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The naïve algorithm using three nested loops uses Ω(n 3) communication bandwidth. Cannon's algorithm, also known as the 2D algorithm, is a communication-avoiding algorithm that partitions each input matrix into a block matrix whose elements are submatrices of size √ M/3 by √ M/3, where M is the size of fast memory. [28]
(Nested loops occur when one loop is inside of another loop.) One classical usage is to reduce memory access latency or the cache bandwidth necessary due to cache reuse for some common linear algebra algorithms. The technique used to produce this optimization is called loop tiling, [1] also known as loop blocking [2] or strip mine and interchange.
Loop-invariant code motion – this can vastly improve efficiency by moving a computation from inside the loop to outside of it, computing a value just once before the loop begins, if the resultant quantity of the calculation will be the same for every loop iteration (i.e., a loop-invariant quantity). This is particularly important with address ...
A bagplot, or starburst plot, [1] [2] is a method in robust statistics for visualizing two-or three-dimensional statistical data, analogous to the one-dimensional box plot. Introduced in 1999 by Rousseuw et al., the bagplot allows one to visualize the location, spread, skewness , and outliers of a data set.
The variable used in the inner loop switches to the outer loop, and vice versa. It is often done to ensure that the elements of a multi-dimensional array are accessed in the order in which they are present in memory, improving locality of reference. For example, in the code fragment: for j from 0 to 20 for i from 0 to 10 a[i,j] = i + j
Sometimes within the body of a loop there is a desire to skip the remainder of the loop body and continue with the next iteration of the loop. Some languages provide a statement such as continue (most languages), skip , [ 8 ] cycle (Fortran), or next (Perl and Ruby), which will do this.
Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster ... and dy=3: D=2*3-6=0 Loop from 0 to 6 * x=0: plot ...
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;