naginterfaces.library.blas.dvcos

naginterfaces.library.blas.dvcos(j, tolx, x, toly, y)

dvcos computes the cosine of the angle between two real vectors.

For full information please refer to the NAG Library document for f06fa

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06faf.html

Parameters

jint

If the vector $y$ is supplied in $y$, $j$ should be set to $0$. Otherwise, $j$ specifies the index $j$ of the unit vector $e_j$ to be used as $y$.

tolxfloat

The value $\text{tolx}$, used to determine whether ${\parallel x\parallel }_2$ is effectively zero.

If $tolx$ is negative, the value zero is used.

xfloat, array-like, shape $\left(n\right)$

The $n$-element vector $x$.

tolyfloat

The value $\text{toly}$, used to determine whether ${\parallel y\parallel }_2$ is effectively zero.

If $toly$ is negative, the value zero is used.

yfloat, array-like, shape $\left(n\right)$

If $1\le j\le n$, $y$ is not referenced. Otherwise, $y$ holds the vector $y$.

Returns

vcosfloat

The cosine of the angle between $x$ and $y$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

dvcos returns the cosine of the angle between two $n$-element real vectors $x$ and $y$, given by the expression

$$\frac{x^{T}y}{{\parallel x\parallel }_2{\parallel y\parallel }_2}\text{.}$$

If $1\le j\le n$, $y$ is taken to be the unit vector $e_j$, in which case the array $y$ is not referenced.

If ${\parallel x\parallel }_2\le \text{tolx}$, the function returns $2.0$; if ${\parallel x\parallel }_2>\text{tolx}$ but ${\parallel y\parallel }_2\le \text{tol}y$, the function returns $-2.0$; otherwise the value returned is in the range $(-1.0,1.0)$.