mldivide: Matlab backslash operator In pracma: Practical Numerical Math Functions

Description

Emulate the Matlab backslash operator “\” through QR decomposition.

Usage

 1 2 mldivide(A, B, pinv = TRUE) mrdivide(A, B, pinv = TRUE)

Arguments

 A, B Numerical or complex matrices; A and B must have the same number of rows (for mldivide) or the same number of columns (for mrdivide) pinv logical; shall SVD decomposition be used; default true.

Details

mldivide performs matrix left division (and mrdivide matrix right division). If A is scalar it performs element-wise division.

If A is square, mldivide is roughly the same as inv(A) %*% B except it is computed in a different way — using QR decomposition.

If pinv = TRUE, the default, the SVD will be used as pinv(t(A)%*%A)%*%t(A)%*%B to generate results similar to Matlab. Otherwise, qr.solve will be used.

If A is not square, x <- mldivide(A, b) returnes a least-squares solution that minimizes the length of the vector A %*% x - b (which is equivalent to norm(A %*% x - b, "F").

Value

If A is an n-by-p matrix and B n-by-q, then the result of mldivide(A, B) is a p-by-q matrix (mldivide).

Note

mldivide(A, B) corresponds to A\B in Matlab notation.

Examples

 1 2 3 4 5 6 7 8 # Solve a system of linear equations A <- matrix(c(8,1,6, 3,5,7, 4,9,2), nrow = 3, ncol = 3, byrow = TRUE) b <- c(1, 1, 1) mldivide(A, b) # 0.06666667 0.06666667 0.06666667 A <- rbind(1:3, 4:6) mldivide(A, c(1,1)) # -0.5 0 0.5 ,i.e. Matlab/Octave result mldivide(A, c(1,1), pinv = FALSE) # -1 1 0 R qr.solve result

Example output

[,1]
[1,] 0.06666667
[2,] 0.06666667
[3,] 0.06666667
[,1]
[1,] -5.000000e-01
[2,]  3.025358e-15
[3,]  5.000000e-01
[,1]
[1,]   -1
[2,]    1
[3,]    0

pracma documentation built on Dec. 11, 2021, 9:57 a.m.