nag_sort_realvec_search (m01na) is based on Professor Niklaus Wirth's implementation of the Binary Search algorithm (see Wirth (2004)), but with two modifications. First, if the sought-after item is less than the value of the first element of the array to be searched,

0

is returned. Second, if a value equal to the sought-after item is not found, the index of the immediate lower value is returned.

References

Wirth N (2004) Algorithms and Data Structures 35–36 Prentice Hall

Parameters

Compulsory Input Parameters

1: $valid$ – logical scalar: If valid is set to true argument checking will be performed. If valid is set to false nag_sort_realvec_search (m01na) will be called without argument checking (which includes checking that array rv is sorted in ascending order) and the function will return with $ifail = 0$ . See Further Comments for further details.
2: $rv (m2)$ – double array: Elements m1 to m2 contain double values to be searched.

Constraint: elements m1 to m2 of rv must be sorted in ascending order.
3: $item$ – double scalar: The sought-after item.

Optional Input Parameters

1: $m1$ – int64int32nag_int scalar: Default: $1$
The index of the first element of rv to be searched.

Constraint: $m1 \geq 1$ .
2: $m2$ – int64int32nag_int scalar: Default: the dimension of the array rv.
The index of the last element of rv to be searched.

Constraint: $m2 \geq m1$ .

Output Parameters

1: $result$ – int64int32nag_int scalar: The result of the function.
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

(Note: these errors will only be returned if

valid = true

$ifail = 2$: On entry, rv must be sorted in ascending order.

$ifail = 3$: Constraint: $m1 \geq 1$ .

$ifail = 4$: Constraint: $m1 \leq m2$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

The argument valid should be used with caution. Set it to false only if you are confident that the other arguments are correct, in particular that array rv is in fact arranged in ascending order. If you wish to search the same array rv many times, you are recommended to set valid to true on first call of nag_sort_realvec_search (m01na) and to false on subsequent calls, in order to minimize the amount of time spent checking rv, which may be significant if rv is large.

The time taken by nag_sort_realvec_search (m01na) is

O (\log (n))

, where

n = m2 - m1 + 1

, when

valid = false

Example

This example reads a list of double precision numbers and sought-after items and performs the search for these items.

Open in the MATLAB editor: m01na_example

function m01na_example


fprintf('m01na example results\n\n');

rv = [0.5  0.6  1.1  1.2  1.3  1.3  2.1  2.3 ...
      2.3  4.1  5.8  5.9  6.5  6.5  8.6  9.9];
item  = [     2.1  0.4  7.1 10];

m1 = int64([ 1    1    1    5]);
m2 = int64([10   16   16   16]);

validate = true;
for j = 1:4
  [result, ifail] = m01na( ...
                           validate, rv, item(j), 'm1', m1(j), 'm2', m2(j));
  validate = false;

  fprintf('Search for %7.1f in index range [%2d:%2d]: index = %2d\n', ...
          item(j), m1(j), m2(j), result);
end

m01na example results

Search for     2.1 in index range [ 1:10]: index =  7
Search for     0.4 in index range [ 1:16]: index =  0
Search for     7.1 in index range [ 1:16]: index = 14
Search for    10.0 in index range [ 5:16]: index = 16

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox