I need to find all the lines in the file that contain a specific number in one of the fields. For the matrix A at the beginning of this section, verify that A*inv(A)=inv(A)*A=eye(3). I have structured data files (each about 30 GB). The n × n identity matrix I is represented in MATLAB by eye(n). If A is a square matrix with |A| = 0, then inv(A) represents the inverse of A, denoted in mathematics by A −1. The magnitude or Euclidean norm of the vector v, given by ![]() For more information, see Array Indexing. In this case, the logical array being used as an index is the same size as the other array, but this is not a requirement. Since B is a logical matrix, this operation is called logical indexing. It can create vectors, subscript arrays, and specify for iterations. The result is a column vector of the elements in A that are less than 9. Hence, if you need to input the column vector The colon is one of the most useful operators in MATLAB ®. The matrix class is designed to behave like matrix variables in Matlab. A vector is a 1-dimensional matrix, either a vertical vector (N × 1) or horizontal vector (1 × N). It is formed by interchanging the rows and columns. Similarly, A.*B is not matrix multiplication but merely multiplies the corresponding positions in the two matrices.ĭet(A) is the determinant of A, written |A|.Ī' is the transpose of A and is written in mathematics as A T. Note: A.^2 does not square the matrix but squares each element in the matrix. However, B+C and C*A produce error messages. Hence calculate after the prompt D=2*A-B, F=A*B, G=A*C, Asq=A^2. Providing they have compatible shapes they can be multiplied using the established rules for matrix multiplication. Extracts the diagonal of the matrix as a column vector. Providing matrices have the same shape they can be added or subtracted. (v) tril (A) triu (A) A' Inv (A) Creates a diagonal matrix with the vector v in the diagonal. ![]() Hence A(:,2) is column number 2 in the matrix A while is the first row of B. The comma separates the row number(s) from the column number(s).Ī single colon “:” before the comma means “take all rows”, whereas a single colon after the comma means “take all columns”. The element A(i,j) is in the i th row and j th column. For example, run the following M-file mat.m: To construct a matrix with m rows and n columns (called an “m by n matrix”, written m×n matrix), each row in the array ends with a semicolon. If A is a cell array of character vectors. If more than one element has equal magnitude, then the elements are sorted by phase angle on the interval (. If A is complex, then by default, sort sorts the elements by magnitude. ![]() If A is a scalar, then sort (A) returns A. But you are aware that a rectangular array represents a matrix and a single array column represents a column vector. Input array, specified as a vector, matrix, or multidimensional array. The matrix analysis functions det, rcond, hess, and expm also show significant increase in speed on large double-precision arrays.Each array that was discussed in Section 4 was, in effect, a row vector or row matrix. 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. The function performs operations that easily partition into sections that execute concurrently.
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