaceregrid__interp_a06cc3d7cc7ce4321646cc5599a83544d}} integer, parameter \hyperlink{namespaceregrid__interp_a06cc3d7cc7ce4321646cc5599a83544d}{interpolation\+\_\+ppm\+\_\+h4} = 4 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$3) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_a35916399421e799d1ad987663817350e}\label{namespaceregrid__interp_a35916399421e799d1ad987663817350e}} integer, parameter \hyperlink{namespaceregrid__interp_a35916399421e799d1ad987663817350e}{interpolation\+\_\+ppm\+\_\+ih4} = 5 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$3) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_a201c2e2dd8cc9581406f2e1066caa50b}\label{namespaceregrid__interp_a201c2e2dd8cc9581406f2e1066caa50b}} integer, parameter \hyperlink{namespaceregrid__interp_a201c2e2dd8cc9581406f2e1066caa50b}{interpolation\+\_\+p3m\+\_\+ih4ih3} = 6 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$4) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_ae72fa5caf83881dda1ec2c4130bcb261}\label{namespaceregrid__interp_ae72fa5caf83881dda1ec2c4130bcb261}} integer, parameter \hyperlink{namespaceregrid__interp_ae72fa5caf83881dda1ec2c4130bcb261}{interpolation\+\_\+p3m\+\_\+ih6ih5} = 7 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$4) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_a18c34dfd8e5582e94c76fa0dee5c8390}\label{namespaceregrid__interp_a18c34dfd8e5582e94c76fa0dee5c8390}} integer, parameter \hyperlink{namespaceregrid__interp_a18c34dfd8e5582e94c76fa0dee5c8390}{interpolation\+\_\+pqm\+\_\+ih4ih3} = 8 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$4) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_acd2d0f29f9e3383c6f97969c028a46cc}\label{namespaceregrid__interp_acd2d0f29f9e3383c6f97969c028a46cc}} integer, parameter \hyperlink{namespaceregrid__interp_acd2d0f29f9e3383c6f97969c028a46cc}{interpolation\+\_\+pqm\+\_\+ih6ih5} = 9 \begin{DoxyCompactList}\small\item\em O(h$^\wedge$5) \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_ab5894f4be17b065c3939294014200a32}\label{namespaceregrid__interp_ab5894f4be17b065c3939294014200a32}} real, parameter, public \hyperlink{namespaceregrid__interp_ab5894f4be17b065c3939294014200a32}{nr\+\_\+offset} = 1e-\/6 \begin{DoxyCompactList}\small\item\em When the N-\/R algorithm produces an estimate that lies outside \mbox{[}0,1\mbox{]}, the estimate is set to be equal to the boundary location, 0 or 1, plus or minus an offset, respectively, when the derivative is zero at the boundary \mbox{[}nondim\mbox{]}. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_a6543421d37edc724a8a7928ccf54a21c}\label{namespaceregrid__interp_a6543421d37edc724a8a7928ccf54a21c}} integer, parameter, public \hyperlink{namespaceregrid__interp_a6543421d37edc724a8a7928ccf54a21c}{nr\+\_\+iterations} = 8 \begin{DoxyCompactList}\small\item\em Maximum number of Newton-\/\+Raphson iterations. Newton-\/\+Raphson iterations are used to build the new grid by finding the coordinates associated with target densities and interpolations of degree larger than 1. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_aa85701b7a23c13c6ac8b19916b13bb3e}\label{namespaceregrid__interp_aa85701b7a23c13c6ac8b19916b13bb3e}} real, parameter, public \hyperlink{namespaceregrid__interp_aa85701b7a23c13c6ac8b19916b13bb3e}{nr\+\_\+tolerance} = 1e-\/12 \begin{DoxyCompactList}\small\item\em Tolerance for Newton-\/\+Raphson iterations (stop when increment falls below this) \mbox{[}nondim\mbox{]}. \end{DoxyCompactList}\end{DoxyCompactItemize} \textbf{ }\par \begin{DoxyCompactItemize} \item \mbox{\Hypertarget{namespaceregrid__interp_a3ef8c1375e14fdf87fcd6997f54808eb}\label{namespaceregrid__interp_a3ef8c1375e14fdf87fcd6997f54808eb}} integer, parameter \hyperlink{namespaceregrid__interp_a3ef8c1375e14fdf87fcd6997f54808eb}{degree\+\_\+1} = 1 \begin{DoxyCompactList}\small\item\em Interpolant degrees. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_ae60a96eeb669ff4dfa45f8518742a454}\label{namespaceregrid__interp_ae60a96eeb669ff4dfa45f8518742a454}} integer, parameter \hyperlink{namespaceregrid__interp_ae60a96eeb669ff4dfa45f8518742a454}{degree\+\_\+2} = 2 \begin{DoxyCompactList}\small\item\em Interpolant degrees. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_a3c0fdeca3856901e56168587dfa1ae9f}\label{namespaceregrid__interp_a3c0fdeca3856901e56168587dfa1ae9f}} integer, parameter \hyperlink{namespaceregrid__interp_a3c0fdeca3856901e56168587dfa1ae9f}{degree\+\_\+3} = 3 \begin{DoxyCompactList}\small\item\em Interpolant degrees. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_af4b7a5ee9f8833f1defeb74cf10ae79d}\label{namespaceregrid__interp_af4b7a5ee9f8833f1defeb74cf10ae79d}} integer, parameter \hyperlink{namespaceregrid__interp_af4b7a5ee9f8833f1defeb74cf10ae79d}{degree\+\_\+4} = 4 \begin{DoxyCompactList}\small\item\em Interpolant degrees. \end{DoxyCompactList}\item \mbox{\Hypertarget{namespaceregrid__interp_af4013d842f389abc724a0d2f34366eda}\label{namespaceregrid__interp_af4013d842f389abc724a0d2f34366eda}} integer, parameter, public \hyperlink{namespaceregrid__interp_af4013d842f389abc724a0d2f34366eda}{degree\+\_\+max} = 5 \begin{DoxyCompactList}\small\item\em Interpolant degrees. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespaceregrid__interp_abaef8cc7e1258b61710adbd6fb742122}\label{namespaceregrid__interp_abaef8cc7e1258b61710adbd6fb742122}} \index{regrid\+\_\+interp@{regrid\+\_\+interp}!build\+\_\+and\+\_\+interpolate\+\_\+grid@{build\+\_\+and\+\_\+interpolate\+\_\+grid}} \index{build\+\_\+and\+\_\+interpolate\+\_\+grid@{build\+\_\+and\+\_\+interpolate\+\_\+grid}!regrid\+\_\+interp@{regrid\+\_\+interp}} \subsubsection{\texorpdfstring{build\+\_\+and\+\_\+interpolate\+\_\+grid()}{build\_and\_interpolate\_grid()}} {\footnotesize\ttfamily subroutine, public regrid\+\_\+interp\+::build\+\_\+and\+\_\+interpolate\+\_\+grid (\begin{DoxyParamCaption}\item[{type(\hyperlink{structregrid__interp_1_1interp__cs__type}{interp\+\_\+cs\+\_\+type}), intent(in)}]{CS, }\item[{real, dimension(n0), intent(in)}]{densities, }\item[{integer, intent(in)}]{n0, }\item[{real, dimension(n0), intent(in)}]{h0, }\item[{real, dimension(n0+1), intent(in)}]{x0, }\item[{real, dimension(n1+1), intent(in)}]{target\+\_\+values, }\item[{integer, intent(in)}]{n1, }\item[{real, dimension(n1), intent(inout)}]{h1, }\item[{real, dimension(n1+1), intent(inout)}]{x1, }\item[{real, intent(in), optional}]{h\+\_\+neglect, }\item[{real, intent(in), optional}]{h\+\_\+neglect\+\_\+edge }\end{DoxyParamCaption})} Build a grid by interpolating for target values. