### Description

MDArray version 0.5.5.2 has been released. MDArray is a multi dimensional array implemented
for JRuby inspired by NumPy (www.numpy.org) and Masahiro Tanaka´s Narray (narray.rubyforge.org).
MDArray stands on the shoulders of Java-NetCDF and Parallel Colt. At this point MDArray has
libraries for linear algebra, mathematical, trigonometric and descriptive statistics methods.

NetCDF-Java Library is a Java interface to NetCDF files, as well as to many other types of
scientific data formats. It is developed and distributed by Unidata (http://www.unidata.ucar.edu).

Parallel Colt (https://sites.google.com/site/piotrwendykier/software/parallelcolt is a
multithreaded version of Colt (http://acs.lbl.gov/software/colt/). Colt provides a set of
Open Source Libraries for High Performance Scientific and Technical Computing in Java.
Scientific and technical computing is characterized by demanding problem sizes and a need for
high performance at reasonably small memory footprint.

**Code Quality Rank**: L5

**Monthly Downloads**: 172

**Programming language**: Ruby

**License**: BSD 2-clause "Simplified" License

**Latest version**: v0.5.7

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## README

## Announcement

MDArray version 0.5.5.2 has been released. MDArray is a multi dimensional array implemented
for JRuby inspired by NumPy (www.numpy.org) and Masahiro Tanaka´s Narray (narray.rubyforge.org).

MDArray stands on the shoulders of Java-NetCDF and Parallel Colt. At this point MDArray has
libraries for linear algebra, mathematical, trigonometric and descriptive statistics methods.

NetCDF-Java Library is a Java interface to NetCDF files, as well as to many other types of scientific data formats. It is developed and distributed by Unidata (http://www.unidata.ucar.edu).

Parallel Colt (https://sites.google.com/site/piotrwendykier/software/parallelcolt is a multithreaded version of Colt (http://acs.lbl.gov/software/colt/). Colt provides a set of Open Source Libraries for High Performance Scientific and Technical Computing in Java. Scientific and technical computing is characterized by demanding problem sizes and a need for high performance at reasonably small memory footprint.

## What´s new:

Version 0.5.5.2 is a bug fix for a class StringArray. In Java-NetCDF when passing "string" as type an ObjectArray is created and not a StringArray. This version fix this issue and gets a StringArray when the "string" type is selected.

## MDArray and SciRuby:

MDArray subscribes fully to the SciRuby Manifesto (http://sciruby.com/).

“Ruby has for some time had no equivalent to the beautifully constructed NumPy, SciPy, and matplotlib libraries for Python.

We believe that the time for a Ruby science and visualization package has come. Sometimes when a solution of sugar and water becomes super-saturated, from it precipitates a pure, delicious, and diabetes-inducing crystal of sweetness, induced by no more than the tap of a finger. So is occurring now, we believe, with numeric and visualization libraries for Ruby.”

## MDArray main properties are:

- Homogeneous multidimensional array, a table of elements (usually numbers), all of the same type, indexed by a tuple of positive integers;
- Support for many linear algebra methods (see bellow);
- Easy calculation for large numerical multi dimensional arrays;
- Basic types are: boolean, byte, short, int, long, float, double, string, structure;
- Based on JRuby, which allows importing Java libraries;
- Operator: +,-,
*,/,%,**, >, >=, etc.; - Functions: abs, ceil, floor, truncate, is_zero, square, cube, fourth;
- Binary Operators: &, |,
^{,}~ (binary_ones_complement), <<, >>; - Ruby Math functions: acos, acosh, asin, asinh, atan, atan2, atanh, cbrt, cos, erf, exp, gamma, hypot, ldexp, log, log10, log2, sin, sinh, sqrt, tan, tanh, neg;
- Boolean operations on boolean arrays: and, or, not;
- Fast descriptive statistics from Parallel Colt (complete list found bellow);
- Easy manipulation of arrays: reshape, reduce dimension, permute, section, slice, etc.;
- Support for reading and writing NetCDF-3 files;
- Reading of two dimensional arrays from CSV files (mainly for debugging and simple testing purposes);
- StatList: a list that can grow/shrink and that can compute Parallel Colt descriptive statistics;
- Experimental lazy evaluation (still slower than eager evaluation).

## Supported linear algebra methods:

- backwardSolve: Solves the upper triangular system U*x=b;
- chol: Constructs and returns the cholesky-decomposition of the given matrix.
- cond: Returns the condition of matrix A, which is the ratio of largest to smallest singular value.
- det: Returns the determinant of matrix A.
- eig: Constructs and returns the Eigenvalue-decomposition of the given matrix.
- forwardSolve: Solves the lower triangular system L*x=b;
- inverse: Returns the inverse or pseudo-inverse of matrix A.
- kron: Computes the Kronecker product of two real matrices.
- lu: Constructs and returns the LU-decomposition of the given matrix.
- mult: Inner product of two vectors; Sum(x[i] * y[i]).
- mult: Linear algebraic matrix-vector multiplication; z = A * y.
- mult: Linear algebraic matrix-matrix multiplication; C = A x B.
- multOuter: Outer product of two vectors; Sets A[i,j] = x[i] * y[j].
- norm1: Returns the one-norm of vector x, which is Sum(abs(x[i])).
- norm1: Returns the one-norm of matrix A, which is the maximum absolute column sum.
- norm2: Returns the two-norm (aka euclidean norm) of vector x; equivalent to Sqrt(mult(x,x)).
- norm2: Returns the two-norm of matrix A, which is the maximum singular value; obtained from SVD.
- normF: Returns the Frobenius norm of matrix A, which is Sqrt(Sum(A[i]2)).
- normF: Returns the Frobenius norm of matrix A, which is Sqrt(Sum(A[i,j]2)).
- normInfinity: Returns the infinity norm of vector x, which is Max(abs(x[i])).
- normInfinity: Returns the infinity norm of matrix A, which is the maximum absolute row sum.
- pow: Linear algebraic matrix power; B = Ak <==> B = A*A*...*A.
- qr: Constructs and returns the QR-decomposition of the given matrix.
- rank: Returns the effective numerical rank of matrix A, obtained from Singular Value Decomposition.
- solve: Solves A*x = b.
- solve: Solves A*X = B.
- solveTranspose: Solves X*A = B, which is also A'*X' = B'.
- svd: Constructs and returns the SingularValue-decomposition of the given matrix.
- trace: Returns the sum of the diagonal elements of matrix A; Sum(A[i,i]).
- trapezoidalLower: Modifies the matrix to be a lower trapezoidal matrix.
- vectorNorm2: Returns the two-norm (aka euclidean norm) of vector X.vectorize();
- xmultOuter: Outer product of two vectors; Returns a matrix with A[i,j] = x[i] * y[j].
- xpowSlow: Linear algebraic matrix power; B = Ak <==> B = A*A*...*A.

## Properties´ methods tested on matrices:

- density: Returns the matrix's fraction of non-zero cells; A.cardinality() / A.size().
- generate_non_singular!: Modifies the given square matrix A such that it is diagonally dominant by row and column, hence non-singular, hence invertible.
- diagonal?: A matrix A is diagonal if A[i,j] == 0 whenever i != j.
- diagonally_dominant_by_column?: A matrix A is diagonally dominant by column if the absolute value of each diagonal element is larger than the sum of the absolute values of the off-diagonal elements in the corresponding column.
- diagonally_dominant_by_row?: A matrix A is diagonally dominant by row if the absolute value of each diagonal element is larger than the sum of the absolute values of the off-diagonal elements in the corresponding row.
- identity?: A matrix A is an identity matrix if A[i,i] == 1 and all other cells are zero.
- lower_bidiagonal?: A matrix A is lower bidiagonal if A[i,j]==0 unless i==j || i==j+1.
- lower_triangular?: A matrix A is lower triangular if A[i,j]==0 whenever i < j.
- nonnegative?: A matrix A is non-negative if A[i,j] >= 0 holds for all cells.
- orthogonal?: A square matrix A is orthogonal if A*transpose(A) = I.
- positive?: A matrix A is positive if A[i,j] > 0 holds for all cells.
- singular?: A matrix A is singular if it has no inverse, that is, iff det(A)==0.
- skew_symmetric?: A square matrix A is skew-symmetric if A = -transpose(A), that is A[i,j] == -A[j,i].
- square?: A matrix A is square if it has the same number of rows and columns.
- strictly_lower_triangular?: A matrix A is strictly lower triangular if A[i,j]==0 whenever i <= j.
- strictly_triangular?: A matrix A is strictly triangular if it is triangular and its diagonal elements all equal 0.
- strictly_upper_triangular?: A matrix A is strictly upper triangular if A[i,j]==0 whenever i >= j.
- symmetric?: A matrix A is symmetric if A = tranpose(A), that is A[i,j] == A[j,i].
- triangular?: A matrix A is triangular iff it is either upper or lower triangular.
- tridiagonal?: A matrix A is tridiagonal if A[i,j]==0 whenever Math.abs(i-j) > 1.
- unit_triangular?: A matrix A is unit triangular if it is triangular and its diagonal elements all equal 1.
- upper_bidiagonal?: A matrix A is upper bidiagonal if A[i,j]==0 unless i==j || i==j-1.
- upper_triangular?: A matrix A is upper triangular if A[i,j]==0 whenever i > j.
- zero?: A matrix A is zero if all its cells are zero.
- lower_bandwidth: The lower bandwidth of a square matrix A is the maximum i-j for which A[i,j] is nonzero and i > j.
- semi_bandwidth: Returns the semi-bandwidth of the given square matrix A.
- upper_bandwidth: The upper bandwidth of a square matrix A is the maximum j-i for which A[i,j] is nonzero and j > i.

## Descriptive statistics methods imported from Parallel Colt:

- auto_correlation, correlation, covariance, durbin_watson, frequencies, geometric_mean,
- harmonic_mean, kurtosis, lag1, max, mean, mean_deviation, median, min, moment, moment3,
- moment4, pooled_mean, pooled_variance, product, quantile, quantile_inverse,
- rank_interpolated, rms, sample_covariance, sample_kurtosis, sample_kurtosis_standard_error,
- sample_skew, sample_skew_standard_error, sample_standard_deviation, sample_variance,
- sample_weighted_variance, skew, split, standard_deviation, standard_error, sum,
- sum_of_inversions, sum_of_logarithms, sum_of_powers, sum_of_power_deviations,
- sum_of_squares, sum_of_squared_deviations, trimmed_mean, variance, weighted_mean,
- weighted_rms, weighted_sums, winsorized_mean.

## Double and Float methods from Parallel Colt:

- acos, asin, atan, atan2, ceil, cos, exp, floor, greater, IEEEremainder, inv, less, lg,
- log, log2, rint, sin, sqrt, tan.

## Double, Float, Long and Int methods from Parallel Colt:

- abs, compare, div, divNeg, equals, isEqual (is_equal), isGreater (is_greater),
- isles (is_less), max, min, minus, mod, mult, multNeg (mult_neg), multSquare (mult_square),
- neg, plus (add), plusAbs (plus_abs), pow (power), sign, square.

## Long and Int methods from Parallel Colt

- and, dec, factorial, inc, not, or, shiftLeft (shift_left), shiftRightSigned (shift_right_signed), shiftRightUnsigned (shift_right_unsigned), xor.

## MDArray installation and download:

- Install Jruby
- jruby –S gem install mdarray

## MDArray Homepages:

## Contributors:

Contributors are welcome.

## MDArray History:

- 30/Dec/2014: Version 0.5.5.2 - Fix for StringArray
- 16/Nov/2014: Version 0.5.5.1 - Small bug fix
- 14/Nov/2013: Version 0.5.5 - Support for linear algebra methods
- 07/Aug/2013: Version 0.5.4 - Support for reading and writing NetCDF-3 files
- 24/Jun/2013: Version 0.5.3 – Over 90% Performance improvements for methods imported from Parallel Colt and over 40% performance improvements for all other methods (implemented in Ruby);
- 16/Mai/2013: Version 0.5.0 - All loops transferred to Java with over 50% performance improvements. Descriptive statistics from Parallel Colt;
- 19/Apr/2013: Version 0.4.3 - Fixes a simple, but fatal bug in 0.4.2. No new features;
- 17/Apr/2013: Version 0.4.2 - Adds simple statistics and boolean operators;
- 05/Apr/2013: Version 0.4.0 – Initial release.