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https://github.com/rbotafogo/mdarray

Multidimensional array similar to NumPy and NArray
https://github.com/rbotafogo/mdarray

colt jruby linear-algebra matrix mdarray multidimensional-arrays ruby rubydatascience

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Multidimensional array similar to NumPy and NArray

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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:

==================



  + http://rubygems.org/gems/mdarray

  + https://github.com/rbotafogo/mdarray/wiki



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.