NAG Library Function Document

nag_zsymv (f16tac)

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 the upper or lower triangular part of $A$ is stored.

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

The upper triangular part of $A$ is stored.

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

The lower triangular part of $A$ is stored.

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

3:     n – IntegerInput

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

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

4:     alpha – ComplexInput

On entry: the scalar $\alpha$.

5:     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 $n$ symmetric 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.

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

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

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 $x$.

8:     incx – IntegerInput

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

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

9:     beta – ComplexInput

On entry: the scalar $\beta$.

10:   y[$\mathit{dim}$] – ComplexInput/Output

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

On entry: the vector $y$.

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

On exit: the updated vector $y$.

11:   incy – IntegerInput

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

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

12:   fail – NagError *Input/Output

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

6  Error Indicators and Warnings

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

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 (f16tace.c)

10.2  Program Data

Program Data (f16tace.d)

10.3  Program Results

Program Results (f16tace.r)