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em cs} & A control structure for \hyperlink{namespaceregrid__interp}{regrid\+\_\+interp}\\ \hline \mbox{\tt in} & {\em n0} & The number of points on the input grid\\ \hline \mbox{\tt in} & {\em n1} & The number of points on the output grid\\ \hline \mbox{\tt in} & {\em densities} & Input cell densities \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]}\\ \hline \mbox{\tt in} & {\em target\+\_\+values} & Target values of interfaces \mbox{[}R $\sim$$>$ kg m-\/3\mbox{]}\\ \hline \mbox{\tt in} & {\em h0} & Initial cell widths \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in} & {\em x0} & Source interface positions \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in,out} & {\em h1} & Output cell widths \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in,out} & {\em x1} & Target interface positions \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in} & {\em h\+\_\+neglect} & A negligibly small width for the purpose of cell reconstructions \mbox{[}H\mbox{]} in the same units as h0.\\ \hline \mbox{\tt in} & {\em h\+\_\+neglect\+\_\+edge} & A negligibly small width for the purpose of edge value calculations \mbox{[}H\mbox{]} in the same units as h0. \\ \hline \end{DoxyParams} Definition at line 309 of file regrid\+\_\+interp.\+F90. \begin{DoxyCode} 309 \textcolor{keywordtype}{type}(interp\_cs\_type), \textcolor{keywordtype}{intent(in)} :: cs\textcolor{comment}{ !< A control structure for regrid\_interp} 310 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: n0\textcolor{comment}{ !< The number of points on the input grid} 311 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: n1\textcolor{comment}{ !< The number of points on the output grid} 312 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0)}, \textcolor{keywordtype}{intent(in)} :: densities\textcolor{comment}{ !< Input cell densities [R ~> kg m-3]} 313 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n1+1)}, \textcolor{keywordtype}{intent(in)} :: target\_values\textcolor{comment}{ !< Target values of interfaces [R ~> kg m-3]} 314 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0)}, \textcolor{keywordtype}{intent(in)} :: h0\textcolor{comment}{ !< Initial cell widths [H]} 315 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0+1)}, \textcolor{keywordtype}{intent(in)} :: x0\textcolor{comment}{ !< Source interface positions [H]} 316 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n1)}, \textcolor{keywordtype}{intent(inout)} :: h1\textcolor{comment}{ !< Output cell widths [H]} 317 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n1+1)}, \textcolor{keywordtype}{intent(inout)} :: x1\textcolor{comment}{ !< Target interface positions [H]} 318 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: h\_neglect\textcolor{comment}{ !< A negligibly small width for the} 319 \textcolor{comment}{ !! purpose of cell reconstructions [H]} 320 \textcolor{comment}{ !! in the same units as h0.} 321 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: h\_neglect\_edge\textcolor{comment}{ !< A negligibly small width} 322 \textcolor{comment}{ !! for the purpose of edge value calculations [H]} 323 \textcolor{comment}{ !! in the same units as h0.} 324 325 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0,2)} :: ppoly0\_e \textcolor{comment}{! Polynomial edge values [R ~> kg m-3]} 326 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0,2)} :: ppoly0\_s \textcolor{comment}{! Polynomial edge slopes [R H-1]} 327 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0,DEGREE\_MAX+1)} :: ppoly0\_c \textcolor{comment}{! Polynomial interpolant coeficients on the local 0-1 grid [R ~> kg m-3]} 328 \textcolor{keywordtype}{integer} :: degree 329 330 \textcolor{keyword}{call }regridding\_set\_ppolys(cs, densities, n0, h0, ppoly0\_e, ppoly0\_s, ppoly0\_c, & 331 degree, h\_neglect, h\_neglect\_edge) 332 \textcolor{keyword}{call }interpolate\_grid(n0, h0, x0, ppoly0\_e, ppoly0\_c, target\_values, degree, & 333 n1, h1, x1, answers\_2018=cs%answers\_2018) \end{DoxyCode} \mbox{\Hypertarget{namespaceregrid__interp_a30dfad0833745d069498db25c1538238}\label{namespaceregrid__interp_a30dfad0833745d069498db25c1538238}} \index{regrid\+\_\+interp@{regrid\+\_\+interp}!get\+\_\+polynomial\+\_\+coordinate@{get\+\_\+polynomial\+\_\+coordinate}} \index{get\+\_\+polynomial\+\_\+coordinate@{get\+\_\+polynomial\+\_\+coordinate}!regrid\+\_\+interp@{regrid\+\_\+interp}} \subsubsection{\texorpdfstring{get\+\_\+polynomial\+\_\+coordinate()}{get\_polynomial\_coordinate()}} {\footnotesize\ttfamily real function regrid\+\_\+interp\+::get\+\_\+polynomial\+\_\+coordinate (\begin{DoxyParamCaption}\item[{integer, intent(in)}]{N, }\item[{real, dimension(n), intent(in)}]{h, }\item[{real, dimension(n+1), intent(in)}]{x\+\_\+g, }\item[{real, dimension(n,2), intent(in)}]{edge\+\_\+values, }\item[{real, dimension(n,\hyperlink{namespaceregrid__interp_af4013d842f389abc724a0d2f34366eda}{degree\+\_\+max}+1), intent(in)}]{ppoly\+\_\+coefs, }\item[{real, intent(in)}]{target\+\_\+value, }\item[{integer, intent(in)}]{degree, }\item[{logical, intent(in), optional}]{answers\+\_\+2018 }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Given a target value, find corresponding coordinate for given polynomial. Here, \textquotesingle{}ppoly\textquotesingle{} is assumed to be a piecewise discontinuous polynomial of degree \textquotesingle{}degree\textquotesingle{} throughout the domain defined by \textquotesingle{}grid\textquotesingle{}. A target value is given and we need to determine the corresponding grid coordinate to define the new grid. If the target value is out of range, the grid coordinate is simply set to be equal to one of the boundary coordinates, which results in vanished layers near the boundaries. IT IS A\+S\+S\+U\+M\+ED T\+H\+AT T\+HE P\+I\+E\+C\+E\+W\+I\+SE P\+O\+L\+Y\+N\+O\+M\+I\+AL IS M\+O\+N\+O\+T\+O\+N\+I\+C\+A\+L\+LY I\+N\+C\+R\+E\+A\+S\+I\+NG. IF T\+H\+IS IS N\+OT T\+HE C\+A\+SE, T\+HE N\+EW G\+R\+ID M\+AY BE I\+L\+L-\/\+D\+E\+F\+I\+N\+ED. It is assumed that the number of cells defining \textquotesingle{}grid\textquotesingle{} and \textquotesingle{}ppoly\textquotesingle{} are the same. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em n} & Number of grid cells\\ \hline \mbox{\tt in} & {\em h} & Grid cell thicknesses \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in} & {\em x\+\_\+g} & Grid interface locations \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in} & {\em edge\+\_\+values} & Edge values of interpolating polynomials \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in} & {\em ppoly\+\_\+coefs} & Coefficients of interpolating polynomials \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in} & {\em target\+\_\+value} & Target value to find position for \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in} & {\em degree} & Degree of the interpolating polynomials\\ \hline \mbox{\tt in} & {\em answers\+\_\+2018} & If true use older, less acccurate expressions.\\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} The position of x\+\_\+g at which target\+\_\+value is found \mbox{[}H\mbox{]} \end{DoxyReturn} Definition at line 354 of file regrid\+\_\+interp.\+F90. \begin{DoxyCode} 354 \textcolor{comment}{! Arguments} 355 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: n\textcolor{comment}{ !< Number of grid cells} 356 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(N)}, \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< Grid cell thicknesses [H]} 357 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(N+1)}, \textcolor{keywordtype}{intent(in)} :: x\_g\textcolor{comment}{ !< Grid interface locations [H]} 358 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(N,2)}, \textcolor{keywordtype}{intent(in)} :: edge\_values\textcolor{comment}{ !< Edge values of interpolating polynomials [A]} 359 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(N,DEGREE\_MAX+1)}, \textcolor{keywordtype}{intent(in)} :: ppoly\_coefs\textcolor{comment}{ !< Coefficients of interpolating polynomials [A]} 360 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{intent(in)} :: target\_value\textcolor{comment}{ !< Target value to find position for [A]} 361 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: degree\textcolor{comment}{ !< Degree of the interpolating polynomials} 362 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: answers\_2018\textcolor{comment}{ !< If true use older, less acccurate expressions.} 363 \textcolor{keywordtype}{real} :: x\_tgt\textcolor{comment}{ !< The position of x\_g at which target\_value is found [H]} 364 365 \textcolor{comment}{! Local variables} 366 \textcolor{keywordtype}{real} :: xi0 \textcolor{comment}{! normalized target coordinate [nondim]} 367 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(DEGREE\_MAX)} :: a \textcolor{comment}{! polynomial coefficients [A]} 368 \textcolor{keywordtype}{real} :: numerator 369 \textcolor{keywordtype}{real} :: denominator 370 \textcolor{keywordtype}{real} :: delta \textcolor{comment}{! Newton-Raphson increment [nondim]} 371 \textcolor{comment}{! real :: x ! global target coordinate} 372 \textcolor{keywordtype}{real} :: eps \textcolor{comment}{! offset used to get away from boundaries [nondim]} 373 \textcolor{keywordtype}{real} :: grad \textcolor{comment}{! gradient during N-R iterations [A]} 374 \textcolor{keywordtype}{integer} :: i, k, iter \textcolor{comment}{! loop indices} 375 \textcolor{keywordtype}{integer} :: k\_found \textcolor{comment}{! index of target cell} 376 \textcolor{keywordtype}{character(len=200)} :: mesg 377 \textcolor{keywordtype}{logical} :: use\_2018\_answers \textcolor{comment}{! If true use older, less acccurate expressions.} 378 379 eps = nr\_offset 380 k\_found = -1 381 use\_2018\_answers = .true. ; \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(answers\_2018)) use\_2018\_answers = answers\_2018 382 383 \textcolor{comment}{! If the target value is outside the range of all values, we} 384 \textcolor{comment}{! force the target coordinate to be equal to the lowest or} 385 \textcolor{comment}{! largest value, depending on which bound is overtaken} 386 \textcolor{keywordflow}{if} ( target\_value <= edge\_values(1,1) ) \textcolor{keywordflow}{then} 387 x\_tgt = x\_g(1) 388 \textcolor{keywordflow}{return} \textcolor{comment}{! return because there is no need to look further} 389 \textcolor{keywordflow}{ endif} 390 391 \textcolor{comment}{! Since discontinuous edge values are allowed, we check whether the target} 392 \textcolor{comment}{! value lies between two discontinuous edge values at interior interfaces} 393 \textcolor{keywordflow}{do} k = 2,n 394 \textcolor{keywordflow}{if} ( ( target\_value >= edge\_values(k-1,2) ) .AND. ( target\_value <= edge\_values(k,1) ) ) \textcolor{keywordflow}{then} 395 x\_tgt = x\_g(k) 396 \textcolor{keywordflow}{return} \textcolor{comment}{! return because there is no need to look further} 397 \textcolor{keywordflow}{ endif} 398 \textcolor{keywordflow}{ enddo} 399 400 \textcolor{comment}{! If the target value is outside the range of all values, we} 401 \textcolor{comment}{! force the target coordinate to be equal to the lowest or} 402 \textcolor{comment}{! largest value, depending on which bound is overtaken} 403 \textcolor{keywordflow}{if} ( target\_value >= edge\_values(n,2) ) \textcolor{keywordflow}{then} 404 x\_tgt = x\_g(n+1) 405 \textcolor{keywordflow}{return} \textcolor{comment}{! return because there is no need to look further} 406 \textcolor{keywordflow}{ endif} 407 408 \textcolor{comment}{! At this point, we know that the target value is bounded and does not} 409 \textcolor{comment}{! lie between discontinuous, monotonic edge values. Therefore,} 410 \textcolor{comment}{! there is a unique solution. We loop on all cells and find which one} 411 \textcolor{comment}{! contains the target value. The variable k\_found holds the index value} 412 \textcolor{comment}{! of the cell where the taregt value lies.