naginterfaces.library.matop.real_​band_​pack

naginterfaces.library.matop.real_band_pack(job, kl, ku, a, b)

real_band_pack copies a real band matrix stored in a packed array into an unpacked array, or vice versa.

For full information please refer to the NAG Library document for f01zc

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f01/f01zcf.html

Parameters

jobstr, length 1

Specifies whether the band matrix is to be packed or unpacked.

$job=\text{'P'}$ (Pack)

The band matrix is to be packed into array $b$.

$job=\text{'U'}$ (Unpack)

The band matrix is to be unpacked into array $a$.

klint

$k_l$, the number of subdiagonals of the band matrix.

kuint

$k_u$, the number of superdiagonals of the band matrix.

afloat, array-like, shape $(m,n)$

If $job=\text{'P'}$, the leading $m\times n$ part of $a$ must contain the band matrix stored in unpacked form. Elements of the array that lie outside the banded part of the matrix are not referenced and need not be assigned.

bfloat, array-like, shape $((kl+ku+1),min(m+ku,n))$

If $job=\text{'U'}$, $b$ must contain the band matrix in packed form, in the leading $(k_l+k_u+1)\times min(m+k_u,n)$ part of the array. The matrix is packed column by column, with the leading diagonal of the matrix in row $(k_u+1)$ of $b$, the first superdiagonal starting at position $2$ in row $k_u$, the first subdiagonal starting at position $1$ in row $(k_u+2)$, and so on. Elements of $b$ that are not needed to store the band matrix, for instance the leading $k_u\times k_u$ triangle, are not referenced and need not be assigned.

Returns

afloat, ndarray, shape $(m,n)$

If $job=\text{'U'}$, the leading $m\times n$ part of $a$ contains the band matrix stored in unpacked form. Elements of the leading $m\times n$ part of $a$ that are not within the banded part of the matrix are assigned the value zero.

bfloat, ndarray, shape $((kl+ku+1),min(m+ku,n))$

If $job=\text{'P'}$, $b$ contains the band matrix stored in packed form. Elements of $b$ that are not needed to store the band matrix are not referenced.

Raises

NagValueError

(errno $1$)

On entry, $job=⟨value⟩$.

Constraint: $job=\text{'P'}$ or $\text{'U'}$.

(errno $2$)

On entry, $kl=⟨value⟩$.

Constraint: $kl\ge 0$.

(errno $3$)

On entry, $ku=⟨value⟩$.

Constraint: $ku\ge 0$.

(errno $5$)

On entry, $\text{ldb}=⟨value⟩$, $kl=⟨value⟩$ and $ku=⟨value⟩$.

Constraint: $\text{ldb}\ge kl+ku+1$.

(errno $6$)

On entry, $n=⟨value⟩$.

Constraint: $n>0$.

(errno $6$)

On entry, $m=⟨value⟩$.

Constraint: $m>0$.

Notes

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

real_band_pack unpacks a band matrix that is stored in a packed array, or packs a band matrix that is stored in an unpacked array. The band matrix has $m$ rows, $n$ columns, $k_l$ nonzero subdiagonals, and $k_u$ nonzero superdiagonals. This function is intended for possible use in conjunction with functions from submodule blas, submodule lapacklin and submodule lapackeig, where functions that use band matrices store them in the packed form described below.