NAG FL Interface
f01dff (real_​tri_​matmul)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{uplo}$ – Character(1) Input

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

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

$C$ is upper triangular.

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

$C$ is lower triangular.

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

2: $\mathbf{transa}$ – Character(1) Input

On entry: specifies whether the operation involves $A$ or $A^{\mathrm{T}}$.

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

The operation involves $A$.

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

The operation involves $A^{\mathrm{T}}$.

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

3: $\mathbf{transb}$ – Character(1) Input

On entry: specifies whether the operation involves $B$ or $B^{\mathrm{T}}$.

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

The operation involves $B$.

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

The operation involves $B^{\mathrm{T}}$.

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

4: $\mathbf{n}$ – Integer Input

On entry: $n$, the order of the triangular matrices $A$, $B$, and $C$.

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

5: $\mathbf{alpha}$ – Real (Kind=nag_wp) Input

On entry: the scalar $\alpha$.

6: $\mathbf{a}(\mathbf{lda},*)$ – Real (Kind=nag_wp) array Input

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

On entry: the $n\times n$ triangular matrix $A$.

• If $\mathbf{uplo}=\text{'U'}$,
  • if $\mathbf{transa}=\text{'N'}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced;
  • if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$,
  • if $\mathbf{transa}=\text{'N'}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced;
  • if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced.

7: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f01dff is called.

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

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

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

On entry: the $n\times n$ triangular matrix $B$.

• If $\mathbf{uplo}=\text{'U'}$,
  • if $\mathbf{transa}=\text{'N'}$, $B$ is upper triangular and the elements of the array below the diagonal are not referenced;
  • if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$, $B$ is lower triangular and the elements of the array above the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$,
  • if $\mathbf{transa}=\text{'N'}$, $B$ is lower triangular and the elements of the array above the diagonal are not referenced;
  • if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$, $B$ is upper triangular and the elements of the array below the diagonal are not referenced.

9: $\mathbf{ldb}$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which f01dff is called.

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

10: $\mathbf{beta}$ – Real (Kind=nag_wp) Input

On entry: the scalar $\beta$.

11: $\mathbf{c}(\mathbf{ldc},*)$ – Real (Kind=nag_wp) array Input/Output

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

• If $\mathbf{uplo}=\text{'U'}$, $C$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$, $C$ is lower triangular and the elements of the array above the diagonal are not referenced.

On entry: the $n\times n$ matrix $C$.

If $\mathbf{beta}=0$, c need not be set.

On exit: the triangular part of $C$, as specified by uplo, is updated.

12: $\mathbf{ldc}$ – Integer Input

On entry: the first dimension of the array c as declared in the (sub)program from which f01dff is called.

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

13: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{uplo}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

$\mathbf{ifail}=2$

On entry, $\mathbf{transa}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{transa}=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

$\mathbf{ifail}=3$

On entry, $\mathbf{transb}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{transb}=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=5$

On entry, $\mathbf{lda}=⟨\mathit{\text{value}}⟩$, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lda}\ge \max (1,\mathbf{n})$.

$\mathbf{ifail}=6$

On entry, $\mathbf{ldb}=⟨\mathit{\text{value}}⟩$, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldb}\ge \max (1,\mathbf{n})$.

$\mathbf{ifail}=7$

On entry, $\mathbf{ldc}=⟨\mathit{\text{value}}⟩$, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldc}\ge \max (1,\mathbf{n})$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results