} 413 \textcolor{keywordflow}{do} k = 1,n 414 \textcolor{keywordflow}{if} ( ( target\_value > edge\_values(k,1) ) .AND. ( target\_value < edge\_values(k,2) ) ) \textcolor{keywordflow}{then} 415 k\_found = k 416 \textcolor{keywordflow}{exit} 417 \textcolor{keywordflow}{ endif} 418 \textcolor{keywordflow}{ enddo} 419 420 \textcolor{comment}{! At this point, 'k\_found' should be strictly positive. If not, this is} 421 \textcolor{comment}{! a major failure because it means we could not find any target cell} 422 \textcolor{comment}{! despite the fact that the target value lies between the extremes. It} 423 \textcolor{comment}{! means there is a major problem with the interpolant. This needs to be} 424 \textcolor{comment}{! reported.} 425 \textcolor{keywordflow}{if} ( k\_found == -1 ) \textcolor{keywordflow}{then} 426 \textcolor{keyword}{write}(mesg,*) \textcolor{stringliteral}{'Could not find target coordinate'}, target\_value, \textcolor{stringliteral}{'in get\_polynomial\_coordinate. This is '}//& 427 \textcolor{stringliteral}{'caused by an inconsistent interpolant (perhaps not monotonically increasing):'}, & 428 target\_value, edge\_values(1,1), edge\_values(n,2) 429 \textcolor{keyword}{call }mom\_error( fatal, mesg ) 430 \textcolor{keywordflow}{ endif} 431 432 \textcolor{comment}{! Reset all polynomial coefficients to 0 and copy those pertaining to} 433 \textcolor{comment}{! the found cell} 434 a(:) = 0.0 435 \textcolor{keywordflow}{do} i = 1,degree+1 436 a(i) = ppoly\_coefs(k\_found,i) 437 \textcolor{keywordflow}{ enddo} 438 439 \textcolor{comment}{! Guess the middle of the cell to start Newton-Raphson iterations} 440 xi0 = 0.5 441 442 \textcolor{comment}{! Newton-Raphson iterations} 443 \textcolor{keywordflow}{do} iter = 1,nr\_iterations 444 445 \textcolor{keywordflow}{if} (use\_2018\_answers) \textcolor{keywordflow}{then} 446 numerator = a(1) + a(2)*xi0 + a(3)*xi0*xi0 + a(4)*xi0*xi0*xi0 + & 447 a(5)*xi0*xi0*xi0*xi0 - target\_value 448 denominator = a(2) + 2*a(3)*xi0 + 3*a(4)*xi0*xi0 + 4*a(5)*xi0*xi0*xi0 449 \textcolor{keywordflow}{else} \textcolor{comment}{! These expressions are mathematicaly equivalent but more accurate.} 450 numerator = (a(1) - target\_value) + xi0*(a(2) + xi0*(a(3) + xi0*(a(4) + a(5)*xi0))) 451 denominator = a(2) + xi0*(2.*a(3) + xi0*(3.*a(4) + 4.*a(5)*xi0)) 452 \textcolor{keywordflow}{ endif} 453 454 delta = -numerator / denominator 455 456 xi0 = xi0 + delta 457 458 \textcolor{comment}{! Check whether new estimate is out of bounds. If the new estimate is} 459 \textcolor{comment}{! indeed out of bounds, we manually set it to be equal to the overtaken} 460 \textcolor{comment}{! bound with a small offset towards the interior when the gradient of} 461 \textcolor{comment}{! the function at the boundary is zero (in which case, the Newton-Raphson} 462 \textcolor{comment}{! algorithm does not converge).} 463 \textcolor{keywordflow}{if} ( xi0 < 0.0 ) \textcolor{keywordflow}{then} 464 xi0 = 0.0 465 grad = a(2) 466 \textcolor{keywordflow}{if} ( grad == 0.0 ) xi0 = xi0 + eps 467 \textcolor{keywordflow}{ endif} 468 469 \textcolor{keywordflow}{if} ( xi0 > 1.0 ) \textcolor{keywordflow}{then} 470 xi0 = 1.0 471 \textcolor{keywordflow}{if} (use\_2018\_answers) \textcolor{keywordflow}{then} 472 grad = a(2) + 2*a(3) + 3*a(4) + 4*a(5) 473 \textcolor{keywordflow}{else} \textcolor{comment}{! These expressions are mathematicaly equivalent but more accurate.} 474 grad = a(2) + (2.*a(3) + (3.*a(4) + 4.*a(5))) 475 \textcolor{keywordflow}{ endif} 476 \textcolor{keywordflow}{if} ( grad == 0.0 ) xi0 = xi0 - eps 477 \textcolor{keywordflow}{ endif} 478 479 \textcolor{comment}{! break if converged or too many iterations taken} 480 \textcolor{keywordflow}{if} ( abs(delta) < nr\_tolerance ) \textcolor{keywordflow}{exit} 481 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! end Newton-Raphson iterations} 482 483 x\_tgt = x\_g(k\_found) + xi0 * h(k\_found) \end{DoxyCode} \mbox{\Hypertarget{namespaceregrid__interp_a52b8ce5b52f9d45f8180c6fd75388174}\label{namespaceregrid__interp_a52b8ce5b52f9d45f8180c6fd75388174}} \index{regrid\+\_\+interp@{regrid\+\_\+interp}!interpolate\+\_\+grid@{interpolate\+\_\+grid}} \index{interpolate\+\_\+grid@{interpolate\+\_\+grid}!regrid\+\_\+interp@{regrid\+\_\+interp}} \subsubsection{\texorpdfstring{interpolate\+\_\+grid()}{interpolate\_grid()}} {\footnotesize\ttfamily subroutine, public regrid\+\_\+interp\+::interpolate\+\_\+grid (\begin{DoxyParamCaption}\item[{integer, intent(in)}]{n0, }\item[{real, dimension(n0), intent(in)}]{h0, }\item[{real, dimension(n0+1), intent(in)}]{x0, }\item[{real, dimension(n0,2), intent(in)}]{ppoly0\+\_\+E, }\item[{real, dimension(n0,\hyperlink{namespaceregrid__interp_af4013d842f389abc724a0d2f34366eda}{degree\+\_\+max}+1), intent(in)}]{ppoly0\+\_\+coefs, }\item[{real, dimension(n1+1), intent(in)}]{target\+\_\+values, }\item[{integer, intent(in)}]{degree, }\item[{integer, intent(in)}]{n1, }\item[{real, dimension(n1), intent(inout)}]{h1, }\item[{real, dimension(n1+1), intent(inout)}]{x1, }\item[{logical, intent(in), optional}]{answers\+\_\+2018 }\end{DoxyParamCaption})} Given target values (e.\+g., density), build new grid based on polynomial. Given the grid \textquotesingle{}grid0\textquotesingle{} and the piecewise polynomial interpolant \textquotesingle{}ppoly0\textquotesingle{} (possibly discontinuous), the coordinates of the new grid \textquotesingle{}grid1\textquotesingle{} are determined by finding the corresponding target interface densities. