NAG Library Function Document

nag_ztrsv (f16sjc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     uplo – Nag_UploTypeInput

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

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

$A$ is upper triangular.

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

$A$ is lower triangular.

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

3:     trans – Nag_TransTypeInput

On entry: specifies the operation to be performed.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$

$x\leftarrow A^{-1}x$.

$\mathbf{trans}=\mathrm{Nag\_Trans}$

$x\leftarrow A^{-\mathrm{T}}x$.

$\mathbf{trans}=\mathrm{Nag\_ConjTrans}$

$x\leftarrow A^{-\mathrm{H}}x$.

Constraint: $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$.

4:     diag – Nag_DiagTypeInput

On entry: specifies whether $A$ has nonunit or unit diagonal elements.

$\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$

The diagonal elements are stored explicitly.

$\mathbf{diag}=\mathrm{Nag\_UnitDiag}$

The diagonal elements are assumed to be $1$ and are not referenced.

Constraint: $\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$ or $\mathrm{Nag\_UnitDiag}$.

5:     n – IntegerInput

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

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

6:     alpha – ComplexInput

On entry: the scalar $\alpha$.

7:     a[$\mathit{dim}$] – const ComplexInput

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

On entry: the $n$ by $n$ triangular matrix $A$.

If $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $A_{ij}$ is stored in $\mathbf{a}\left[\left(j-1\right)\times \mathbf{pda}+i-1\right]$.

If $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $A_{ij}$ is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$.

If $\mathbf{uplo}=\mathrm{Nag\_Upper}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.

If $\mathbf{uplo}=\mathrm{Nag\_Lower}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

If $\mathbf{diag}=\mathrm{Nag\_UnitDiag}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.

8:     pda – IntegerInput

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

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

9:     x[$\mathit{dim}$] – ComplexInput/Output

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

On entry: the vector $x$.

On exit: the solution vector $x$.

10:   incx – IntegerInput

On entry: the increment in the subscripts of x between successive elements of $x$.

Constraint: $\mathbf{incx}\ne 0$.

11:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INT

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

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

NE_INT_2

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

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f16sjce.c)

10.2  Program Data

Program Data (f16sjce.d)

10.3  Program Results

Program Results (f16sjce.r)