![]() ![]() The matrix analysis functions det, rcond, hess, and expm also show significant increase in speed on large double-precision arrays. ![]() The matrix multiply (X*Y) and matrix power (X^p) operators show significant increase in speed on large double-precision arrays (on order of 10,000 elements). As a general rule, complicated functions speed up more than simple functions. The operation is not memory-bound processing time is not dominated by memory access time. For example, most functions speed up only when the array contains several thousand elements or more. The data size is large enough so that any advantages of concurrent execution outweigh the time required to partition the data and manage separate execution threads. They should require few sequential operations. These sections must be able to execute with little communication between processes. a*b must equal x*y for this to work.The function performs operations that easily partition into sections that execute concurrently. ![]() It takes a matrix M that used to have x rows and y columns and turns it into a matrix with a rows and b columns. With a matrix, diag pulls out the diagonal elements and makes a vector out of them. See in the snippet below a successful deletion of the fourth element of a vector, and what happens when I try to delete just one element from a 4x3 matrix.Ī null assignment can have only one non-colon index.ĭiag on a vector creates a matrix whose diagonal is the initial vector and whose other elements are zero. This is a 3-dimensional slice of meanvalues and MATLAB expects the right-hand-side to be a 3-D matrix of the right. Unless all the minwindex values are the same, it refers to indices that are all the rows and columns and the union of all the minwindex values. Using empty brackets to delete elements from a matrix works if you are going to delete a whole row or a whole column, but not just one element. namely, subscript indices are independent and do not work with a matrix of values. Create a random matrix A of order 500 that is constructed so that its condition number, cond(A), is 1e10, and its norm, norm(A), is 1.The exact solution x is a random vector of length 500, and the right side is b Ax. Deleting is not the same as assigning zero to the value of that element. Examine why solving a linear system by inverting the matrix using inv(A)b is inferior to solving it directly using the backslash operator, x Ab. Use empty brackets to delete an element from a vector or a row/column from a matrix. To append vectors to a matrix you need to make sure the dimensions work out so that all rows have the same number of elements. This reshape() function is used to reshape the specified matrix using the given size vector. This conversion can be done using reshape() function along with the Transpose operation. If it is not the next consecutive position, MATLAB pads the elements in between with zeros. Conversion of a Matrix into a Row Vector. 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. If all input arguments are empty and have compatible sizes, then cat returns an empty array whose size is equal to the output size as when the inputs are nonempty. A MATLAB user recently posed this question in the newsgroup: If I want to shift the rows of an m-by-n matrix A by k places, I use A(:,n-k+1:n 1:n-k). For example, cat(2,1 2,) returns the row vector 1 2. 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. When concatenating an empty array to a nonempty array, cat omits the empty array in the output. 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. We've already practiced using parentheses to address a certain element of a vector. ![]()
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