naginterfaces.library.linsys.real_​blkdiag_​fac_​solve

naginterfaces.library.linsys.real_blkdiag_fac_solve(trans, blkstr, a, pivot, b)

real_blkdiag_fac_solve calculates the approximate solution of a set of real linear equations with multiple right-hand sides, $AX=B$ or $A^{T}X=B$, where $A$ is an almost block-diagonal matrix which has been factorized by matop.real_gen_blkdiag_lu.

For full information please refer to the NAG Library document for f04lh

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f04/f04lhf.html

Parameters

transstr, length 1

Specifies the equations to be solved.

$trans=\text{'N'}$

Solve $AX=B$.

$trans=\text{'T'}$

Solve $A^{T}X=B$.

blkstrint, array-like, shape $(3,\text{nbloks})$

Information which describes the block structure of $A$, as supplied to real_blkdiag_fac_solve.

afloat, array-like, shape $\left(\text{lena}\right)$

The elements in the factorization of $A$, as returned by real_blkdiag_fac_solve.

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

Details of the interchanges in the factorization, as returned by real_blkdiag_fac_solve.

bfloat, array-like, shape $(n,\text{ir})$

The $n\times r$ right-hand side matrix $B$.

Returns

bfloat, ndarray, shape $(n,\text{ir})$

$b$ is overwritten by the $n\times r$ solution matrix $X$.

Raises

NagValueError

(errno $1$)

On entry, $\text{lena}$ is too small. $\text{lena}=⟨value⟩$. Minimum possible dimension: $⟨value⟩$.

(errno $1$)

On entry, the following equality does not hold: $blkstr[1,0]+sum\left(blkstr\right[1,k-1]-blkstr[2,k-2]:k=2,\text{nbloks})=n$.

(errno $1$)

On entry, the following equality does not hold: $sum(blkstr[0,k-1]:k=1,\text{nbloks})=n$.

(errno $1$)

On entry, $K=⟨value⟩$, $blkstr[2,K-1]=⟨value⟩$, $blkstr[2,K-2]=⟨value⟩$ and $blkstr[1,K-1]=⟨value⟩$.

Constraint: $blkstr[2,K-1]+blkstr[2,K-2]\ge blkstr[1,K-1]$.

(errno $1$)

On entry, the following inequality was not satisfied for: $J=⟨value⟩$. $sum(blkstr[1,k-1]-blkstr[2,k-1]:k=1,J)\le$ $sum(blkstr[0,k-1]:k=1,J)\le$ $blkstr[1,0]+sum(blkstr[1,k-1]-blkstr[2,k-2]:k=2,J)$.

(errno $1$)

On entry, $K=⟨value⟩$, $blkstr[1,K-1]=⟨value⟩$, $blkstr[2,K-1]=⟨value⟩$ and $blkstr[0,K-1]=⟨value⟩$.

Constraint: $blkstr[1,K-1]-blkstr[2,K-1]\le blkstr[0,K-1]$.

(errno $1$)

On entry, $K=⟨value⟩$, $blkstr[1,K-1]=⟨value⟩$ and $blkstr[0,K-1]=⟨value⟩$.

Constraint: $blkstr[1,K-1]\ge blkstr[0,K-1]$.

(errno $1$)

On entry, $K=⟨value⟩$ and $blkstr[2,K-1]=⟨value⟩$.

Constraint: $blkstr[2,K-1]\ge 0$.

(errno $1$)

On entry, $K=⟨value⟩$ and $blkstr[1,K-1]=⟨value⟩$.

Constraint: $blkstr[1,K-1]\ge 1$.

(errno $1$)

On entry, $K=⟨value⟩$ and $blkstr[0,K-1]=⟨value⟩$.

Constraint: $blkstr[0,K-1]\ge 1$.

(errno $1$)

On entry, $n=⟨value⟩$ and $\text{nbloks}=⟨value⟩$.

Constraint: $n\ge \text{nbloks}$.

(errno $1$)

On entry, $\text{nbloks}=⟨value⟩$.

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

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $1$)

On entry, $\text{ir}=⟨value⟩$.

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

(errno $1$)

On entry, $trans\ne \text{'N'}$ or $\text{'T'}$: $trans=⟨value⟩$.

Notes

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

real_blkdiag_fac_solve solves a set of real linear equations $AX=B$ or $A^{T}X=B$, where $A$ is almost block-diagonal. $A$ must first be factorized by matop.real_gen_blkdiag_lu. real_blkdiag_fac_solve then computes $X$ by forward and backward substitution over the blocks.

References

Diaz, J C, Fairweather, G and Keast, P, 1983, Fortran packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination, ACM Trans. Math. Software (9), 358–375