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em n0} & Number of points on source grid\\ \hline \mbox{\tt in} & {\em n1} & Number of points on target grid\\ \hline \mbox{\tt in} & {\em h0} & Thicknesses of source grid cells \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in} & {\em x0} & Source interface positions \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in} & {\em ppoly0\+\_\+e} & Edge values of interpolating polynomials \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in} & {\em ppoly0\+\_\+coefs} & Coefficients of interpolating polynomials \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in} & {\em target\+\_\+values} & Target values of interfaces \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in} & {\em degree} & Degree of interpolating polynomials\\ \hline \mbox{\tt in,out} & {\em h1} & Thicknesses of target grid cells \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in,out} & {\em x1} & Target interface positions \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in} & {\em answers\+\_\+2018} & If true use older, less acccurate expressions. \\ \hline \end{DoxyParams} Definition at line 272 of file regrid\+\_\+interp.\+F90. \begin{DoxyCode} 272 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: n0\textcolor{comment}{ !< Number of points on source grid} 273 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: n1\textcolor{comment}{ !< Number of points on target grid} 274 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0)}, \textcolor{keywordtype}{intent(in)} :: h0\textcolor{comment}{ !< Thicknesses of source grid cells [H]} 275 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0+1)}, \textcolor{keywordtype}{intent(in)} :: x0\textcolor{comment}{ !< Source interface positions [H]} 276 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0,2)}, \textcolor{keywordtype}{intent(in)} :: ppoly0\_e\textcolor{comment}{ !< Edge values of interpolating polynomials [A]} 277 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0,DEGREE\_MAX+1)}, & 278 \textcolor{keywordtype}{intent(in)} :: ppoly0\_coefs\textcolor{comment}{ !< Coefficients of interpolating polynomials [A]} 279 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n1+1)}, \textcolor{keywordtype}{intent(in)} :: target\_values\textcolor{comment}{ !< Target values of interfaces [A]} 280 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: degree\textcolor{comment}{ !< Degree of interpolating polynomials} 281 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n1)}, \textcolor{keywordtype}{intent(inout)} :: h1\textcolor{comment}{ !< Thicknesses of target grid cells [H]} 282 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n1+1)}, \textcolor{keywordtype}{intent(inout)} :: x1\textcolor{comment}{ !< Target interface positions [H]} 283 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: answers\_2018\textcolor{comment}{ !< If true use older, less acccurate expressions.} 284 285 \textcolor{comment}{! Local variables} 286 \textcolor{keywordtype}{logical} :: use\_2018\_answers \textcolor{comment}{! If true use older, less acccurate expressions.} 287 \textcolor{keywordtype}{integer} :: k \textcolor{comment}{! loop index} 288 \textcolor{keywordtype}{real} :: t \textcolor{comment}{! current interface target density} 289 290 \textcolor{comment}{! Make sure boundary coordinates of new grid coincide with boundary} 291 \textcolor{comment}{! coordinates of previous grid} 292 x1(1) = x0(1) 293 x1(n1+1) = x0(n0+1) 294 295 \textcolor{comment}{! Find coordinates for interior target values} 296 \textcolor{keywordflow}{do} k = 2,n1 297 t = target\_values(k) 298 x1(k) = get\_polynomial\_coordinate( n0, h0, x0, ppoly0\_e, ppoly0\_coefs, t, degree, & 299 answers\_2018=answers\_2018 ) 300 h1(k-1) = x1(k) - x1(k-1) 301 \textcolor{keywordflow}{ enddo} 302 h1(n1) = x1(n1+1) - x1(n1) 303 \end{DoxyCode} \mbox{\Hypertarget{namespaceregrid__interp_ab4d21d91c26022a3e79268be4fe14d44}\label{namespaceregrid__interp_ab4d21d91c26022a3e79268be4fe14d44}} \index{regrid\+\_\+interp@{regrid\+\_\+interp}!interpolation\+\_\+scheme@{interpolation\+\_\+scheme}} \index{interpolation\+\_\+scheme@{interpolation\+\_\+scheme}!regrid\+\_\+interp@{regrid\+\_\+interp}} \subsubsection{\texorpdfstring{interpolation\+\_\+scheme()}{interpolation\_scheme()}} {\footnotesize\ttfamily integer function regrid\+\_\+interp\+::interpolation\+\_\+scheme (\begin{DoxyParamCaption}\item[{character(len=$\ast$), intent(in)}]{interp\+\_\+scheme }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Numeric value of interpolation\+\_\+scheme corresponding to scheme name. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em interp\+\_\+scheme} & Name of the interpolation scheme Valid values include \char`\"{}\+P1\+M\+\_\+\+H2\char`\"{}, \char`\"{}\+P1\+M\+\_\+\+H4\char`\"{}, \char`\"{}\+P1\+M\+\_\+\+I\+H2\char`\"{}, \char`\"{}\+P\+L\+M\char`\"{}, \char`\"{}\+P\+P\+M\+\_\+\+H4\char`\"{}, \char`\"{}\+P\+P\+M\+\_\+\+I\+H4\char`\"{}, \char`\"{}\+P3\+M\+\_\+\+I\+H4\+I\+H3\char`\"{}, \char`\"{}\+P3\+M\+\_\+\+I\+H6\+I\+H5\char`\"{}, \char`\"{}\+P\+Q\+M\+\_\+\+I\+H4\+I\+H3\char`\"{}, and \char`\"{}\+P\+Q\+M\+\_\+\+I\+H6\+I\+H5\char`\"{} \\ \hline \end{DoxyParams} Definition at line 488 of file regrid\+\_\+interp.\+F90. \begin{DoxyCode} 488 \textcolor{keywordtype}{character(len=*)}, \textcolor{keywordtype}{intent(in)} :: interp\_scheme\textcolor{comment}{ !< Name of the interpolation scheme} 489 \textcolor{comment}{ !! Valid values include "P1M\_H2", "P1M\_H4", "P1M\_IH2", "PLM", "PPM\_H4",} 490 \textcolor{comment}{ !! "PPM\_IH4", "P3M\_IH4IH3", "P3M\_IH6IH5", "PQM\_IH4IH3", and "PQM\_IH6IH5"} 491 492 \textcolor{keywordflow}{select case} ( uppercase(trim(interp\_scheme)) ) 493 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"P1M\_H2"}); interpolation\_scheme = interpolation\_p1m\_h2 494 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"P1M\_H4"}); interpolation\_scheme = interpolation\_p1m\_h4 495 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"P1M\_IH2"}); interpolation\_scheme = interpolation\_p1m\_ih4 496 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"PLM"}); interpolation\_scheme = interpolation\_plm 497 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"PPM\_H4"}); interpolation\_scheme = interpolation\_ppm\_h4 498 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"PPM\_IH4"}); interpolation\_scheme = interpolation\_ppm\_ih4 499 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"P3M\_IH4IH3"}); interpolation\_scheme = interpolation\_p3m\_ih4ih3 500 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"P3M\_IH6IH5"}); interpolation\_scheme = interpolation\_p3m\_ih6ih5 501 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"PQM\_IH4IH3"}); interpolation\_scheme = interpolation\_pqm\_ih4ih3 502 \textcolor{keywordflow}{case} (\textcolor{stringliteral}{"PQM\_IH6IH5"}); interpolation\_scheme = interpolation\_pqm\_ih6ih5 503 \textcolor{keywordflow}{ case default} ; \textcolor{keyword}{call }mom\_error(fatal, \textcolor{stringliteral}{"regrid\_interp: "}//& 504 \textcolor{stringliteral}{"Unrecognized choice for INTERPOLATION\_SCHEME ("}//trim(interp\_scheme)//\textcolor{stringliteral}{")."