NAG Library Function Document

nag_dgtsv (f07cac)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 2.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of linear equations, i.e., the order of the matrix $A$.

Constraint: $\mathbf{n}\ge 0$.

3:    $\mathbf{nrhs}$ – IntegerInput

On entry: $r$, the number of right-hand sides, i.e., the number of columns of the matrix $B$.

Constraint: $\mathbf{nrhs}\ge 0$.

4:    $\mathbf{dl}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension, dim, of the array dl must be at least $\max \left(1,\mathbf{n}-1\right)$.

On entry: must contain the $\left(n-1\right)$ subdiagonal elements of the matrix $A$.

On exit: if no constraints are violated, dl is overwritten by the ($n-2$) elements of the second superdiagonal of the upper triangular matrix $U$ from the $LU$ factorization of $A$, in $\mathbf{dl}\left[0\right],\mathbf{dl}\left[1\right],\dots ,\mathbf{dl}\left[n-3\right]$.

5:    $\mathbf{d}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension, dim, of the array d must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: must contain the $n$ diagonal elements of the matrix $A$.

On exit: if no constraints are violated, d is overwritten by the $n$ diagonal elements of the upper triangular matrix $U$ from the $LU$ factorization of $A$.

6:    $\mathbf{du}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension, dim, of the array du must be at least $\max \left(1,\mathbf{n}-1\right)$.

On entry: must contain the $\left(n-1\right)$ superdiagonal elements of the matrix $A$.

On exit: if no constraints are violated, du is overwritten by the $\left(n-1\right)$ elements of the first superdiagonal of $U$.

7:    $\mathbf{b}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension, dim, of the array b must be at least

• $\max \left(1,\mathbf{pdb}\times \mathbf{nrhs}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdb}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $B$ is stored in

• $\mathbf{b}\left[\left(j-1\right)\times \mathbf{pdb}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{b}\left[\left(i-1\right)\times \mathbf{pdb}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $n$ by $r$ right-hand side matrix $B$.

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, the $n$ by $r$ solution matrix $X$.

8:    $\mathbf{pdb}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array b.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{nrhs}\right)$.

9:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{nrhs}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nrhs}\ge 0$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}>0$.

NE_INT_2

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{nrhs}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{nrhs}\right)$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_SINGULAR

Element $〈\mathit{\text{value}}〉$ of the diagonal is exactly zero, and the solution has not been computed. The factorization has not been completed unless $\mathbf{n}=〈\mathit{\text{value}}〉$.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f07cace.c)

10.2  Program Data

Program Data (f07cace.d)

10.3  Program Results

Program Results (f07cace.r)