# Changelog¶

Nutils is being actively developed and the API is continuously evolving. The following overview lists user facing changes as well as newly added features in inverse chronological order.

## New in v7.0 (in development)¶

• Function module split into function and evaluable

The function module has been split into a high-level, numpy-like function module and a lower-level evaluable module. The evaluable module is agnostic to the so-called points axis. Scripts that don’t use custom implementations of function.Array should work without modification.

Custom implementations of the old function.Array should now derive from evaluable.Array. Furthermore, an accompanying implementation of function.Array should be added with a prepare_eval method that returns the former.

The following example implementation of an addition

>>> class Add(function.Array):
...   def __init__(self, a, b):
...     super().__init__(args=[a, b], shape=a.shape, dtype=a.dtype)
...   def evalf(self, a, b):
...     return a+b


should be converted to

>>> class Add(function.Array):
...   def __init__(self, a: function.Array, b: function.Array) -> None:
...     self.a = a
...     self.b = b
...     super().__init__(shape=a.shape, dtype=a.dtype)
...   def prepare_eval(self, **kwargs) -> evaluable.Array:
...     a = self.a.prepare_eval(**kwargs)
...     b = self.b.prepare_eval(**kwargs)
...
...   def __init__(self, a, b):
...     super().__init__(args=[a, b], shape=a.shape, dtype=a.dtype)
...   def evalf(self, a, b):
...     return a+b

• Functions generating or consuming axes in expressions

The expression syntax now supports functions that generate and/or consume axes. The namespace has built-in support for sum, norm2 and J (jacobian):

'sum:i(u_ij)' # sum the first axis of u
'norm2:i(u_i)' # 2-norm of u
'J:i(x_i)' # jacobian of x


If all axes of function arguments are consumed, it is allowed to omit the indices:

'norm2(u)'
'J(x)'

• New derivative and normal syntax

The Namespace now supports writing derivatives and normals as functions:

'd(u, x_i)' # alternative for 'u_,i', deprecates 'u_,x_i'
'd(u, x_i, x_j)' # alternative for 'u_,ij'
'surfgrad(u, x_i)' # alternative for 'u_;i', deprecates 'u_;x_i'
'd(u, ?a)' # deprecates 'u_,?a'
'n(x_i)' # deprecates 'n:x_i'

• User-defined functions in Namespace

The Namespace can be initialized with a dictionary of user-defined functions:

>>> def mul(a, b):
...   return a[(...,)+(None,)*b.ndim] * b[(None,)*a.ndim]
>>> ns = Namespace(functions=dict(mul=mul))

>>> 'mul(a_i, b_j)' @ ns # equivalent to 'a_i b_j' @ ns

• Solve multiple residuals to multiple targets

In problems involving multiple fields, where formerly it was required to nutils.function.chain() the bases in order to construct and solve a block system, an alternative possibility is now to keep the residuals and targets separate and reference the several parts at the solving phase:

# old, still valid approach
>>> ns.ubasis, ns.pbasis = function.chain([ubasis, pbasis])
>>> ns.u_i = 'ubasis_ni ?dofs_n'
>>> ns.p = 'pbasis_n ?dofs_n'

# new, alternative approach
>>> ns.ubasis = ubasis
>>> ns.pbasis = pbasis
>>> ns.u_i = 'ubasis_ni ?u_n'
>>> ns.p = 'pbasis_n ?p_n'

# common: problem definition
>>> ns.σ_ij = '(u_i,j + u_j,i) / Re - p δ_ij'
>>> ures = topo.integral('ubasis_ni,j σ_ij d:x d:x' @ ns, degree=4)
>>> pres = topo.integral('pbasis_n u_,kk d:x' @ ns, degree=4)

# old approach: solving a single residual to a single target
>>> dofs = solver.newton('dofs', ures + pres).solve(1e-10)

# new approach: solving multiple residuals to multiple targets
>>> state = solver.newton(['u', 'p'], [ures, pres]).solve(1e-10)


In the new, multi-target approach, the return value is no longer an array but a dictionary that maps a target to its solution. If additional arguments were specified to newton (or any of the other solvers) then these are copied into the return dictionary so as to form a complete state, which can directly be used as an arguments to subsequent evaluations.

If an argument is specified for a solve target then its value is used as an initial guess (newton, minimize) or initial condition (thetamethod). This replaces the lhs0 argument which is not supported for multiple targets.

• New thetamethod argument historysuffix deprecates target0

To explicitly refer to the history state in nutils.solver.thetamethod() and its derivatives impliciteuler and cranknicolson, instead of specifiying the target through the target0 parameter, the new argument historysuffix specifies only the suffix to be added to the main target. Hence, the following three invocations are equivalent:

# deprecated
>>> solver.impliciteuler('target', residual, inertia, target0='target0')
# new syntax
>>> solver.impliciteuler('target', residual, inertia, historysuffix='0')
# equal, since '0' is the default suffix
>>> solver.impliciteuler('target', residual, inertia)

• In-place modification of newton, minimize, pseudotime iterates

When nutils.solver.newton, nutils.solver.minimize or nutils.solver.pseudotime are used as iterators, the generated vectors are now modified in place. Therefore, if iterates are stored for analysis, be sure to use the .copy method.

• Deprecated function.elemwise

The function function.elemwise has been deprecated. Use function.Elemwise instead:

>>> function.elemwise(topo.transforms, values) # deprecated
>>> function.Elemwise(values, topo.f_index) # new

• Removed transforms attribute of bases

The transforms attribute of bases has been removed due to internal restructurings. The transforms attribute of the topology on which the basis was created can be used as a replacement:

>>> reftopo = topo.refined
>>> refbasis = reftopo.basis(...)
>>> supp = refbasis.get_support(...)
>>> #topo = topo.refined_by(refbasis.transforms[supp]) # no longer valid
>>> topo = topo.refined_by(reftopo.transforms[supp]) # still valid


## New in v6.0 “garak-guksu”¶

Release date: 2020-04-29.

• Sparse module

The new nutils.sparse module introduces a data type and a suite of manipulation methods for arbitrary dimensional sparse data. The existing integrate and integral methods now create data of this type under the hood, and then convert it to a scalar, Numpy array or nutils.matrix.Matrix upon return. To prevent this conversion and receive the sparse objects instead use the new nutils.sample.Sample.integrate_sparse() or nutils.sample.eval_integrals_sparse().

• External dependency for parsing gmsh files

The nutils.mesh.gmsh() method now depends on the external meshio module to parse .msh files:

$python3 -m pip install --user --upgrade meshio  • Change dof order in basis.vector When creating a vector basis using topo.basis(..).vector(nd), the order of the degrees of freedom changed from grouping by vector components to grouping by scalar basis functions: [b0, 0] [b0, 0] [b1, 0] [ 0, b0] [.., ..] old [b1, 0] [bn, 0] ------> [ 0, b1] [ 0, b0] new [.., ..] [.., ..] [bn, 0] [ 0, bn] [ 0, bn]  This should not affect applications unless the solution vector is manipulated directly, such as might happen in unit tests. If required for legacy purposes the old vector can be retrieved using old = new.reshape(-1,nd).T.ravel(). Note that the change does not extend to nutils.function.vectorize(). • Change from stickybar to bottombar For nutils.cli.run() to draw a status bar, it now requires the external bottombar module to be installed: $ python3 -m pip install --user bottombar


This replaces stickybar, which is no longer used. In addition to the log uri and runtime the status bar will now show the current memory usage, if that information is available. On Windows this requires psutil to be installed; on Linux and OSX it should work by default.

• Support for gmsh ‘msh4’ file format

The nutils.mesh.gmsh() method now supports input in the ‘msh4’ file format, in addition to the ‘msh2’ format which remains supported for backward compatibility. Internally, nutils.mesh.parsegmsh() now takes file contents instead of a file name.

• New command line option: gracefulexit

The new boolean command line option gracefulexit determines what happens when an exception reaches nutils.cli.run(). If true (default) then the exception is handled as before and a system exit is initiated with an exit code of 2. If false then the exception is reraised as-is. This is useful in particular when combined with an external debugging tool.

• Log tracebacks at debug level

The way exceptions are handled by nutils.cli.run() is changed from logging the entire exception and traceback as a single error message, to logging the exceptions as errors and tracebacks as debug messages. Additionally, the order of exceptions and traceback is fully reversed, such that the most relevant message is the first thing shown and context follows.

• Solve leniently to relative tolerance in Newton systems

The nutils.solver.newton method now sets the relative tolerance of the linear system to 1e-3 unless otherwise specified via linrtol. This is mainly useful for iterative solvers which can save computational effort by having their stopping criterion follow the current Newton residual, but it may also help with direct solvers to warn of ill conditioning issues. Iterations furthermore use nutils.matrix.Matrix.solve_leniently(), thus proceeding after warning that tolerances have not been met in the hope that Newton convergence might be attained regardless.

• Linear solver arguments

The methods nutils.solver.newton, nutils.solver.minimize, nutils.solver.pseudotime, nutils.solver.solve_linear() and nutils.solver.optimize() now receive linear solver arguments as keyword arguments rather than via the solveargs dictionary, which is deprecated. To avoid name clashes with the remaining arguments, argument names must be prefixed by lin:

>>> solver.solve_linear('lhs', res,
...   solveargs=dict(solver='gmres')) # deprecated syntax

>>> solver.solve_linear('lhs', res,
...   linsolver='gmres') # new syntax

• Iterative refinement

Direct solvers enter an iterative refinement loop in case the first pass did not meet the configured tolerance. In machine precision mode (atol=0, rtol=0) this refinement continues until the residual stagnates.

• Matrix solver tolerances

The absolute and/or relative tolerance for solutions of a linear system can now be specified in nutils.matrix.Matrix.solve() via the atol resp. rtol arguments, regardless of backend and solver. If the backend returns a solution that violates both tolerances then an exception is raised of type nutils.matrix.ToleranceNotReached, from which the solution can still be obtained via the .best attribute. Alternatively the new method nutils.matrix.Matrix.solve_leniently() always returns a solution while logging a warning if tolerances are not met. In case both tolerances are left at their default value or zero then solvers are instructed to produce a solution to machine precision, with subsequent checks disabled.

• Use stringly for command line parsing

Nutils now depends on stringly (version 1.0b1) for parsing of command line arguments. The new implementation of nutils.cli.run() is fully backwards compatible, but the preferred method of annotating function arguments is now as demonstrated in all of the examples.

For new Nutils installations Stringly will be installed automatically as a dependency. For existing setups it can be installed manually as follows:

