NAG Library Function Document

nag_zptsv (f07jnc)

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 Nag_ColMajor.

2:     n – IntegerInput

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

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

3:     nrhs – IntegerInput

On entry: $r$, the number of right-hand sides, i.e., the number of columns of the matrix $B$.

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

4:     d[$\mathit{dim}$] – doubleInput/Output

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

On entry: the $n$ diagonal elements of the tridiagonal matrix $A$.

On exit: the $n$ diagonal elements of the diagonal matrix $D$ from the factorization $A=LD{L}^{\mathrm{H}}$.

5:     e[$\mathit{dim}$] – ComplexInput/Output

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

On entry: the $\left(n-1\right)$ subdiagonal elements of the tridiagonal matrix $A$.

On exit: the $\left(n-1\right)$ subdiagonal elements of the unit bidiagonal factor $L$ from the $LD{L}^{\mathrm{H}}$ factorization of $A$. (e can also be regarded as the superdiagonal of the unit bidiagonal factor $U$ from the $U^{\mathrm{H}}DU$ factorization of $A$.)

6:     b[$\mathit{dim}$] – ComplexInput/Output

Note: the dimension, dim, of the array b must be at least

• $\max \left(1,\mathbf{pdb}\times \mathbf{nrhs}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdb}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $B$ is stored in

• $\mathbf{b}\left[\left(j-1\right)\times \mathbf{pdb}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{b}\left[\left(i-1\right)\times \mathbf{pdb}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $n$ by $r$ right-hand side matrix $B$.

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$NE_NOERROR, the $n$ by $r$ solution matrix $X$.

7:     pdb – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{nrhs}\right)$.

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_INT

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

On entry, $\mathbf{nrhs}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nrhs}\ge 0$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}>0$.

NE_INT_2

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

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{nrhs}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{nrhs}\right)$.

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.

NE_MAT_NOT_POS_DEF

The leading minor of order $〈\mathit{\text{value}}〉$ is not positive definite, and the solution has not been computed. The factorization has not been completed unless $\mathbf{n}=〈\mathit{\text{value}}〉$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07jnce.c)

9.2  Program Data

Program Data (f07jnce.d)

9.3  Program Results

Program Results (f07jnce.r)