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Illustration of difference between row- and column-major ordering. In computing, row-major order and column-major order are methods for storing multidimensional arrays in linear storage such as random access memory. The difference between the orders lies in which elements of an array are contiguous in memory.
A two-dimensional array stored as a one-dimensional array of one-dimensional arrays (rows) Many languages support only one-dimensional arrays. In those languages, a multi-dimensional array is typically represented by an Iliffe vector, a one-dimensional array of references to arrays of one dimension less. A two-dimensional array, in particular ...
Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty. [3] [4] [5] Because the additions are performed in isolation from the rest of the coding, they may not produce the optimally most ...
For example, if d = gcd(N,M) is not small, one can perform the transposition using a small amount (NM/d) of additional storage, with at most three passes over the array (Alltop, 1975; Dow, 1995). Two of the passes involve a sequence of separate, small transpositions (which can be performed efficiently out of place using a small buffer) and one ...
is how one would use Fortran to create arrays from the even and odd entries of an array. Another common use of vectorized indices is a filtering operation. Consider a clipping operation of a sine wave where amplitudes larger than 0.5 are to be set to 0.5. Using S-Lang, this can be done by y = sin(x); y[where(abs(y)>0.5)] = 0.5;
In Java associative arrays are implemented as "maps", which are part of the Java collections framework. Since J2SE 5.0 and the introduction of generics into Java, collections can have a type specified; for example, an associative array that maps strings to strings might be specified as follows:
NumPy's np.concatenate([a1,a2]) operation does not actually link the two arrays but returns a new one, filled with the entries from both given arrays in sequence. Reshaping the dimensionality of an array with np.reshape(...) is only possible as long as the number of elements in the array does not change.
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: