If it is not the next consecutive position, MATLAB pads the elements in between with zeros. To append an element to a vector just specify a value at the desired position. M(,) addresses the intersection of rows a and b and columns c through d and e. For example v() addresses elements a, b, and c through d. Use a square bracket to address nonconsecutive elements in a vector or matrix. M(:,a) addresses column a, M(a,:) addresses row a, M(:,a:b) addresses columns a through b, M(a:b,:) addresses rows a through b, M(a:b,c:d) addresses the intersection of rows a through b and columns c through d. For example, v(:) addresses all the elements of a vector, v(a:b) addresses elements a through b in vector v. Use the colon operator to address a range of elements in a vector or matrix. It's just like playing Battleship except both the columns and rows are designated by numbers. Then I ask it for the element in the second row and third column. In the example below I make a 3x3 matrix M. M(1,1) addresses the element in the top left corner of the matrix M. For example, v(1) addresses the first element in a vector v. You can also use that technique to address a specific spot in a matrix. I used this a long time ago to map contours in the solutions of sets of 50 x 50 quadratic equations associated with the behavior of electric power systems.We've already practiced using parentheses to address a certain element of a vector. If this situation is what you have, it is much faster than starting fresh on each matrix. If you don't get convegence you use SVD to restart. You need one or two iterations to get convergence. So the idea is that you initialize using SVD on the first matrix, but thereafter you step from matrix to matrix, using the null space vector of one as the starting point for the iteration for the next one. Using this technique would require that you be able to make small steps from matrix to matrix by say varying a parameter. Newton's method uses first derivatives to converge to a solution, and so would use Gaussian elimination to solve 9x9 systems. If so, you may be able to speed things up by using Newton's method to solve successive instances of the system of quadratic equations Ax = 0, |x|^2 = 1, starting from a previous null space vector. I wondered if the matrixes are related rather than just being random, so that the null spaces you are seeking can be considered to be like 1-dimensional tangents to a curve in N-space (N = 9). Note that these 3x3 determinants are just triple products you can save computation by reusing the cross products. If you assume your 4x3 matrix is not actually rank-deficient, you can find your (single) null-space vector without any conditionals at all: the matrix is small enough that you can use Cramer's rule efficiently.Īctually, since you don't actually care about the scale of your null vector, you don't have to divide by the determinant - you can just take the determinants of the minors: x1 x2 x3 It might actually be harder to determine how to store your result: if your matrix is rank-deficient, what do you want your CUDA program to do about it? If necessary, you should be able to do some form of pivoting using conditional assignment. Simple if statements that can be optimized into conditional assignment are much better (or you can use the ?: operator). I think the most important thing for CUDA is to find an algorithm that doesn't depend on conditional branching (which is quite slow on graphics hardware). - Setting the host, Nrows x Ncols matrixĭouble *h_A = (double *)malloc(Nrows * Ncols * sizeof(double)) Įxtern "C" int iDivUp(int a, int b) Int *devInfo gpuErrchk(cudaMalloc(&devInfo, sizeof(int))) - cuSOLVE input/output parameters/arrays To associate a stream to each task you can use cudaStreamCreate() Below I report an example on how using cuSOLVER's SVD to calculate the null space of a matrix.īe aware that the problem you are focusing on concerns the calculation of several small matrices, so you should adapt the example I'm providing below by using streams to make sense for your case. SVD should be preferred when accuracy is required, see also Null-space of a rectangular dense matrix.Īs of February 2015, CUDA 7 (now in release candidate) makes SVD available through its new cuSOLVER library. In the anwers above, it has been already pointed out how the null space of a matrix can be calculated by using the QR or the SVD approach.
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