NAG Library Routine Document

F06WCF (DSFRK)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{TRANSR}$ – CHARACTER(1)Input

On entry: specifies whether the RFP representation of $C$ is normal or transposed.

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

The matrix $C$ is stored in normal RFP format.

$\mathbf{TRANSR}=\text{'T'}$

The matrix $C$ is stored in transposed RFP format.

Constraint: $\mathbf{TRANSR}=\text{'N'}$ or $\text{'T'}$.

2:     $\mathrm{UPLO}$ – CHARACTER(1)Input

On entry: specifies whether the upper or lower triangular part of $C$ is stored in RFP format.

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

The upper triangular part of $C$ is stored in RFP format.

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

The lower triangular part of $C$ is stored in RFP format.

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

3:     $\mathrm{TRANS}$ – CHARACTER(1)Input

On entry: specifies the operation to be performed.

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

$C\leftarrow \alpha A{A}^{\mathrm{T}}+\beta C$.

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

$C\leftarrow \alpha A^{\mathrm{T}}A+\beta C$.

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

4:     $\mathrm{N}$ – INTEGERInput

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

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

5:     $\mathrm{K}$ – INTEGERInput

On entry: $k$, the number of columns of $A$ if $\mathbf{TRANS}=\text{'N'}$, or the number of rows of $A$ if $\mathbf{TRANS}=\text{'T'}$.

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

6:     $\mathrm{ALPHA}$ – REAL (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

7:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – REAL (KIND=nag_wp) arrayInput

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{K}\right)$ if $\mathbf{TRANS}=\text{'N'}$ and at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{TRANS}=\text{'T'}$.

On entry: the matrix $A$; $A$ is $n$ by $k$ if $\mathbf{TRANS}=\text{'N'}$, or $k$ by $n$ if $\mathbf{TRANS}=\text{'T'}$. If $\mathbf{ALPHA}=0.0$, A is not referenced.

8:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06WCF (DSFRK) is called.

Constraints:

• if $\mathbf{TRANS}=\text{'N'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$;
• if $\mathbf{TRANS}=\text{'T'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{K}\right)$.

9:     $\mathrm{BETA}$ – REAL (KIND=nag_wp)Input

On entry: the scalar $\beta$.

10:   $\mathrm{CR}\left(\mathbf{N}\times \left(\mathbf{N}+1\right)/2\right)$ – REAL (KIND=nag_wp) arrayInput/Output

On entry: the upper or lower triangular part (as specified by UPLO) of the $n$ by $n$ symmetric matrix $C$, stored in RFP format (as specified by TRANSR). The storage format is described in detail in Section 3.3.3 in the F07 Chapter Introduction.

On exit: the updated matrix $C$, that is its upper or lower triangular part stored in RFP format.

6  Error Indicators and Warnings

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f06wcfe.f90)

10.2  Program Data

Program Data (f06wcfe.d)

10.3  Program Results

Program Results (f06wcfe.r)