Functions of Data objects

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Functions of Data objects

This section lists the most important functions for Data class objects a. A complete list and a more detailed description of the functionality can be found on http://esys.esscc.uq.edu.au/docs.html.
$\begin{funcdesc}{saveVTK}{filename,**kwdata} writes \class{Data}\xspace defined ... ...n the allowed combinations of \class{FunctionSpace}\xspace apply. \end{funcdesc}$

$\begin{funcdesc}{saveDX}{filename,**kwdata} writes \class{Data}\xspace defined b... ...n the allowed combinations of \class{FunctionSpace}\xspace apply. \end{funcdesc}$

$\begin{funcdesc}{kronecker}{d} returns a {rank-2 \class{Data}\xspace object}\xsp... ...is an integer a $(d,d)$\ \module{numpy}\xspace array is returned. \end{funcdesc}$

$\begin{funcdesc}{identityTensor}{d} is a synonym for \code{kronecker} (see above). \end{funcdesc}$

$\begin{funcdesc}{identityTensor4}{d} returns a {rank-4 \class{Data}\xspace objec... ...n integer a $(d,d,d,d)$\ \module{numpy}\xspace array is returned. \end{funcdesc}$

$\begin{funcdesc}{unitVector}{i,d} returns a {rank-1 \class{Data}\xspace object}\... ...n integer a $(d,)$\ \module{numpy}\xspace array is returned. \par \end{funcdesc}$

$\begin{funcdesc}{Lsup}{a} returns the $L^{sup}$\ norm of \var{arg}. This is the ... ...data sample points}\index{data sample!points}\xspace of \var{a}. \end{funcdesc}$

$\begin{funcdesc}{sup}{a} returns the maximum value over all components and all {data sample points}\index{data sample!points}\xspace of \var{a}. \end{funcdesc}$

$\begin{funcdesc}{inf}{a} returns the minimum value over all components and all {data sample points}\index{data sample!points}\xspace of \var{a} \end{funcdesc}$

$\begin{funcdesc}{minval}{a} returns at each {data sample points}\index{data sample!points}\xspace the minimum value over all components. \end{funcdesc}$

$\begin{funcdesc}{maxval}{a} returns at each {data sample points}\index{data sample!points}\xspace the maximum value over all components. \end{funcdesc}$

$\begin{funcdesc}{length}{a} returns at Euclidean norm at each {data sample point... ...m\hackscore{ijkl} \var{a} \left[i,j,k,l\right]^2} \end{equation} \end{funcdesc}$

$\begin{funcdesc}{trace}{a\optional{,axis_offset=0}} returns the trace of \var{a}... ...t]=\sum\hackscore{k} \var{a} \left[i,k,k,j\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{transpose}{a\optional{, axis_offset=None}} returns the transpos... ...\left[i,j,k,l\right]=\var{a} \left[j,k,l,i\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{swap_axes}{a\optional{, axis0=0 \optional{, axis1=1 }}} returns... ...\left[i,j,k,l\right]=\var{a} \left[i,k,j,l\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{symmetric}{a} returns the symmetric part of \var{a}. This is \code{(a+transpose(a))/2}. \end{funcdesc}$

$\begin{funcdesc}{nonsymmetric}{a} returns the non--symmetric part of \var{a}. This is \code{(a-transpose(a))/2}. \end{funcdesc}$

$\begin{funcdesc}{inverse}{a} return the inverse of \var{a}. This is \begin{equa... ... restricted to arguments of shape \code{(2,2)} and \code{(3,3)}. \end{funcdesc}$

$\begin{funcdesc}{eigenvalues}{a} return the eigenvalues of \var{a}. This is \be... ... restricted to arguments of shape \code{(2,2)} and \code{(3,3)}. \end{funcdesc}$

$\begin{funcdesc}{eigenvalues_and_eigenvectors}{a} return the eigenvalues and eig... ... restricted to arguments of shape \code{(2,2)} and \code{(3,3)}. \end{funcdesc}$

$\begin{funcdesc}{maximum}{*a} returns the maximum value over all arguments at al... ...on}at all {data sample points}\index{data sample!points}\xspace . \end{funcdesc}$

$\begin{funcdesc}{minimum}{*a} returns the minimum value over all arguments at al... ...on}at all {data sample points}\index{data sample!points}\xspace . \end{funcdesc}$

$\begin{funcdesc}{clip}{a\optional{, minval=0.}\optional{, maxval=1.}} cuts back ... ...er than \var{maxval} or corresponding value of \var{a} otherwise. \end{funcdesc}$

