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# ind2sub

> Convert a linear index to an array of subscripts.

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<section class="intro">

</section>

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<!-- Package usage documentation. -->

<section class="usage">

## Usage

```javascript
var ind2sub = require( '@stdlib/ndarray/base/ind2sub' );
```

#### ind2sub( shape, strides, offset, order, idx, mode )

Converts a linear index to an array of subscripts.

```javascript
var shape = [ 2, 2 ];
var order = 'row-major';
var strides = [ 2, 1 ];
var offset = 0;

var subscripts = ind2sub( shape, strides, offset, order, 1, 'throw' );
// returns [ 0, 1 ]
```

The function supports the following modes:

-   **throw**: specifies that the function should throw an error when a linear index exceeds array dimensions.
-   **normalize**: specifies that the function should normalize negative indices and throw an error when a linear index exceeds array dimensions.
-   **wrap**: specifies that the function should wrap around a linear index exceeding array dimensions using modulo arithmetic.
-   **clamp**: specifies that the function should set a linear index exceeding array dimensions to either `0` (minimum linear index) or the maximum linear index.

```javascript
var shape = [ 2, 2 ];
var order = 'row-major';
var strides = [ 2, 1 ];
var offset = 0;

var idx = ind2sub( shape, strides, offset, order, -2, 'wrap' );
// returns [ 1, 0 ]

idx = ind2sub( shape, strides, offset, order, 10, 'clamp' );
// returns [ 1, 1 ]
```

The `order` parameter specifies whether an array is `row-major` (C-style) or `column-major` (Fortran-style).

```javascript
var shape = [ 2, 2 ];
var order = 'column-major';
var strides = [ 1, 2 ];
var offset = 0;

var idx = ind2sub( shape, strides, offset, order, 2, 'throw' );
// returns [ 0, 1 ]
```

#### ind2sub.assign( shape, strides, offset, order, idx, mode, out )

Converts a linear index to an array of subscripts and assigns results to a provided output array.

```javascript
var shape = [ 2, 2 ];
var order = 'row-major';
var strides = [ 2, 1 ];
var offset = 0;

var out = [ 0, 0 ];
var subscripts = ind2sub.assign( shape, strides, offset, order, 1, 'throw', out );
// returns [ 0, 1 ]

var bool = ( subscripts === out );
// returns true
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

## Notes

-   When provided a stride array containing negative strides, if an `offset` is greater than `0`, the function interprets the linear index as an index into the underlying data buffer for the array, thus returning subscripts from the perspective of that buffer. If an `offset` is equal to `0`, the function treats the linear index as an index into an array view, thus returning subscripts from the perspective of that view.

    ```text
    Dims: 2x2
    Buffer: [ 1, 2, 3, 4 ]

    View = [ a00, a01,
             a10, a11 ]

    Strides: 2,1
    Offset: 0

    View = [ 1, 2,
             3, 4 ]

    Strides: 2,-1
    Offset: 1

    View = [ 2, 1,
             4, 3 ]

    Strides: -2,1
    Offset: 2

    View = [ 3, 4,
             1, 2 ]

    Strides: -2,-1
    Offset: 3

    View = [ 4, 3,
             2, 1 ]
    ```

    ```javascript
    var shape = [ 2, 2 ];
    var order = 'row-major';
    var strides = [ -2, 1 ];
    var offset = 2;
    var mode = 'throw';

    // From the perspective of a view...
    var s = ind2sub( shape, strides, 0, order, 0, mode );
    // returns [ 0, 0 ]

    s = ind2sub( shape, strides, 0, order, 1, mode );
    // returns [ 0, 1 ]

    s = ind2sub( shape, strides, 0, order, 2, mode );
    // returns [ 1, 0 ]

    s = ind2sub( shape, strides, 0, order, 3, mode );
    // returns [ 1, 1 ]

    // From the perspective of an underlying buffer...
    s = ind2sub( shape, strides, offset, order, 0, mode );
    // returns [ 1, 0 ]

    s = ind2sub( shape, strides, offset, order, 1, mode );
    // returns [ 1, 1 ]

    s = ind2sub( shape, strides, offset, order, 2, mode );
    // returns [ 0, 0 ]

    s = ind2sub( shape, strides, offset, order, 3, mode );
    // returns [ 0, 1 ]
    ```

    In short, from the perspective of a view, view data is always ordered.

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
var strides2offset = require( '@stdlib/ndarray/base/strides2offset' );
var numel = require( '@stdlib/ndarray/base/numel' );
var randu = require( '@stdlib/random/base/randu' );
var abs = require( '@stdlib/math/base/special/abs' );
var ind2sub = require( '@stdlib/ndarray/base/ind2sub' );

// Specify array characteristics:
var shape = [ 3, 3, 3 ];
var order = 'row-major';

// Compute array meta data:
var ndims = shape.length;
var strides = shape2strides( shape, order );
var len = numel( shape );

// Determine stride indices to be used for formatting how views are displayed...
var s0;
var s1;
if ( order === 'column-major' ) {
    s0 = ndims - 1;
    s1 = s0 - 1;
} else { // row-major
    s0 = 0;
    s1 = s0 + 1;
}

// Initialize a linear array...
var arr = [];
var i;
for ( i = 0; i < len; i++ ) {
    arr.push( 0 );
}

// Generate random views and display the mapping of elements in the linear array to view subscripts...
var offset;
var row;
var j;
var s;
for ( i = 0; i < 20; i++ ) {
    // Randomly flip the sign of one of the strides...
    j = discreteUniform( 0, ndims-1 );
    strides[ j ] *= ( randu() < 0.5 ) ? -1 : 1;
    offset = strides2offset( shape, strides );

    // Print view meta data...
    console.log( '' );
    console.log( 'Dimensions: %s.', shape.join( 'x' ) );
    console.log( 'Strides: %s.', strides.join( ',' ) );
    console.log( 'View (subscripts):' );

    // Print the mapping of elements in the linear array to view subscripts...
    row = '  ';
    for ( j = 0; j < len; j++ ) {
        s = ind2sub( shape, strides, offset, order, j, 'throw' );
        row += '(' + s.join( ',' ) + ')';
        if ( ndims === 1 && j === len-1 ) {
            console.log( row );
        } else if ( ndims === 2 && (j+1)%abs( strides[ s0 ] ) === 0 ) {
            console.log( row );
            row = '  ';
        } else if ( ndims > 2 && (j+1)%abs( strides[ s1 ] ) === 0 ) {
            console.log( row );
            if ( (j+1)%abs( strides[ s0 ] ) === 0 ) {
                console.log( '' );
            }
            row = '  ';
        } else {
            row += ', ';
        }
    }
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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</section>

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<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/ndarray/base/ind2sub.h"
```

