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# $Id$ |
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|
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## @file util.py |
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|
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""" |
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@brief Utility functions for escript |
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""" |
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|
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import numarray |
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import escript |
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# |
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# escript constants (have to be consistent witj utilC.h |
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# |
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UNKNOWN=-1 |
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EPSILON=1.e-15 |
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Pi=numarray.pi |
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# some solver options: |
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NO_REORDERING=0 |
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MINIMUM_FILL_IN=1 |
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NESTED_DISSECTION=2 |
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# solver methods |
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DEFAULT_METHOD=0 |
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DIRECT=1 |
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CHOLEVSKY=2 |
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PCG=3 |
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CR=4 |
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CGS=5 |
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BICGSTAB=6 |
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SSOR=7 |
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ILU0=8 |
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ILUT=9 |
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JACOBI=10 |
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GMRES=11 |
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PRES20=12 |
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|
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METHOD_KEY="method" |
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SYMMETRY_KEY="symmetric" |
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TOLERANCE_KEY="tolerance" |
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|
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# supported file formats: |
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VRML=1 |
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PNG=2 |
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JPEG=3 |
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JPG=3 |
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PS=4 |
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OOGL=5 |
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BMP=6 |
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TIFF=7 |
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OPENINVENTOR=8 |
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RENDERMAN=9 |
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PNM=10 |
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|
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# |
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# wrapper for various functions: if the argument has attribute the function name |
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# as an argument it calls the correspong methods. Otherwise the coresponsing numarray |
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# function is called. |
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# |
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# functions involving the underlying Domain: |
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# |
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def grad(arg,where=None): |
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""" |
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@brief returns the spatial gradient of the Data object arg |
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|
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@param arg: Data object representing the function which gradient to be calculated. |
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@param where: FunctionSpace in which the gradient will be. If None Function(dom) where dom is the |
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domain of the Data object arg. |
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""" |
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if isinstance(arg,escript.Data): |
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if where==None: |
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return arg.grad() |
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else: |
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return arg.grad(where) |
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else: |
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return arg*0. |
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|
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def integrate(arg,what=None): |
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""" |
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@brief return the integral if the function represented by Data object arg over its domain. |
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|
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@param arg |
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""" |
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if not what==None: |
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arg2=escript.Data(arg,what) |
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else: |
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arg2=arg |
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if arg2.getRank()==0: |
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return arg2.integrate()[0] |
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else: |
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return arg2.integrate() |
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|
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def interpolate(arg,where): |
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""" |
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@brief interpolates the function represented by Data object arg into the FunctionSpace where. |
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|
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@param arg |
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@param where |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.interpolate(where) |
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else: |
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return arg |
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|
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# functions returning Data objects: |
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|
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def transpose(arg,axis=None): |
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""" |
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@brief returns the transpose of the Data object arg. |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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# hack for transpose |
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r=arg.getRank() |
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if r!=2: raise ValueError,"Tranpose only avalaible for rank 2 objects" |
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s=arg.getShape() |
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out=escript.Data(0.,(s[1],s[0]),arg.getFunctionSpace()) |
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for i in range(s[0]): |
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for j in range(s[1]): |
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out[j,i]=arg[i,j] |
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return out |
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# end hack for transpose |
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if axis==None: axis=arg.getRank()/2 |
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return arg.transpose(axis) |
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else: |
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if axis==None: axis=arg.rank/2 |
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return numarray.transpose(arg,axis=axis) |
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|
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def trace(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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# hack for trace |
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r=arg.getRank() |
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if r!=2: raise ValueError,"trace only avalaible for rank 2 objects" |
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s=arg.getShape() |
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out=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(min(s)): |
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out+=arg[i,i] |
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return out |
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# end hack for trace |
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return arg.trace() |
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else: |
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return numarray.trace(arg) |
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|
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def exp(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.exp() |
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else: |
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return numarray.exp(arg) |
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|
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def sqrt(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.sqrt() |
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else: |
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return numarray.sqrt(arg) |
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|
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def sin(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.sin() |
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else: |
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return numarray.sin(arg) |
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|
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def tan(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.tan() |
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else: |
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return numarray.tan(arg) |
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|
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def cos(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.cos() |
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else: |
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return numarray.cos(arg) |
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|
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def maxval(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.maxval() |
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elif isinstance(arg,float) or isinstance(arg,int): |
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return arg |
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else: |
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return arg.max() |
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|
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def minval(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.minval() |
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elif isinstance(arg,float) or isinstance(arg,int): |
