Multidimensional Arrays Sample Clauses

Multidimensional Arrays. There are many problems in image processing where double precision is unneces- sary. This is usually the case when the source image is saved in a grayscale 8-bit format (integers from 0 to 255). From the computational point of view, single pre- cision has two advantages over double precision: arithmetic operations are faster with single precision numbers and they require only half the storage of double precision numbers. All algorithms in Colt 1.2.0 that use floating-point numbers are implemented in double precision, in particular, only double precision multidi- mensional arrays are available. Therefore, in Parallel Colt we have added single precision equivalents to all double precision based objects. In Colt, a single contiguous one-dimensional Java array is used to store elements of all dense 2D and 3D matrices. The elements of 2D matrices are addressed in row-major order and the elements of 3D matrices are addressed in (in decreasing order of significance): slice-major, row-major and column-major order. However, there are two problems with this approach. First, matrix decomposition algorithms typically expect input matrices to use column-major order. Second, since Java array indices must be 32-bit integer values, the 1D array cannot contain more than 231 elements, which is a significant limitation for large-scale problems. To overcome these difficulties, Parallel Colt provides additional data structures for dense matrices: a 2D dense matrix addressed in column-major order as well as 2D and 3D dense matrices where elements are stored in two-dimensional and three-dimensional Java arrays respectively. The original Colt project supports three types of 2D sparse matrices: row- compressed, tridiagonal, and the general sparse matrix that uses a hashmap to store the nonzero elements. However, it is beneficial for some applications to use alternative sparse storage schemes. Therefore, in Parallel Colt we have added a column-compressed sparse matrix (for fast column access) and a diagonal matrix (for more efficient computations involving only a single diagonal). Another new and important type of object added to Parallel Colt is a multi- dimensional array of complex numbers. This object is essential for operations involving FFTs. Because there is no primitive type for complex numbers in Java, we decided to store an array of complex numbers as a one-dimensional array of doubles (or floats), interleaving the real and the imaginary parts. This type of storage guarant...