# Nutils 4 Eliche

Nutils 4.0 was released on June 11th, 2019.

Nutils 4.1 was released on August 28th, 2018.

## What's New?

These are the main additions and changes since Nutils 3 Dragon Beard.

### 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htopo.basis('spline', degree=2) # no longer valid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.enforcetypestypes.apply_annotations
• util.frozendicttypes.frozendict
• numeric.consttypes.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.