}) 505 \textcolor{keywordflow}{ end select} \end{DoxyCode} \mbox{\Hypertarget{namespaceregrid__interp_a3d1406836d089b4553421776277e1339}\label{namespaceregrid__interp_a3d1406836d089b4553421776277e1339}} \index{regrid\+\_\+interp@{regrid\+\_\+interp}!regridding\+\_\+set\+\_\+ppolys@{regridding\+\_\+set\+\_\+ppolys}} \index{regridding\+\_\+set\+\_\+ppolys@{regridding\+\_\+set\+\_\+ppolys}!regrid\+\_\+interp@{regrid\+\_\+interp}} \subsubsection{\texorpdfstring{regridding\+\_\+set\+\_\+ppolys()}{regridding\_set\_ppolys()}} {\footnotesize\ttfamily subroutine, public regrid\+\_\+interp\+::regridding\+\_\+set\+\_\+ppolys (\begin{DoxyParamCaption}\item[{type(\hyperlink{structregrid__interp_1_1interp__cs__type}{interp\+\_\+cs\+\_\+type}), intent(in)}]{CS, }\item[{real, dimension(n0), intent(in)}]{densities, }\item[{integer, intent(in)}]{n0, }\item[{real, dimension(n0), intent(in)}]{h0, }\item[{real, dimension(n0,2), intent(inout)}]{ppoly0\+\_\+E, }\item[{real, dimension(n0,2), intent(inout)}]{ppoly0\+\_\+S, }\item[{real, dimension(n0,\hyperlink{namespaceregrid__interp_af4013d842f389abc724a0d2f34366eda}{degree\+\_\+max}+1), intent(inout)}]{ppoly0\+\_\+coefs, }\item[{integer, intent(inout)}]{degree, }\item[{real, intent(in), optional}]{h\+\_\+neglect, }\item[{real, intent(in), optional}]{h\+\_\+neglect\+\_\+edge }\end{DoxyParamCaption})} Builds an interpolated profile for the densities within each grid cell. It may happen that, given a high-\/order interpolator, the number of available layers is insufficient (e.\+g., there are two available layers for a third-\/order P\+PM ih4 scheme). In these cases, we resort to the simplest continuous linear scheme (P1M h2). \begin{DoxyParams}[1]{Parameters} \mbox{\tt in} & {\em cs} & Interpolation control structure\\ \hline \mbox{\tt in} & {\em n0} & Number of cells on source grid\\ \hline \mbox{\tt in} & {\em densities} & Actual cell densities \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in} & {\em h0} & cell widths on source grid \mbox{[}H\mbox{]}\\ \hline \mbox{\tt in,out} & {\em ppoly0\+\_\+e} & Edge value of polynomial \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in,out} & {\em ppoly0\+\_\+s} & Edge slope of polynomial \mbox{[}A H-\/1\mbox{]}\\ \hline \mbox{\tt in,out} & {\em ppoly0\+\_\+coefs} & Coefficients of polynomial \mbox{[}A\mbox{]}\\ \hline \mbox{\tt in,out} & {\em degree} & The degree of the polynomials\\ \hline \mbox{\tt in} & {\em h\+\_\+neglect} & A negligibly small width for the purpose of cell reconstructions \mbox{[}H\mbox{]} in the same units as h0.\\ \hline \mbox{\tt in} & {\em h\+\_\+neglect\+\_\+edge} & A negligibly small width for the purpose of edge value calculations \mbox{[}H\mbox{]} in the same units as h0. \\ \hline \end{DoxyParams} Definition at line 80 of file regrid\+\_\+interp.\+F90. \begin{DoxyCode} 80 \textcolor{keywordtype}{type}(interp\_cs\_type), \textcolor{keywordtype}{intent(in)} :: cs\textcolor{comment}{ !< Interpolation control structure} 81 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: n0\textcolor{comment}{ !< Number of cells on source grid} 82 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0)}, \textcolor{keywordtype}{intent(in)} :: densities\textcolor{comment}{ !< Actual cell densities [A]} 83 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0)}, \textcolor{keywordtype}{intent(in)} :: h0\textcolor{comment}{ !< cell widths on source grid [H]} 84 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0,2)}, \textcolor{keywordtype}{intent(inout)} :: ppoly0\_e\textcolor{comment}{ !< Edge value of polynomial [A]} 85 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0,2)}, \textcolor{keywordtype}{intent(inout)} :: ppoly0\_s\textcolor{comment}{ !< Edge slope of polynomial [A H-1]} 86 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{dimension(n0,DEGREE\_MAX+1)}, \textcolor{keywordtype}{intent(inout)} :: ppoly0\_coefs\textcolor{comment}{ !< Coefficients of polynomial [A]} 87 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(inout)} :: degree\textcolor{comment}{ !< The degree of the polynomials} 88 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: h\_neglect\textcolor{comment}{ !< A negligibly small width for the} 89 \textcolor{comment}{ !! purpose of cell reconstructions [H]} 90 \textcolor{comment}{ !! in the same units as h0.} 91 \textcolor{keywordtype}{real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: h\_neglect\_edge\textcolor{comment}{ !< A negligibly small width} 92 \textcolor{comment}{ !! for the purpose of edge value calculations [H]} 93 \textcolor{comment}{ !! in the same units as h0.} 94 \textcolor{comment}{! Local variables} 95 \textcolor{keywordtype}{logical} :: extrapolate 96 97 \textcolor{comment}{! Reset piecewise polynomials} 98 ppoly0\_e(:,:) = 0.0 99 ppoly0\_s(:,:) = 0.0 100 ppoly0\_coefs(:,:) = 0.0 101 102 extrapolate = cs%boundary\_extrapolation 103 104 \textcolor{comment}{! Compute the interpolated profile of the density field and build grid} 105 \textcolor{keywordflow}{select case} (cs%interpolation\_scheme) 106 107 \textcolor{keywordflow}{case} ( interpolation\_p1m\_h2 ) 108 degree = degree\_1 109 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 110 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 111 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 112 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 113 \textcolor{keywordflow}{ endif} 114 115 \textcolor{keywordflow}{case} ( interpolation\_p1m\_h4 ) 116 degree = degree\_1 117 \textcolor{keywordflow}{if} ( n0 >= 4 ) \textcolor{keywordflow}{then} 118 \textcolor{keyword}{call }edge\_values\_explicit\_h4( n0, h0, densities, ppoly0\_e, h\_neglect\_edge, answers\_2018=cs %answers\_2018 ) 119 \textcolor{keywordflow}{else} 120 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 121 \textcolor{keywordflow}{ endif} 122 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 123 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 124 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 125 \textcolor{keywordflow}{ endif} 126 127 \textcolor{keywordflow}{case} ( interpolation\_p1m\_ih4 ) 128 degree = degree\_1 129 \textcolor{keywordflow}{if} ( n0 >= 4 ) \textcolor{keywordflow}{then} 130 \textcolor{keyword}{call }edge\_values\_implicit\_h4( n0, h0, densities, ppoly0\_e, h\_neglect\_edge, answers\_2018=cs %answers\_2018 ) 131 \textcolor{keywordflow}{else} 132 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 133 \textcolor{keywordflow}{ endif} 134 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 135 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 136 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 137 \textcolor{keywordflow}{ endif} 138 139 \textcolor{keywordflow}{case} ( interpolation\_plm ) 140 degree = degree\_1 141 \textcolor{keyword}{call }plm\_reconstruction( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect ) 142 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 143 \textcolor{keyword}{call }plm\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect ) 144 \textcolor{keywordflow}{ endif} 145 146 \textcolor{keywordflow}{case} ( interpolation\_ppm\_h4 ) 147 \textcolor{keywordflow}{if} ( n0 >= 4 ) \textcolor{keywordflow}{then} 148 degree = degree\_2 149 \textcolor{keyword}{call }edge\_values\_explicit\_h4( n0, h0, densities, ppoly0\_e, h\_neglect\_edge, answers\_2018=cs %answers\_2018 ) 150 \textcolor{keyword}{call }ppm\_reconstruction( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 151 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 152 \textcolor{keyword}{call }ppm\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, & 153 ppoly0\_coefs, h\_neglect ) 154 \textcolor{keywordflow}{ endif} 155 \textcolor{keywordflow}{else} 156 degree = degree\_1 157 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 158 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 159 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 160 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 161 \textcolor{keywordflow}{ endif} 162 \textcolor{keywordflow}{ endif} 163 164 \textcolor{keywordflow}{case} ( interpolation\_ppm\_ih4 ) 165 \textcolor{keywordflow}{if} ( n0 >= 4 ) \textcolor{keywordflow}{then} 166 degree = degree\_2 167 \textcolor{keyword}{call }edge\_values\_implicit\_h4( n0, h0, densities, ppoly0\_e, h\_neglect\_edge, answers\_2018=cs %answers\_2018 ) 168 \textcolor{keyword}{call }ppm\_reconstruction( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 169 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 170 \textcolor{keyword}{call }ppm\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, & 171 ppoly0\_coefs, h\_neglect ) 172 \textcolor{keywordflow}{ endif} 173 \textcolor{keywordflow}{else} 174 degree = degree\_1 175 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 176 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 177 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 178 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 179 \textcolor{keywordflow}{ endif} 180 \textcolor{keywordflow}{ endif} 181 182 \textcolor{keywordflow}{case} ( interpolation\_p3m\_ih4ih3 ) 183 \textcolor{keywordflow}{if} ( n0 >= 4 ) \textcolor{keywordflow}{then} 184 degree = degree\_3 185 \textcolor{keyword}{call }edge\_values\_implicit\_h4( n0, h0, densities, ppoly0\_e, h\_neglect\_edge, answers\_2018=cs %answers\_2018 ) 186 \textcolor{keyword}{call }edge\_slopes\_implicit\_h3( n0, h0, densities, ppoly0\_s, h\_neglect, answers\_2018=cs%answers\_2018 ) 187 \textcolor{keyword}{call }p3m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_s, & 188 ppoly0\_coefs, h\_neglect, answers\_2018=cs%answers\_2018 ) 189 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 190 \textcolor{keyword}{call }p3m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_s, & 191 ppoly0\_coefs, h\_neglect, h\_neglect\_edge ) 192 \textcolor{keywordflow}{ endif} 193 \textcolor{keywordflow}{else} 194 degree = degree\_1 195 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 196 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 197 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 198 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 199 \textcolor{keywordflow}{ endif} 200 \textcolor{keywordflow}{ endif} 201 202 \textcolor{keywordflow}{case} ( interpolation\_p3m\_ih6ih5 ) 203 \textcolor{keywordflow}{if} ( n0 >= 6 ) \textcolor{keywordflow}{then} 204 degree = degree\_3 205 \textcolor{keyword}{call }edge\_values\_implicit\_h6( n0, h0, densities, ppoly0\_e, h\_neglect\_edge, answers\_2018=cs %answers\_2018 ) 206 \textcolor{keyword}{call }edge\_slopes\_implicit\_h5( n0, h0, densities, ppoly0\_s, h\_neglect, answers\_2018=cs%answers\_2018 ) 207 \textcolor{keyword}{call }p3m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_s, & 208 ppoly0\_coefs, h\_neglect, answers\_2018=cs%answers\_2018 ) 209 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 210 \textcolor{keyword}{call }p3m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_s, & 211 ppoly0\_coefs, h\_neglect, h\_neglect\_edge ) 212 \textcolor{keywordflow}{ endif} 213 \textcolor{keywordflow}{else} 214 degree = degree\_1 215 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 216 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 217 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 218 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 219 \textcolor{keywordflow}{ endif} 220 \textcolor{keywordflow}{ endif} 221 222 \textcolor{keywordflow}{case} ( interpolation\_pqm\_ih4ih3 ) 223 \textcolor{keywordflow}{if} ( n0 >= 4 ) \textcolor{keywordflow}{then} 224 degree = degree\_4 225 \textcolor{keyword}{call }edge\_values\_implicit\_h4( n0, h0, densities, ppoly0\_e, h\_neglect\_edge, answers\_2018=cs %answers\_2018 ) 226 \textcolor{keyword}{call }edge\_slopes\_implicit\_h3( n0, h0, densities, ppoly0\_s, h\_neglect, answers\_2018=cs%answers\_2018 ) 227 \textcolor{keyword}{call }pqm\_reconstruction( n0, h0, densities, ppoly0\_e, ppoly0\_s, & 228 ppoly0\_coefs, h\_neglect, answers\_2018=cs%answers\_2018 ) 229 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 230 \textcolor{keyword}{call }pqm\_boundary\_extrapolation\_v1( n0, h0, densities, ppoly0\_e, ppoly0\_s, & 231 ppoly0\_coefs, h\_neglect ) 232 \textcolor{keywordflow}{ endif} 233 \textcolor{keywordflow}{else} 234 degree = degree\_1 235 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 236 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 237 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 238 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 239 \textcolor{keywordflow}{ endif} 240 \textcolor{keywordflow}{ endif} 241 242 \textcolor{keywordflow}{case} ( interpolation\_pqm\_ih6ih5 ) 243 \textcolor{keywordflow}{if} ( n0 >= 6 ) \textcolor{keywordflow}{then} 244 degree = degree\_4 245 \textcolor{keyword}{call }edge\_values\_implicit\_h6( n0, h0, densities, ppoly0\_e, h\_neglect\_edge, answers\_2018=cs %answers\_2018 ) 246 \textcolor{keyword}{call }edge\_slopes\_implicit\_h5( n0, h0, densities, ppoly0\_s, h\_neglect, answers\_2018=cs%answers\_2018 ) 247 \textcolor{keyword}{call }pqm\_reconstruction( n0, h0, densities, ppoly0\_e, ppoly0\_s, & 248 ppoly0\_coefs, h\_neglect, answers\_2018=cs%answers\_2018 ) 249 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 250 \textcolor{keyword}{call }pqm\_boundary\_extrapolation\_v1( n0, h0, densities, ppoly0\_e, ppoly0\_s, & 251 ppoly0\_coefs, h\_neglect ) 252 \textcolor{keywordflow}{ endif} 253 \textcolor{keywordflow}{else} 254 degree = degree\_1 255 \textcolor{keyword}{call }edge\_values\_explicit\_h2( n0, h0, densities, ppoly0\_e ) 256 \textcolor{keyword}{call }p1m\_interpolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs, h\_neglect, answers\_2018=cs %answers\_2018 ) 257 \textcolor{keywordflow}{if} (extrapolate) \textcolor{keywordflow}{then} 258 \textcolor{keyword}{call }p1m\_boundary\_extrapolation( n0, h0, densities, ppoly0\_e, ppoly0\_coefs ) 259 \textcolor{keywordflow}{ endif} 260 \textcolor{keywordflow}{ endif} 261 \textcolor{keywordflow}{ end select} 262 \end{DoxyCode} \mbox{\Hypertarget{namespaceregrid__interp_a9ed8b5720d74090e95ca0074240a0d8a}\label{namespaceregrid__interp_a9ed8b5720d74090e95ca0074240a0d8a}} \index{regrid\+\_\+interp@{regrid\+\_\+interp}!set\+\_\+interp\+\_\+extrap@{set\+\_\+interp\+\_\+extrap}} \index{set\+\_\+interp\+\_\+extrap@{set\+\_\+interp\+\_\+extrap}!regrid\+\_\+interp@{regrid\+\_\+interp}} \subsubsection{\texorpdfstring{set\+\_\+interp\+\_\+extrap()}{set\_interp\_extrap()}} {\footnotesize\ttfamily subroutine, public regrid\+\_\+interp\+::set\+\_\+interp\+\_\+extrap (\begin{DoxyParamCaption}\item[{type(\hyperlink{structregrid__interp_1_1interp__cs__type}{interp\+\_\+cs\+\_\+type}), intent(inout)}]{CS, }\item[{logical, intent(in)}]{extrap }\end{DoxyParamCaption})} Store the boundary\+\_\+extrapolation value in the interp\+\_\+\+CS. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in,out} & {\em cs} & A control structure for \hyperlink{namespaceregrid__interp}{regrid\+\_\+interp}\\ \hline \mbox{\tt in} & {\em extrap} & Indicate whether high-\/order boundary extrapolation should be used in boundary cells \\ \hline \end{DoxyParams} Definition at line 520 of file regrid\+\_\+interp.\+F90. \begin{DoxyCode} 520 \textcolor{keywordtype}{type}(interp\_cs\_type), \textcolor{keywordtype}{intent(inout)} :: cs\textcolor{comment}{ !< A control structure for regrid\_interp} 521 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{intent(in)} :: extrap\textcolor{comment}{ !< Indicate whether high-order boundary} 522 \textcolor{comment}{ !! extrapolation should be used in boundary cells} 523 524 cs%boundary\_extrapolation = extrap \end{DoxyCode} \mbox{\Hypertarget{namespaceregrid__interp_ae77f3027ed51829db5d4ed6dbc744550}\label{namespaceregrid__interp_ae77f3027ed51829db5d4ed6dbc744550}} \index{regrid\+\_\+interp@{regrid\+\_\+interp}!set\+\_\+interp\+\_\+scheme@{set\+\_\+interp\+\_\+scheme}} \index{set\+\_\+interp\+\_\+scheme@{set\+\_\+interp\+\_\+scheme}!regrid\+\_\+interp@{regrid\+\_\+interp}} \subsubsection{\texorpdfstring{set\+\_\+interp\+\_\+scheme()}{set\_interp\_scheme()}} {\footnotesize\ttfamily subroutine, public regrid\+\_\+interp\+::set\+\_\+interp\+\_\+scheme (\begin{DoxyParamCaption}\item[{type(\hyperlink{structregrid__interp_1_1interp__cs__type}{interp\+\_\+cs\+\_\+type}), intent(inout)}]{CS, }\item[{character(len=$\ast$), intent(in)}]{interp\+\_\+scheme }\end{DoxyParamCaption})} Store the interpolation\+\_\+scheme value in the interp\+\_\+\+CS based on the input string. \begin{DoxyParams}[1]{Parameters} \mbox{\tt in,out} & {\em cs} & A control structure for \hyperlink{namespaceregrid__interp}{regrid\+\_\+interp}\\ \hline \mbox{\tt in} & {\em interp\+\_\+scheme} & Name of the interpolation scheme Valid values include \char`\"{}\+P1\+M\+\_\+\+H2\char`\"{}, \char`\"{}\+P1\+M\+\_\+\+H4\char`\"{}, \char`\"{}\+P1\+M\+\_\+\+I\+H2\char`\"{}, \char`\"{}\+P\+L\+M\char`\"{}, \char`\"{}\+P\+P\+M\+\_\+\+H4\char`\"{}, \char`\"{}\+P\+P\+M\+\_\+\+I\+H4\char`\"{}, \char`\"{}\+P3\+M\+\_\+\+I\+H4\+I\+H3\char`\"{}, \char`\"{}\+P3\+M\+\_\+\+I\+H6\+I\+H5\char`\"{}, \char`\"{}\+P\+Q\+M\+\_\+\+I\+H4\+I\+H3\char`\"{}, and \char`\"{}\+P\+Q\+M\+\_\+\+I\+H6\+I\+H5\char`\"{} \\ \hline \end{DoxyParams} Definition at line 510 of file regrid\+\_\+interp.\+F90. \begin{DoxyCode} 510 \textcolor{keywordtype}{type}(interp\_cs\_type), \textcolor{keywordtype}{intent(inout)} :: cs\textcolor{comment}{ !< A control structure for regrid\_interp} 511 \textcolor{keywordtype}{character(len=*)}, \textcolor{keywordtype}{intent(in)} :: interp\_scheme\textcolor{comment}{ !< Name of the interpolation scheme} 512 \textcolor{comment}{ !! Valid values include "P1M\_H2", "P1M\_H4", "P1M\_IH2", "PLM", "PPM\_H4",} 513 \textcolor{comment}{ !! "PPM\_IH4", "P3M\_IH4IH3", "P3M\_IH6IH5", "PQM\_IH4IH3", and "PQM\_IH6IH5"} 514 515 cs%interpolation\_scheme = interpolation\_scheme(interp\_scheme) \end{DoxyCode}