NAG Library Function Document

nag_approx_quantiles_arbitrary (g01apc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     ind – Integer *Input/Output

On initial entry: must be set to $0$.

On entry: indicates the action required in the current call to nag_approx_quantiles_arbitrary (g01apc).

$\mathbf{ind}=0$

Initialize the communication arrays and attempt to process the first nb values from the data stream. eps, rv and nb must be set and licomm must be at least $10$.

$\mathbf{ind}=1$

Attempt to process the next block of nb values from the data stream. The calling program must update rv and (if required) nb, and re-enter nag_approx_quantiles_arbitrary (g01apc) with all other parameters unchanged.

$\mathbf{ind}=2$

Continue calculation following the reallocation of either or both of the communication arrays rcomm and icomm.

$\mathbf{ind}=3$

Calculate the nq $\epsilon$-approximate quantiles specified in q. The calling program must set q and nq and re-enter nag_approx_quantiles_arbitrary (g01apc) with all other parameters unchanged. This option can be chosen only when $\mathbf{np}\ge ⌈\exp \left(1.0\right)/\mathbf{eps}⌉$.

On exit: indicates output from the call.

$\mathbf{ind}=1$

nag_approx_quantiles_arbitrary (g01apc) has processed np data points and expects to be called again with additional data.

$\mathbf{ind}=2$

Either one or more of the communication arrays rcomm and icomm is too small. The new minimum lengths of rcomm and icomm have been returned in $\mathbf{icomm}\left[0\right]$ and $\mathbf{icomm}\left[1\right]$ respectively. If the new minimum length is greater than the current length then the corresponding communication array needs to be reallocated, its contents preserved and nag_approx_quantiles_arbitrary (g01apc) called again with all other parameters unchanged.

If there is more data to be processed, it is recommended that lrcomm and licomm are made significantly bigger than the minimum to limit the number of reallocations.

$\mathbf{ind}=3$

nag_approx_quantiles_arbitrary (g01apc) has returned the requested $\epsilon$-approximate quantiles in qv. These quantiles are based on np data points.

Constraint: $\mathbf{ind}=0$, $1$, $2$ or $3$.

2:     rv[$\mathit{dim}$] – const doubleInput

Note: the dimension, dim, of the array rv must be at least $\mathbf{nb}$ when $\mathbf{ind}=0$, $1$ or $2$.

On entry: if $\mathbf{ind}=0$, $1$ or $2$, the vector containing the current block of data, otherwise rv is not referenced.

3:     nb – IntegerInput

On entry: if $\mathbf{ind}=0$, $1$ or $2$, the size of the current block of data. The size of blocks of data in array rv can vary; therefore nb can change between calls to nag_approx_quantiles_arbitrary (g01apc).

Constraint: if $\mathbf{ind}=0$, $1$ or $2$, $\mathbf{nb}>0$.

4:     eps – doubleInput

On entry: approximation factor $\epsilon$.

Constraint: $\mathbf{eps}>0.0\text{ and }\mathbf{eps}\le 1.0$.

5:     np – Integer *Output

On exit: $m$, the number of elements processed so far.

6:     q[$\mathit{dim}$] – const doubleInput

Note: the dimension, dim, of the array q must be at least $\mathbf{nq}$ when $\mathbf{ind}=3$.

On entry: if $\mathbf{ind}=3$, the quantiles to be calculated, otherwise q is not referenced. Note that $\mathbf{q}\left[i\right]=0.0$, corresponds to the minimum value and $\mathbf{q}\left[i\right]=1.0$ to the maximum value.

Constraint: if $\mathbf{ind}=3$, $0.0\le \mathbf{q}\left[\mathit{i}-1\right]\le 1.0$, for $\mathit{i}=1,2,\dots ,\mathbf{nq}$.

7:     qv[$\mathit{dim}$] – doubleOutput

Note: the dimension, dim, of the array qv must be at least $\mathbf{nq}$ when $\mathbf{ind}=3$.

On exit: if $\mathbf{ind}=3$, $\mathbf{qv}\left[i\right]$ contains the $\epsilon$-approximate quantiles specified by the value provided in $\mathbf{q}\left[i\right]$.