$python3 -m pip install --user --upgrade stringly  • Fixed and fallback lengths in (namespace) expressions The nutils.function.Namespace has two new arguments: length_<indices> and fallback_length. The former can be used to assign fixed lengths to specific indices in expressions, say index i should have length 2, which is used for verification and resolving undefined lengths. The latter is used to resolve remaining undefined lengths: >>> ns = nutils.function.Namespace(length_i=2, fallback_length=3) >>> ns.eval_ij('δ_ij') # using length_i Array<2,2> >>> ns.eval_jk('δ_jk') # using fallback_length Array<3,3>  • Treelog update Nutils now depends on treelog version 1.0b5, which brings improved iterators along with other enhancements. For transitional convenience the backwards incompatible changes have been backported in the nutils.log wrapper, which now emits a warning in case the deprecated methods are used. This wrapper is scheduled for deletion prior to the release of version 6.0. To update treelog to the most recent version use: python -m pip install -U treelog  • Unit type The new nutils.types.unit allows for the creation of a unit system for easy specification of physical quantities. Used in conjunction with nutils.cli.run() this facilitates specifying units from the command line, as well as providing a warning mechanism against incompatible units: >>> U = types.unit.create(m=1, s=1, g=1e-3, N='kg*m/s2', Pa='N/m2') >>> def main(length=U('2m'), F=U('5kN')): ... topo, geom = mesh.rectilinear([numpy.linspace(0,length,10)]) # python myscript.py length=25cm # OK # python myscript.py F=10Pa # error!  • Sample basis Samples now provide a nutils.sample.Sample.basis(): an array that for any point in the sample evaluates to the unit vector corresponding to its index. This new underpinning of nutils.sample.Sample.asfunction() opens the way for sampled arguments, as demonstrated in the last example below: >>> H1 = mysample.asfunction(mydata) # mysample.eval(H1) == mydata >>> H2 = mysample.basis().dot(mydata) # mysample.eval(H2) == mydata >>> ns.Hbasis = mysample.basis() >>> H3 = 'Hbasis_n ?d_n' @ ns # mysample.eval(H3, d=mydata) == mydata  • Higher order gmsh geometries Gmsh element support has been extended to include cubic and quartic meshes in 2D and quadratic meshes in 3D, and parsing the msh file is now a cacheable operation. Additionally, tetrahedra now define bezier points at any order. • Repository location The Nutils repository has moved to https://github.com/evalf/nutils.git. For the time being the old address is maintained by Github as an alias, but in the long term you are advised to update your remote as follows: git remote set-url origin https://github.com/evalf/nutils.git  ## New in v5.0 “farfalle”¶ Release date: 2019-06-11. • Matrix matmul operator, solve with multiple right hand sides The Matrix.matvec method has been deprecated in favour of the new __matmul__ (@) operator, which supports multiplication arrays of any dimension. The nutils.matrix.Matrix.solve() method has been extended to support multiple right hand sides: >>> matrix.matvec(lhs) # deprecated >>> matrix @ lhs # new syntax >>> matrix @ numpy.stack([lhs1, lhs2, lhs3], axis=1) >>> matrix.solve(rhs) >>> matrix.solve(numpy.stack([rhs1, rhs2, rhs3], axis=1)  • MKL’s fgmres method Matrices produced by the MKL backend now support the nutils.matrix.Matrix.solve() argument solver=’fmgres’ to use Intel MKL’s fgmres method. • Thetamethod time target The nutils.solver.thetamethod class, as well as its special cases impliciteuler and cranknicolson, now have a timetarget argument to specify that the formulation contains a time variable: >>> res = topo.integral('...?t... d:x' @ ns, degree=2) >>> solver.impliciteuler('dofs', res, ..., timetarget='t')  • New leveltopo argument for trimming In nutils.topology.Topology.trim(), in case the levelset cannot be evaluated on the to-be-trimmed topology itself, the correct topology can now be specified via the new leveltopo argument. • New unittest assertion assertAlmostEqual64 nutils.testing.TestCase now facilitates comparison against base64 encoded, compressed, and packed data via the new method nutils.testing.TestCase.assertAlmostEqual64(). This replaces numeric.assert_allclose64 which is now deprecated and scheduled for removal in Nutils 6. • Fast locate for structured topology, geometry A special case nutils.topology.Topology.locate() method for structured topologies checks of the geometry is an affine transformation of the natural configuration, in which case the trivial inversion is used instead of expensive Newton iterations: >>> topo, geom = mesh.rectilinear([2, 3]) >>> smp = topo.locate(geom/2-1, [[-.1,.2]]) # locate detected linear geometry: x = [-1. -1.] + [0.5 0.5] xi ~+2.2e-16  • Lazy references, transforms, bases The introduction of sequence abstractions nutils.elementseq and nutils.transformseq, together with and a lazy implementation of nutils.function.Basis basis functions, help to prevent the unnecessary generation of data. In hierarchically refined topologies, in particular, this results in large speedups and a much reduced memory footprint. • Switch to treelog The nutils.log module is deprecated and will be replaced by the externally maintained treelog, which is now an installation dependency. • Replace pariter, parmap by fork, range. The nutils.parallel module is largely rewritten. The old methods pariter and parmap are replaced by the nutils.parallel.fork() context, combined with the shared nutils.parallel.range() iterator: >>> indices = parallel.range(10) >>> with parallel.fork(nprocs=2) as procid: >>> for index in indices: >>> print('procid={}, index={}'.format(procid, index))  ## New in v4.0 “eliche”¶ Release date: 2018-08-22. • Spline basis continuity argument In addition to the knotmultiplicities argument to define the continuity of basis function on structured topologies, the nutils.topology.Topology.basis() method now supports the continuity argument to define the global continuity of basis functions. With negative numbers counting backwards from the degree, the default value of -1 corresponds to a knot multiplicity of 1. • Eval arguments Functions of type nutils.function.Evaluable can receive arguments in addition to element and points by depending on instances of nutils.function.Argument() and having their values specified via nutils.sample.Sample.eval: >>> f = geom.dot(function.Argument('myarg', shape=geom.shape)) >>> f = 'x_i ?myarg_i' @ ns # equivalent operation in namespace >>> topo.sample('uniform', 1).eval(f, myarg=numpy.ones(geom.shape))  • The d:-operator Namespace expression syntax now includes the d: Jacobian operator, allowing one to write 'd:x' @ ns instead of function.J(ns.x). Since including the Jacobian in the integrand is preferred over specifying it separately, the geometry argument of nutils.topology.Topology.integrate() is deprecated: >>> topo.integrate(ns.f, geometry=ns.x) # deprecated >>> topo.integrate(ns.f * function.J(ns.x)) # was and remains valid >>> topo.integrate('f d:x' @ ns) # new namespace syntax  • Truncated hierarchical bsplines Hierarchically refined topologies now support basis truncation, which reduces the supports of individual basis functions while maintaining the spanned space. To select between truncated and non-truncated the basis type must be prefixed with ‘th-‘ or ‘h-‘, respectively. A non-prefixed basis type falls back on the default implementation that fails on all types but discont: >>> htopo.basis('spline', degree=2) # no longer valid >>> htopo.basis('h-spline', degree=2) # new syntax for original basis >>> htopo.basis('th-spline', degree=2) # new syntax for truncated basis >>> htopo.basis('discont', degree=2) # still valid  • Transparent function cache The nutils.cache module provides a memoizing function decorator nutils.cache.function() which reads return values from cache in case a set of function arguments has been seen before. It is similar in function to Python’s functools.lru_cache, except that the cache is maintained on disk and nutils.types.nutils_hash() is used to compare arguments, which means that arguments need not be Python hashable. The mechanism is activated via nutils.cache.enable(): >>> @cache.function >>> def f(x): >>> return x * 2 >>> >>> with cache.enable(): >>> f(10)  If nutils.cli.run() is used then the cache can also be enabled via the new --cache command line argument. With many internal Nutils functions already decorated, including all methods in the nutils.solver() module, transparent caching is available out of the box with no further action required. • New module: types The new nutils.types module unifies and extends components relating to object types. The following preexisting objects have been moved to the new location: util.enforcetypes -> types.apply_annotations util.frozendict -> types.frozendict numeric.const -> types.frozenarray  • MKL matrix, Pardiso solver The new MKL backend generates matrices that are powered by Intel’s Math Kernel Library, which notably includes the reputable Pardiso solver. This requires libmkl to be installed, which is conveniently available through pip: $ pip install mkl


