naginterfaces.library.sort.intmat_​rank_​columns

naginterfaces.library.sort.intmat_rank_columns(im, m1, n1, order)

intmat_rank_columns ranks the columns of a matrix of integer numbers in ascending or descending order.

For full information please refer to the NAG Library document for m01dk

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/m01/m01dkf.html

Parameters

imint, array-like, shape $(\text{m2},\text{n2})$

Rows $m1-1$ to $\text{m2}-1$ of columns $n1$ to $\text{n2}$ of $im$ must contain integer data to be ranked.

m1int

Note: this argument represents an array index; the value you supply must be base-1 for compatibility with the NAG Engine.

The index of the first row of $im$ to be used.

n1int

The index of the first column of $im$ to be ranked.

orderstr, length 1

If $order=\text{'A'}$, the columns will be ranked in ascending (i.e., nondecreasing) order.

If $order=\text{'D'}$, into descending order.

Returns

irankint, ndarray, shape $\left(\text{n2}\right)$

Elements $n1$ to $\text{n2}$ of $irank$ contain the ranks of the corresponding columns of $im$. Note that the ranks are in the range $n1$ to $\text{n2}$: thus, if the $i$th column of $im$ is the first in the rank order, $irank[i-1]$ is set to $n1$.

Raises

NagValueError

(errno $1$)

On entry, $\text{m2}=⟨value⟩$ and $\text{ldm}=⟨value⟩$.

Constraint: $\text{m2}\le \text{ldm}$.

(errno $1$)

On entry, $n1=⟨value⟩$ and $\text{n2}=⟨value⟩$.

Constraint: $n1\le \text{n2}$.

(errno $1$)

On entry, $n1=⟨value⟩$.

Constraint: $n1\ge 1$.

(errno $1$)

On entry, $\text{n2}=⟨value⟩$.

Constraint: $\text{n2}\ge 1$.

(errno $1$)

On entry, $m1=⟨value⟩$ and $\text{m2}=⟨value⟩$.

Constraint: $m1\le \text{m2}$.

(errno $1$)

On entry, $m1=⟨value⟩$.

Constraint: $m1\ge 1$.

(errno $1$)

On entry, $\text{m2}=⟨value⟩$.

Constraint: $\text{m2}\ge 1$.

(errno $2$)

On entry, $order$ has an illegal value: $order=⟨value⟩$.

Notes

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

intmat_rank_columns ranks columns $n1$ to $\text{n2}$ of a matrix, using the data in rows $m1$ to $\text{m2}$ of those columns. The ordering is determined by first ranking the data in row $m1$, then ranking any tied columns according to the data in row $m1+1$, and so on up to row $\text{m2}$.

intmat_rank_columns uses a variant of list-merging, as described on pages 165–166 in Knuth (1973). The function takes advantage of natural ordering in the data, and uses a simple list insertion in a preparatory pass to generate ordered lists of length at least $10$. The ranking is stable: equal columns preserve their ordering in the input data.

References

Knuth, D E, 1973, The Art of Computer Programming (Volume 3), (2nd Edition), Addison–Wesley