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return arg |
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else: |
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return arg.min() |
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|
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def length(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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if arg.isEmpty(): return escript.Data() |
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if arg.getRank()==0: |
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return abs(arg) |
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elif arg.getRank()==1: |
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sum=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(arg.getShape()[0]): |
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sum+=arg[i]**2 |
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return sqrt(sum) |
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elif arg.getRank()==2: |
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sum=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(arg.getShape()[0]): |
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for j in range(arg.getShape()[1]): |
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sum+=arg[i,j]**2 |
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return sqrt(sum) |
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elif arg.getRank()==3: |
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sum=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(arg.getShape()[0]): |
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for j in range(arg.getShape()[1]): |
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for k in range(arg.getShape()[2]): |
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sum+=arg[i,j,k]**2 |
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return sqrt(sum) |
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elif arg.getRank()==4: |
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sum=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(arg.getShape()[0]): |
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for j in range(arg.getShape()[1]): |
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for k in range(arg.getShape()[2]): |
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for l in range(arg.getShape()[3]): |
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sum+=arg[i,j,k,l]**2 |
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return sqrt(sum) |
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else: |
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raise SystemError,"length is not been implemented yet" |
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# return arg.length() |
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else: |
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return sqrt((arg**2).sum()) |
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|
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def deviator(arg): |
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""" |
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@brief |
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|
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@param arg1 |
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""" |
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if isinstance(arg,escript.Data): |
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shape=arg.getShape() |
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else: |
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shape=arg.shape |
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if len(shape)!=2: |
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raise ValueError,"Deviator requires rank 2 object" |
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if shape[0]!=shape[1]: |
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raise ValueError,"Deviator requires a square matrix" |
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return arg-1./(shape[0]*1.)*trace(arg)*kronecker(shape[0]) |
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|
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def inner(arg1,arg2): |
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""" |
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@brief |
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|
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@param arg1, arg2 |
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""" |
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sum=escript.Scalar(0,arg1.getFunctionSpace()) |
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if arg.getRank()==0: |
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return arg1*arg2 |
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elif arg.getRank()==1: |
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sum=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(arg.getShape()[0]): |
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sum+=arg1[i]*arg2[i] |
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elif arg.getRank()==2: |
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sum=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(arg.getShape()[0]): |
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for j in range(arg.getShape()[1]): |
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sum+=arg1[i,j]*arg2[i,j] |
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elif arg.getRank()==3: |
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sum=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(arg.getShape()[0]): |
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for j in range(arg.getShape()[1]): |
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for k in range(arg.getShape()[2]): |
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sum+=arg1[i,j,k]*arg2[i,j,k] |
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elif arg.getRank()==4: |
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sum=escript.Scalar(0,arg.getFunctionSpace()) |
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for i in range(arg.getShape()[0]): |
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for j in range(arg.getShape()[1]): |
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for k in range(arg.getShape()[2]): |
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for l in range(arg.getShape()[3]): |
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sum+=arg1[i,j,k,l]*arg2[i,j,k,l] |
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else: |
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raise SystemError,"inner is not been implemented yet" |
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return sum |
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|
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def sign(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.sign() |
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else: |
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return numarray.greater(arg,numarray.zeros(arg.shape))-numarray.less(arg,numarray.zeros(arg.shape)) |
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|
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# reduction operations: |
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|
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def sum(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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return arg.sum() |
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|
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def sup(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.sup() |
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elif isinstance(arg,float) or isinstance(arg,int): |
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return arg |
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else: |
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return arg.max() |
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|
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def inf(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.inf() |
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elif isinstance(arg,float) or isinstance(arg,int): |
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return arg |
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else: |
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return arg.min() |
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|
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def L2(arg): |
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""" |
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@brief returns the L2-norm of the |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.L2() |
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elif isinstance(arg,float) or isinstance(arg,int): |
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return abs(arg) |
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else: |
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return numarry.sqrt(dot(arg,arg)) |
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|
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def Lsup(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.Lsup() |
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elif isinstance(arg,float) or isinstance(arg,int): |
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return abs(arg) |
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else: |
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return max(numarray.abs(arg)) |
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|
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def Linf(arg): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg,escript.Data): |
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return arg.Linf() |
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elif isinstance(arg,float) or isinstance(arg,int): |
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return abs(arg) |
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else: |
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return min(numarray.abs(arg)) |
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|
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def dot(arg1,arg2): |
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""" |
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@brief |
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|
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@param arg |
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""" |
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if isinstance(arg1,escript.Data): |
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return arg1.dot(arg2) |
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elif isinstance(arg1,escript.Data): |
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return arg2.dot(arg1) |
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else: |
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return numarray.dot(arg1,arg2) |
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|
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def kronecker(d): |
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return numarray.identity(d) |
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|
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def unit(i,d): |
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""" |
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@brief return a unit vector of dimension d with nonzero index i |
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@param d dimension |
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@param i index |
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""" |
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e = numarray.zeros((d,)) |
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e[i] = 1.0 |
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return e |
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