# angle

From rospca v1.0.4
by Tom Reynkens

##### Standardised last principal angle

Standardised last principal angle between the subspaces generated by the columns of `A`

and `B`

.

- Keywords
- algebra

##### Usage

`angle(A, B)`

##### Arguments

- A
Numeric matrix of size \(p\) by \(k\).

- B
Numeric matrix of size \(q\) by \(l\).

##### Details

We compute the last principal angle between the subspaces generated by the columns of `A`

and `B`

using
the algorithm in Bjorck and Golub (1973). This angle takes values between 0 and \(\pi/2\). We divide it by \(\pi/2\) to make it take values between 0 and 1, where 0 indicates that the subspaces are close.

##### Value

Standardised last principal angle between `A`

and `B`

.

##### References

Bjorck, A. and Golub, G. H. (1973), ``Numerical Methods for Computing Angles Between Linear Subspaces," *Mathematics of Computation*, 27, 579--594.

##### Examples

```
# NOT RUN {
tmp <- dataGen(m=1)
P <- eigen(tmp$R)$vectors[,1:2]
PP <- rospca(tmp$data[[1]], k=2)$loadings
angle(P, PP)
# }
```

*Documentation reproduced from package rospca, version 1.0.4, License: GPL (>= 2)*

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