When nutils.cli.run() is used the new matrix type is selected automatically if it is available, or manually using --matrix=MKL.

• Nonlinear minimization

For problems that adhere to an energy structure, the new solver method nutils.solver.minimize() provides an alternative mechanism that exploits this structure to robustly find the energy minimum:

>>> res = sqr.derivative('dofs')
>>> solver.newton('dofs', res, ...)
>>> solver.minimize('dofs', sqr, ...) # equivalent

• Data packing

Two new methods, nutils.numeric.pack() and its inverse nutils.numeric.unpack(), provide lossy compression to floating point data. Primarily useful for regression tests, the convenience method numeric.assert_allclose64 combines data packing with zlib compression and base64 encoding for inclusion in Python codes.

## New in v3.0 “dragon beard”¶

Release date: 2018-02-05.

• New: function.Namespace

The nutils.function.Namespace object represents a container of nutils.function.Array instances:

>>> ns = function.Namespace()
>>> ns.x = geom
>>> ns.basis = domain.basis('std', degree=1).vector(2)


In addition to bundling arrays, arrays can be manipulated using index notation via string expressions using the nutils.expression syntax:

>>> ns.sol_i = 'basis_ni ?dofs_n'
>>> f = ns.eval_i('sol_i,j n_j')

• New: Topology.integral

Analogous to nutils.topology.Topology.integrate(), which integrates a function and returns the result as a (sparse) array, the new method nutils.topology.Topology.integral() with identical arguments results in an nutils.sample.Integral object for postponed evaluation:

>>> x = domain.integrate(f, geometry=geom, degree=2) # direct
>>> integ = domain.integral(f, geometry=geom, degree=2) # indirect
>>> x = integ.eval()


Integral objects support linear transformations, derivatives and substitutions. Their main use is in combination with routines from the nutils.solver module.

• Removed: TransformChain, CanonicalTransformChain

Transformation chains (sequences of transform items) are stored as standard tuples. Former class methods are replaced by module methods:

>>> elem.transform.promote(ndims) # no longer valid
>>> transform.promote(elem.transform, ndims) # new syntax


In addition, every edge_transform and child_transform of Reference objects is changed from (typically unit-length) TransformChain to nutils.transform.TransformItem.