8:     nq – IntegerInput

On entry: if $\mathbf{ind}=3$, the number of quantiles requested, otherwise nq is not referenced.

Constraint: if $\mathbf{ind}=3$, $\mathbf{nq}>0$.

9:     rcomm[lrcomm] – doubleCommunication Array

On entry: if $\mathbf{ind}=1$ or $2$ then the first $l$ elements of rcomm as supplied to nag_approx_quantiles_arbitrary (g01apc) must be identical to the first $l$ elements of rcomm returned from the last call to nag_approx_quantiles_arbitrary (g01apc), where $l$ is the value of lrcomm used in the last call. In other words, the contents of rcomm must not be altered between calls to this function. If rcomm needs to be reallocated then its contents must be preserved. If $\mathbf{ind}=0$ then rcomm need not be set.

On exit: rcomm holds information required by subsequent calls to nag_approx_quantiles_arbitrary (g01apc)

10:   lrcomm – IntegerInput

On entry: the dimension of the array rcomm.

Constraints:

• if $\mathbf{ind}=0$, $\mathbf{lrcomm}\ge 1$;
• otherwise $\mathbf{lrcomm}\ge \mathbf{icomm}\left[0\right]$.

11:   icomm[licomm] – IntegerCommunication Array

On entry: if $\mathbf{ind}=1$ or $2$ then the first $l$ elements of icomm as supplied to nag_approx_quantiles_arbitrary (g01apc) must be identical to the first $l$ elements of icomm returned from the last call to nag_approx_quantiles_arbitrary (g01apc), where $l$ is the value of licomm used in the last call. In other words, the contents of icomm must not be altered between calls to this function. If icomm needs to be reallocated then its contents must be preserved. If $\mathbf{ind}=0$ then icomm need not be set.

On exit: $\mathbf{icomm}\left[0\right]$ holds the minimum required length for rcomm and $\mathbf{icomm}\left[1\right]$ holds the minimum required length for icomm. The remaining elements of icomm are used for communication between subsequent calls to nag_approx_quantiles_arbitrary (g01apc).

12:   licomm – IntegerInput

On entry: the dimension of the array icomm.

Constraints:

• if $\mathbf{ind}=0$, $\mathbf{licomm}\ge 10$;
• otherwise $\mathbf{licomm}\ge \mathbf{icomm}\left[1\right]$.

13:   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_ARRAY_SIZE

On entry, $\mathbf{licomm}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{licomm}\ge 10$.

On entry, $\mathbf{lrcomm}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lrcomm}\ge 1$.

NE_BAD_PARAM

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

NE_ILLEGAL_COMM

The contents of icomm have been altered between calls to this function.

The contents of rcomm have been altered between calls to this function.

NE_INT

On entry, $\mathbf{ind}=0$, $1$ or $2$ and $\mathbf{nb}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{ind}=0$, $1$ or $2$ then $\mathbf{nb}>0$.

On entry, $\mathbf{ind}=3$ and $\mathbf{nq}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{ind}=3$ then $\mathbf{nq}>0$.

On entry, $\mathbf{ind}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ind}=0$, $1$, $2$ or $3$.

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_Q_OUT_OF_RANGE

On entry, $\mathbf{ind}=3$ and $\mathbf{q}\left[⟨\mathit{\text{value}}⟩\right]=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{ind}=3$ then $0.0\le \mathbf{q}\left[i\right]\le 1.0$ for all $i$.

NE_REAL

On entry, $\mathbf{eps}=⟨\mathit{\text{value}}⟩$.
Constraint: $0.0<\mathbf{eps}\le 1.0$.

NE_TOO_SMALL

Number of data elements streamed, $⟨\mathit{\text{value}}⟩$ is not sufficient for a quantile query when $\mathbf{eps}=⟨\mathit{\text{value}}⟩$.
Supply more data or reprocess the data with a higher eps value.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g01apce.c)

10.2  Program Data

Program Data (g01apce.d)

10.3  Program Results

Program Results (g01apce.r)