<!-- lint disable maximum-heading-length -->

#### stdlib_ndarray_ind2sub( ndims, \*shape, \*strides, offset, order, idx, mode, \*out )

Computes the minimum and maximum linear indices in an underlying data buffer accessible to an array view.

```c
#include "stdlib/ndarray/index_modes.h"
#include "stdlib/ndarray/orders.h"
#include <stdint.h>

int64_t ndims = 2;
int64_t shape[] = { 3, 3 };
int64_t strides[] = { -3, 1 };
int64_t offset = 6;

int64_t out[ 2 ];

int8_t status = stdlib_ndarray_ind2sub( ndims, shape, strides, offset, STDLIB_NDARRAY_ROW_MAJOR, 7, STDLIB_NDARRAY_INDEX_ERROR, out );
if ( status == -1 ) {
    // Handle error...
}
```

The function accepts the following arguments:

-   **ndims**: `[in] int64_t` number of dimensions.
-   **shape**: `[in] int64_t*` array shape (dimensions).
-   **strides**: `[in] int64_t*` array strides.
-   **offset**: `[in] int64_t` index offset.
-   **order**: `[in] enum STDLIB_NDARRAY_ORDER` specifies whether an array is row-major (C-style) or column-major (Fortran-style).
-   **idx**: `[in] int64_t` linear index in an array view.
-   **mode**: `[in] enum STDLIB_NDARRAY_INDEX_MODE` specifies how to handle a linear index which exceeds array dimensions.
-   **out**: `[out] int64_t*` output array.

```c
int8_t stdlib_ndarray_ind2sub( const int64_t ndims, const int64_t *shape, const int64_t *strides, const int64_t offset, const enum STDLIB_NDARRAY_ORDER order, const int64_t idx, const enum STDLIB_NDARRAY_INDEX_MODE mode, int64_t *out );
```

</section>

<!-- /.usage -->

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</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/ndarray/base/ind2sub.h"
#include "stdlib/ndarray/index_modes.h"
#include "stdlib/ndarray/orders.h"
#include <stdint.h>
#include <stdio.h>
#include <inttypes.h>

int main( void ) {
    int64_t ndims = 2;
    int64_t shape[] = { 3, 3 };
    int64_t strides[] = { -3, 1 };
    int64_t offset = 6;

    int64_t out[ 2 ];

    stdlib_ndarray_ind2sub( ndims, shape, strides, offset, STDLIB_NDARRAY_ROW_MAJOR, 7, STDLIB_NDARRAY_INDEX_ERROR, out );

    int i;
    printf( "subscripts = { " );
    for ( i = 0; i < ndims; i++ ) {
        printf( "%"PRId64"", out[ i ] );
        if ( i < ndims-1 ) {
            printf( ", " );
        }
    }
    printf( " }\n" );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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</section>

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</section>

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