# 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.