Just before I started wrting this I thought that maybe I should look up and see what gather actually does.ĭo make sure you move the result of backslash back to the GPU so that subsequent operations take place on the GPU. Your suggestion of rhs clearly works no matter how big xRange because I can get results for it even when the program falls over which just leaves me the question of why U1 = gather(AA)\gather(rhs) works and works quickly whereas U1 = AA\rhs does not anbd gives NaN. However, that does not make sense when you get to the for loop. So everything is now on the graphics card after a lot of one off calculations on setup. All the others are well zeroed and therefore sparse or else they are simply vectors. However, this all sounds fine until I realised that U, which is the output, sits quite happily in the gpu card memory. However, trying to create A or AD or AS on the graphics card runs out of memory much faster (54+). This is where, if xRange (300+) is very large that the program runs out of memory. My limited understanding of implementation suggests that the problem is AS. The time when I used the CPU only before I had the NVIDIA (xRange = 320) was 23+ hours for a single run whereas this morning 360 xRangetook 5 minutes. When I tried for 400 because the card appeared to be less than "full" it fell over because my CPU/RAm at 128GB ran out of memory!, not the card!. I have therefore used the main memory to create the large matrices and to sparse them and then loaded them to the card. I have been watching carefully the Task manager as the computer handles the code. The "out of memory" seemed to happen because the graphics card maintained both versions. It transpires that the whilst the graphics card works sparse OK it appears to me that it manages memory poorly. I tried to be clever and went for 240 and it fell over but I have spent a bit of time thinking about sparse. Firstly everything ran fine up to 200 xRange. A 1, A 2, is used to select a matrix (not a matrix entry) from a collection of matrices.This morning has been very productive. The entry in row i, column j of matrix A is indicated by ( A) ij, A ij or a ij. Index notation is often the clearest way to express definitions, and is used as standard in the literature. a and entries of vectors and matrices are italic (they are numbers from a field), e.g. This article will use the following notational conventions: matrices are represented by capital letters in bold, e.g. Ĭomputing matrix products is a central operation in all computational applications of linear algebra. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. The product of matrices A and B is denoted as AB. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. The result matrix has the number of rows of the first and the number of columns of the second matrix. Mathematical operation in linear algebra For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
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