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 JavaNetCDF and Parallel Colt. At this point MDArray has
libraries for linear algebra, mathematical, trigonometric and descriptive statistics methods.
NetCDFJava 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.
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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 JavaNetCDF and Parallel Colt. At this point MDArray has
libraries for linear algebra, mathematical, trigonometric and descriptive statistics methods.
NetCDFJava 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 JavaNetCDF 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 supersaturated, from it precipitates a pure, delicious, and diabetesinducing 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 NetCDF3 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 choleskydecomposition 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 Eigenvaluedecomposition of the given matrix.
 forwardSolve: Solves the lower triangular system L*x=b;
 inverse: Returns the inverse or pseudoinverse of matrix A.
 kron: Computes the Kronecker product of two real matrices.
 lu: Constructs and returns the LUdecomposition of the given matrix.
 mult: Inner product of two vectors; Sum(x[i] * y[i]).
 mult: Linear algebraic matrixvector multiplication; z = A * y.
 mult: Linear algebraic matrixmatrix multiplication; C = A x B.
 multOuter: Outer product of two vectors; Sets A[i,j] = x[i] * y[j].
 norm1: Returns the onenorm of vector x, which is Sum(abs(x[i])).
 norm1: Returns the onenorm of matrix A, which is the maximum absolute column sum.
 norm2: Returns the twonorm (aka euclidean norm) of vector x; equivalent to Sqrt(mult(x,x)).
 norm2: Returns the twonorm 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 QRdecomposition 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 SingularValuedecomposition 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 twonorm (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 nonzero 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 nonsingular, 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 offdiagonal 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 offdiagonal 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 nonnegative 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 skewsymmetric 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(ij) > 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==j1.
 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 ij for which A[i,j] is nonzero and i > j.
 semi_bandwidth: Returns the semibandwidth of the given square matrix A.
 upper_bandwidth: The upper bandwidth of a square matrix A is the maximum ji 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 NetCDF3 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.