NAG Library Function Document

nag_dsyev (f08fac)

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:     job – Nag_JobTypeInput

On entry: indicates whether eigenvectors are computed.

$\mathbf{job}=\mathrm{Nag\_EigVals}$

Only eigenvalues are computed.

$\mathbf{job}=\mathrm{Nag\_DoBoth}$

Eigenvalues and eigenvectors are computed.

Constraint: $\mathbf{job}=\mathrm{Nag\_EigVals}$ or $\mathrm{Nag\_DoBoth}$.

3:     uplo – Nag_UploTypeInput

On entry: if $\mathbf{uplo}=\mathrm{Nag\_Upper}$, the upper triangular part of $A$ is stored.

If $\mathbf{uplo}=\mathrm{Nag\_Lower}$, the lower triangular part of $A$ is stored.

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

4:     n – IntegerInput

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

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

5:     a[$\mathit{dim}$] – doubleInput/Output

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.

On exit: if $\mathbf{job}=\mathrm{Nag\_DoBoth}$, then a contains the orthonormal eigenvectors of the matrix $A$.

If $\mathbf{job}=\mathrm{Nag\_EigVals}$, then on exit the lower triangle (if $\mathbf{uplo}=\mathrm{Nag\_Lower}$) or the upper triangle (if $\mathbf{uplo}=\mathrm{Nag\_Upper}$) of a, including the diagonal, is overwritten.

6:     pda – IntegerInput

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

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

7:     w[n] – doubleOutput

On exit: the eigenvalues in ascending order.

8:     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_CONVERGENCE

The algorithm failed to converge; $⟨\mathit{\text{value}}⟩$ off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

NE_INT

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

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

NE_INT_2

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f08face.c)

10.2  Program Data

Program Data (f08face.d)

10.3  Program Results

Program Results (f08face.r)