NAG FL Interface
f07caf (dgtsv)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

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

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

2: $\mathbf{nrhs}$ – Integer Input

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

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

3: $\mathbf{dl}\left(*\right)$ – Real (Kind=nag_wp) array Input/Output

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

On entry: must contain the $(n-1)$ 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 $\mathbf{dl}\left(1\right),\mathbf{dl}\left(2\right),\dots ,\mathbf{dl}\left(n-2\right)$.

4: $\mathbf{d}\left(*\right)$ – Real (Kind=nag_wp) array Input/Output

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

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 $A$.

5: $\mathbf{du}\left(*\right)$ – Real (Kind=nag_wp) array Input/Output

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

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

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

6: $\mathbf{b}(\mathbf{ldb},*)$ – Real (Kind=nag_wp) array Input/Output

Note: the second dimension of the array b must be at least $\max (1,\mathbf{nrhs})$.

to solve the equations $Ax=b$, where $b$ is a single right-hand side, b may be supplied as a one-dimensional array with length $\mathbf{ldb}=\max (1,\mathbf{n})$.

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

On exit: if $\mathbf{info}=\mathbf{0}$, the $n\times r$ solution matrix $X$.

7: $\mathbf{ldb}$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which f07caf is called.

Constraint: $\mathbf{ldb}\ge \max (1,\mathbf{n})$.

8: $\mathbf{info}$ – Integer Output

On exit: $\mathbf{info}=0$ unless the routine detects an error (see Section 6).

6 Error Indicators and Warnings

$\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{info}>0$

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

10.2 Program Data

10.3 Program Results