$\begin{funcdesc}{inner}{a0,a1} returns the inner product of \var{a0} and \var{a1... ...,j,k,l\right] \cdot \var{a1} \left[j,i,k,l\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{matrix_mult}{a0,a1} returns the matrix product of \var{a0} and ... ...} \cdot \left[i,k\right]\var{a1} \left[k,j\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{transposed_matrix_mult}{a0,a1} returns the matrix product of th... ...} \cdot \left[k,i\right]\var{a1} \left[k,j\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{matrix_transposed_mult}{a0,a1} returns the matrix product of \v... ...} \cdot \left[i,k\right]\var{a1} \left[j,k\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{outer}{a0,a1} returns the outer product of \var{a0} and \var{a1... ...a0} \left[i\right] \cdot \var{a1}\left[j,k\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{tensor_mult}{a0,a1} returns the tensor product of \var{a0} and ... ...,j,m,n\right] \cdot \var{a1} \left[m,n,k,l\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{transposed_tensor_mult}{a0,a1} returns the tensor product of th... ...,n,i,j\right] \cdot \var{a1} \left[m,n,k,l\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{tensor_transposed_mult}{a0,a1} returns the tensor product of \v... ...,j,m,n\right] \cdot \var{a1} \left[k,l,m,n\right] \end{equation} \end{funcdesc}$

$\begin{funcdesc}{grad}{a\optional{, where=None}} returns the gradient of \var{a}... ...var{a} \left[i,j\right]}{\partial x\hackscore{k}} \end{equation} \end{funcdesc}$

$\begin{funcdesc}{integrate}{a\optional{ ,where=None}} returns the integral of \v... ...surface of the spatial domain and $ds$\ area or line integration. \end{funcdesc}$

$\begin{funcdesc}{interpolate}{a,where} interpolates argument \var{a} into the \class{FunctionSpace}\xspace \var{where}. \end{funcdesc}$

$\begin{funcdesc}{div}{a\optional{ ,where=None}} returns the divergence of \var{a... ...\begin{equation} \code{div(a)}=trace(grad(a),where) \end{equation}\end{funcdesc}$

$\begin{funcdesc}{jump}{a\optional{ ,domain=None}} returns the jump of \var{a} ov... ...polate(a,FunctionOnContactZero(domain))} \end{array}\end{equation}\end{funcdesc}$

$\begin{funcdesc}{L2}{a} returns the $L^2$-norm of \var{a} in its function space.... ...} \code{L2(a)=integrate(length(a)}^2\code{)} \; . \end{equation} \end{funcdesc}$

The following functions operate ``point-wise''. That is, the operation is applied to each component of each point individually.

$\begin{funcdesc}{sin}{a} applies sine function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{cos}{a} applies cosine function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{tan}{a} applies tangent function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{asin}{a} applies arc (inverse) sine function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{acos}{a} applies arc (inverse) cosine function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{atan}{a} applies arc (inverse) tangent function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{sinh}{a} applies hyperbolic sine function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{cosh}{a} applies hyperbolic cosine function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{tanh}{a} applies hyperbolic tangent function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{asinh}{a} applies arc (inverse) hyperbolic sine function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{acosh}{a} applies arc (inverse) hyperbolic cosine function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{atanh}{a} applies arc (inverse) hyperbolic tangent function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{exp}{a} applies exponential function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{sqrt}{a} applies square root function to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{log}{a} applies the natural logarithm to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{log10}{a} applies the base-$10$\ logarithm to \var{a}. \end{funcdesc}$

$\begin{funcdesc}{sign}{a} applies the sign function to \var{a}, that is $1$\ whe... ... is positive, $-1$\ where \var{a} is negative and $0$\ otherwise. \end{funcdesc}$

$\begin{funcdesc}{wherePositive}{a} returns a function which is $1$\ where \var{a} is positive and $0$\ otherwise. \end{funcdesc}$

$\begin{funcdesc}{whereNegative}{a} returns a function which is $1$\ where \var{a} is negative and $0$\ otherwise. \end{funcdesc}$

$\begin{funcdesc}{whereNonNegative}{a} returns a function which is $1$\ where \var{a} is non--negative and $0$\ otherwise. \end{funcdesc}$

$\begin{funcdesc}{whereNonPositive}{a} returns a function which is $1$\ where \var{a} is non--positive and $0$\ otherwise. \end{funcdesc}$

$\begin{funcdesc}{whereZero}{a\optional{, tol=None, \optional{, rtol=1.e-8}}} ret... ...resent, the absolute maximum value of C{a} times C{rtol} is used. \end{funcdesc}$

$\begin{funcdesc}{whereNonZero}{a, \optional{, tol=None, \optional{, rtol=1.e-8}}... ...resent, the absolute maximum value of C{a} times C{rtol} is used. \end{funcdesc}$

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