NAG Library Routine Document

F07UHF (DTPRFS)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: specifies whether $A$ is upper or lower triangular.

$\mathbf{UPLO}=\text{'U'}$

$A$ is upper triangular.

$\mathbf{UPLO}=\text{'L'}$

$A$ is lower triangular.

Constraint: $\mathbf{UPLO}=\text{'U'}$ or $\text{'L'}$.

2:     TRANS – CHARACTER(1)Input

On entry: indicates the form of the equations.

$\mathbf{TRANS}=\text{'N'}$

The equations are of the form $AX=B$.

$\mathbf{TRANS}=\text{'T'}$ or $\text{'C'}$

The equations are of the form $A^{\mathrm{T}}X=B$.

Constraint: $\mathbf{TRANS}=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

3:     DIAG – CHARACTER(1)Input

On entry: indicates whether $A$ is a nonunit or unit triangular matrix.

$\mathbf{DIAG}=\text{'N'}$

$A$ is a nonunit triangular matrix.

$\mathbf{DIAG}=\text{'U'}$

$A$ is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be $1$.

Constraint: $\mathbf{DIAG}=\text{'N'}$ or $\text{'U'}$.

4:     N – INTEGERInput

On entry: $n$, the order of the matrix $A$.

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

5:     NRHS – INTEGERInput

On entry: $r$, the number of right-hand sides.

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

6:     AP($*$) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array AP must be at least $\max \left(1,\mathbf{N}\times \left(\mathbf{N}+1\right)/2\right)$.

On entry: the $n$ by $n$ triangular matrix $A$, packed by columns.

More precisely,

• if $\mathbf{UPLO}=\text{'U'}$, the upper triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{AP}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if $\mathbf{UPLO}=\text{'L'}$, the lower triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{AP}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.

If $\mathbf{DIAG}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced; the same storage scheme is used whether $\mathbf{DIAG}=\text{'N'}$ or ‘U’.

7:     B(LDB,$*$) – REAL (KIND=nag_wp) arrayInput

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{NRHS}\right)$.

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

8:     LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F07UHF (DTPRFS) is called.

Constraint: $\mathbf{LDB}\ge \max \left(1,\mathbf{N}\right)$.

9:     X(LDX,$*$) – REAL (KIND=nag_wp) arrayInput

Note: the second dimension of the array X must be at least $\max \left(1,\mathbf{NRHS}\right)$.

On entry: the $n$ by $r$ solution matrix $X$, as returned by F07UEF (DTPTRS).

10:   LDX – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which F07UHF (DTPRFS) is called.

Constraint: $\mathbf{LDX}\ge \max \left(1,\mathbf{N}\right)$.

11:   FERR(NRHS) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{FERR}\left(\mathit{j}\right)$ contains an estimated error bound for the $\mathit{j}$th solution vector, that is, the $\mathit{j}$th column of $X$, for $\mathit{j}=1,2,\dots ,r$.

12:   BERR(NRHS) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{BERR}\left(\mathit{j}\right)$ contains the component-wise backward error bound $\beta$ for the $\mathit{j}$th solution vector, that is, the $\mathit{j}$th column of $X$, for $\mathit{j}=1,2,\dots ,r$.

13:   WORK($3\times \mathbf{N}$) – REAL (KIND=nag_wp) arrayWorkspace

14:   IWORK(N) – INTEGER arrayWorkspace

15:   INFO – INTEGEROutput

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

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

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

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07uhfe.f90)

9.2  Program Data

Program Data (f07uhfe.d)

9.3  Program Results

Program Results (f07uhfe.r)