• Changed: command line interface

Command line parsers nutils.cli.run() or nutils.cli.choose() dropped support for space separated arguments (–arg value), requiring argument and value to be joined by an equals sign instead:

$python script.py --arg=value  Boolean arguments are specified by omitting the value and prepending ‘no’ to the argument name for negation: $ python script.py --pdb --norichoutput


\$ python script.py arg=value pdb norichoutput

• New: Topology intersections (deprecates common_refinement)

Intersections between topologies can be made using the & operator. In case the operands have different refinement patterns, the resulting topology will consist of the common refinements of the intersection:

>>> intersection = topoA & topoB
>>> interface = topo['fluid'].boundary & ~topo['solid'].boundary

• Changed: Topology.indicator

The nutils.topology.Topology.indicator() method is moved from subtopology to parent topology, i.e. the topology you want to evaluate the indicator on, and now takes the subtopology is an argument:

>>> ind = domain.boundary['top'].indicator() # no longer valid
>>> ind = domain.boundary.indicator(domain.boundary['top']) # new syntax
>>> ind = domain.boundary.indicator('top') # equivalent shorthand

• Changed: Evaluable.eval

The nutils.function.Evaluable.eval method accepts a flexible number of keyword arguments, which are accessible to evalf by depending on the EVALARGS token. Standard keywords are _transforms for transformation chains, _points for integration points, and _cache for the cache object:

>>> f.eval(elem, 'gauss2') # no longer valid
>>> ip, iw = elem.getischeme('gauss2')
>>> tr = elem.transform, elem.opposite
>>> f.eval(_transforms=tr, _points=ip) # new syntax

• New: numeric.const

The numeric.const array represents an immutable, hashable array:

>>> A = numeric.const([[1,2],[3,4]])
>>> d = {A: 1}


Existing arrays can be wrapped into a const object by adding copy=False. The writeable flag of the original array is set to False to prevent subsequent modification:

>> A = numpy.array([1,2,3])
>> Aconst = numeric.const(A, copy=False)
>> A[1] = 4

• New: function annotations

The util.enforcetypes decorator applies conversion methods to annotated arguments:

>>> @util.enforcetypes
>>> def f(a:float, b:tuple)
>>>   print(type(a), type(b))
>>> f(1, [2])
<class 'float'> <class 'tuple'>


The decorator is by default active to constructors of cache.Immutable derived objects, such as function.Evaluable.

• Changed: Evaluable._edit

Evaluable objects have a default edit implementation that re-instantiates the object with the operand applied to all constructor arguments. In situations where the default implementation is not sufficient it can be overridden by implementing the edit method (note: without the underscore):

>>> class B(function.Evaluable):
>>>   def __init__(self, d):
>>>     assert isinstance(d, dict)
>>>     self.d = d
>>>   def edit(self, op):
>>>     return B({key: op(value) for key, value in self.d.items()})

• Changed: function derivatives

The nutils.function.derivative axes argument has been removed; derivative(func, var) now takes the derivative of func to all the axes in var:

>>> der = function.derivative(func, var,
...         axes=numpy.arange(var.ndim)) # no longer valid
>>> der = function.derivative(func, var) # new syntax

• New module: cli

The nutils.util.run function is deprecated and replaced by two new functions, nutils.cli.choose() and nutils.cli.run(). The new functions are very similar to the original, but have a few notable differences:

• cli.choose requires the name of the function to be executed (typically ‘main’), followed by any optional arguments

• cli.run does not require the name of the function to be executed, but only a single one can be specified

• argument conversions follow the type of the argument’s default value, instead of the result of eval

• the --tbexplore option for post-mortem debugging is replaced by --pdb, replacing Nutils’ own traceback explorer by Python’s builtin debugger

• on-line debugging is provided via the ctrl+c signal handler

• function annotations can be used to describe arguments in both help messages and logging output (see examples)

• New module: solver

The nutils.solver module provides infrastructure to facilitate formulating and solving complicated nonlinear problems in a structured and largely automated fashion.

• New: topology.with{subdomain,boundary,interfaces,points}

Topologies have been made fully immutable, which means that the old setitem operation is no longer supported. Instead, to add a subtopology to the domain, its boundary, its interfaces, or points, any of the methods :func:withsubdomain, withboundary, withinterfaces, and withpoints, respectively, will return a copy of the topology with the desired groups added:

>> topo.boundary['wall'] = topo.boundary['left,top'] # no longer valid
>> newtopo = topo.withboundary(wall=topo.boundary['left,top']) # new syntax
>> newtopo = topo.withboundary(wall='left,top') # equivalent shorthand
>> newtopo.boundary['wall'].integrate(...)

