MathNet.Numerics.FSharp 2.5.0

• • MathNet.Numerics (>= 2.5.0)

### Potentially Breaking Changes:

Despite semver this release contains two changes that may break code but without triggering a major version number change. The changes fix semantic bugs and a major usability issue without changing the formal API itself. Most users are not expected to be affected negatively. Nevertheless, this is an exceptional case and we try hard to avoid such changes in the future.

- Statistics: Empty statistics now return NaN instead of either 0 or throwing an exception. *This may break code in case you relied upon the previous unusual and inconsistent behavior.*

- Linear Algebra: More reasonable ToString behavior for matrices and vectors. *This may break code if you relied upon ToString to export your full data to text form intended to be parsed again later. Note that the classes in the MathNet.Numerics.IO library are more appropriate for storing and loading data.*

### Statistics:

- More consistent behavior for empty and single-element data sets: Min, Max, Mean, Variance, Standard Deviation etc. no longer throw exceptions if the data set is empty but instead return NaN. Variance and Standard Deviation will also return NaN if the set contains only a single entry. Population Variance and Population Standard Deviation will return 0 in this case.
- Reworked order statistics (Quantile, Quartile, Percentile, IQR, Fivenum, etc.), now much easier to use and supporting compatibility with all 9 R-types, Excel and Mathematica. The obsolete Percentile class now leverages the new order statistics, fixing a range check bug as side effect.
- New Hybrid Monte Carlo sampler for multivariate distributions.
- New financial statistics: absolute risk and return measures.
- Explicit statistics for sorted arrays, unsorted arrays and sequences/streams. Faster algorithms on sorted data, also avoids multiple enumerations.
- Some statistics like Quantile or empirical inverse CDF can optionally return a parametric function when multiple evaluations are needed, like for plotting.

### Linear Algebra:

- More reasonable ToString behavior for matrices and vectors: `ToString` methods no longer render the whole structure to a string for large data, among others because they used to wreak havoc in debugging and interactive scenarios like F# FSI. Instead, ToString now only renders an excerpt of the data, together with a line about dimension, type and in case of sparse data a sparseness indicator. The intention is to give a good idea about the data in a visually useful way. How much data is shown can be adjusted in the Control class. See also ToTypeString and ToVector/MatrixString.
- Performance: reworked and tuned common parallelization. Some operations are up to 3 magnitudes faster in some extreme cases. Replaced copy loops with native routines. More algorithms are storage-aware (and should thus perform better especially on sparse data).
- Fixed range checks in the Thin-QR decomposition.
- Fixed bug in Gram Schmidt for solving tall matrices.
- Vectors now implement the BCL IList interfaces (fixed-length) for better integration with existing .Net code.
- Matrix/Vector parsing has been updated to be able to parse the new visual format as well (see ToMatrixString).
- DebuggerDisplay attributes for matrices and vectors.
- Map/IndexedMap combinators with storage-aware and partially parallelized implementations for both dense and sparse data.
- Reworked Matrix/Vector construction from arrays, enumerables, indexed enumerables, nested enumerables or by providing an init function/lambda. Non-obsolete constructors now always use the raw data array directly without copying, while static functions always return a matrix/vector independent of the provided data source.
- F#: Improved extensions for matrix and vector construction: create, zeroCreate, randomCreate, init, ofArray2, ofRows/ofRowsList, ofColumns/ofSolumnsList, ofSeqi/Listi (indexed). Storage-aware for performance.
- F#: Updated map/mapi and other combinators to leverage core implementation, added -nz variants where zero-values may be skipped (relevant mostly for sparse matrices).
- F#: Idiomatic slice setters for sub-matrices and sub-vectors
- F#: More examples for matrix/vector creation and linear regression in the F# Sample-package.

### Misc:

- Control: Simpler usage with new static ConfigureAuto and ConfigureSingleThread methods. Resolved misleading configuration logic and naming around disabling parallelization.
- Control: New settings for linear algebra ToString behavior.
- Fixed range check in the Xor-shift pseudo-RNG.
- Parallelization: Reworked our common logic to avoid expensive lambda calls in inner loops. Tunable.
- F#: Examples (and thus the NuGet Sample package) are now F# scripts prepared for experimenting interactively in FSI, instead of normal F# files. Tries to get the assembly references right for most users, both within the Math.NET Numerics solution and the NuGet package.
- Various minor improvements on consistency, performance, tests, xml docs, obsolete attributes, redundant code, argument checks, resources, cleanup, nuget, etc.