• New: circular symmetry

Any topology can be revolved using the new nutils.topology.Topology.revolved() method, which interprets the first geometry dimension as a radius and replaces it by two new dimensions, shifting the remaining axes backward. In addition to the modified topology and geometry, simplifying function is returned as the third return value which replaces all occurrences of the revolution angle by zero. This should only be used after all gradients have been computed:

>> rdomain, rgeom, simplify = domain.revolved(geom)
>> basis = rdomain.basis('spline', degree=2)
>> rdomain.integrate(M, geometry=rgeom, ischeme='gauss2', edit=simplify)

• Renamed mesh.gmesh to mesh.gmsh; added support for periodicity

The gmsh importer was unintentionally misnamed as gmesh; this has been fixed. With that the old name is deprecated and will be removed in future. In addition, support for the non-physical mesh format and externally supplied boundary labels has been removed (see the unit test tests/mesh.py for examples of valid .geo format). Support is added for periodicity and interface groups.

## New in v2.0 “chuka men”¶

Release date: 2016-02-18.

• Changed: jump sign

The jump operator has been changed according to the following definition: jump(f) = opposite(f) - f. In words, it represents the value of the argument from the side that the normal is pointing toward, minus the value from the side that the normal is pointing away from. Compared to the old definition this means the sign is flipped.

• Changed: Topology objects

The Topology base class no longer takes a list of elements in its constructor. Instead, the __iter__ method should be implemented by the derived class, as well as __len__ for the number of elements, and getelem(index) to access individual elements. The ‘elements’ attribute is deprecated.

The nutils.topology.StructuredTopology object no longer accepts an array with elements. Instead, an ‘axes’ argument is provided with information that allows it to generate elements in the fly. The ‘structure’ attribute is deprecated. A newly added shape tuple is now a documented attribute.

• Changed: properties dumpdir, outdir, outrootdir

Two global properties have been renamed as follows:

dumpdir -> outdir
outdir -> outrootdir


The outrootdir defaults to ~/public_html and can be redefined from the command line or in the .nutilsrc configuration file. The outdir defaults to the current directory and is redefined by util.run, nesting the name/date/time subdirectory sequence under outrootdir.

• Changed: sum axis argument

The behaviour of nutils.function.sum is inconsistent with that of the Numpy counterparts. In case no axes argument is specified, Numpy sums over all axes, whereas Nutils sums over the last axis. To undo this mistake and transition to Numpy’s behaviour, calling sum without an axes argument is deprecated and will be forbidden in Nutils 3.0. In Nutils 4.0 it will be reintroduced with the corrected meaning.

• Changed: strict dimension equality in function.outer

The nutils.function.outer() method allows arguments of different dimension by left-padding the smallest prior to multiplication. There is no clear reason for this generality and it hinders error checking. Therefore in future in function.outer(a, b), a.ndim must equal b.ndim. In a brief transition period non-equality emits a warning.

• Changed: Evaluable base class

Relevant only for custom nutils.function.Evaluable objects, the evalf method changes from constructor argument to instance/class method:

>> class MyEval( function.Evaluable):
>>   def __init__(self, ...):
>>     function.Evaluable(args=[...], shape=...)
>>   def evalf( self, ...):
>>     ...


Moreover, the args argument may only contain Evaluable objects. Static information is to be passed through self.

• Removed: _numeric C-extension

At this point Nutils is pure Python. It is no longer necessary to run make to compile extension modules. The numeric.py module remains unchanged.

• Periodic boundary groups

Touching elements of periodic domains are no longer part of the boundary topology. It is still available as boundary of an appropriate non-periodic subtopology:

>> domain.boundary['left'] # no longer valid
>> domain[:,:1].boundary['left'] # still valid

• New module: transform

The new nutils.transform module provides objects and operations relating to affine coordinate transformations.

• Traceback explorer disabled by default

The new command line switch --tbexplore activates the traceback explorer on program failure. To change the default behavior add tbexplore=True to your .nutilsrc file.

• Rich output

The new command line switch --richoutput activates color and unicode output. To change the default behavior add richoutput=True to your .nutilsrc file.