feat: add stats/base/dsempn

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---

Author: gururaj1512

lib/node_modules/@stdlib/stats/base/dsempn/README.md

@@ -70,17 +70,16 @@ where `s` is the sample [standard deviation][standard-deviation].
 var dsempn = require( '@stdlib/stats/base/dsempn' );
 ```
 
-#### dsempn( N, correction, x, stride )
+#### dsempn( N, correction, x, strideX )
 
-Computes the [standard error of the mean][standard-error] of a double-precision floating-point strided array `x` using a two-pass algorithm.
+Computes the [standard error of the mean][standard-error] of a double-precision floating-point strided array using a two-pass algorithm.
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 
 var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
-var N = x.length;
 
-var v = dsempn( N, 1, x, 1 );
+var v = dsempn( x.length, 1, x, 1 );
 // returns ~1.20185
 ```
 
@@ -89,18 +88,16 @@ The function has the following parameters:
 -   **N**: number of indexed elements.
 -   **correction**: degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample [standard deviation][standard-deviation], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
 -   **x**: input [`Float64Array`][@stdlib/array/float64].
--   **stride**: index increment for `x`.
+-   **strideX**: stride length for `x`.
 
-The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [standard error of the mean][standard-error] of every other element in `x`,
+The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [standard error of the mean][standard-error] of every other element in `x`,
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
-var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
-var N = floor( x.length / 2 );
 
-var v = dsempn( N, 1, x, 2 );
+var v = dsempn( 4, 1, x, 2 );
 // returns 1.25
 ```
 
@@ -110,45 +107,39 @@ Note that indexing is relative to the first index. To introduce an offset, use [
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
-var floor = require( '@stdlib/math/base/special/floor' );
 
 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
 
-var N = floor( x0.length / 2 );
-
-var v = dsempn( N, 1, x1, 2 );
+var v = dsempn( 4, 1, x1, 2 );
 // returns 1.25
 ```
 
-#### dsempn.ndarray( N, correction, x, stride, offset )
+#### dsempn.ndarray( N, correction, x, strideX, offsetX )
 
 Computes the [standard error of the mean][standard-error] of a double-precision floating-point strided array using a two-pass algorithm and alternative indexing semantics.
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 
 var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
-var N = x.length;
 
-var v = dsempn.ndarray( N, 1, x, 1, 0 );
+var v = dsempn.ndarray( x.length, 1, x, 1, 0 );
 // returns ~1.20185
 ```
 
 The function has the following additional parameters:
 
--   **offset**: starting index for `x`.
+-   **offsetX**: starting index for `x`.
 
-While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [standard error of the mean][standard-error] for every other value in `x` starting from the second value
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to calculate the [standard error of the mean][standard-error] for every other element in `x` starting from the second element
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
-var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
-var N = floor( x.length / 2 );
 
-var v = dsempn.ndarray( N, 1, x, 2, 1 );
+var v = dsempn.ndarray( 4, 1, x, 2, 1 );
 // returns 1.25
 ```
 
@@ -196,6 +187,125 @@ console.log( v );
 
 <!-- /.examples -->
 
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/stats/base/dsempn.h"
+```
+
+#### stdlib_strided_dsempn( N, correction, \*X, strideX )
+
+Computes the [standard error of the mean][standard-error] of a double-precision floating-point strided array using a two-pass algorithm.
+
+```c
+const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
+
+double v = stdlib_strided_dsempn( 4, 1.0, x, 2 );
+// returns ~1.29099
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **correction**: `[in] double` degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample [standard deviation][standard-deviation], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
+-   **X**: `[in] double*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+
+```c
+double stdlib_strided_dsempn( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX );
+```
+
+#### stdlib_strided_dsempn_ndarray( N, correction, \*X, strideX, offsetX )
+
+Computes the [standard error of the mean][standard-error] of a double-precision floating-point strided array using a two-pass algorithm and alternative indexing semantics.
+
+```c
+const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
+
+double v = stdlib_strided_dsempn_ndarray( 4, 1.0, x, 2, 0 );
+// returns ~1.29099
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **correction**: `[in] double` degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample [standard deviation][standard-deviation], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
+-   **X**: `[in] double*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
+
+```c
+double stdlib_strided_dsempn_ndarray( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/stats/base/dsempn.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Create a strided array:
+    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
+
+    // Specify the number of elements:
+    const int N = 4;
+
+    // Specify the stride length:
+    const int strideX = 2;
+
+    // Compute the arithmetic mean:
+    double v = stdlib_strided_dsempn( N, 1.0, x, strideX );
+
+    // Print the result:
+    printf( "dsempn: %lf\n", v );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
 * * *
 
 <section class="references">

lib/node_modules/@stdlib/stats/base/dsempn/benchmark/benchmark.js

@@ -21,14 +21,20 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pow = require( '@stdlib/math/base/special/pow' );
-var Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var pkg = require( './../package.json' ).name;
 var dsempn = require( './../lib/dsempn.js' );
 
 
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
 // FUNCTIONS //
 
 /**
@@ -39,13 +45,7 @@ var dsempn = require( './../lib/dsempn.js' );
 * @returns {Function} benchmark function
 */
 function createBenchmark( len ) {
-	var x;
-	var i;
-
-	x = new Float64Array( len );
-	for ( i = 0; i < x.length; i++ ) {
-		x[ i ] = ( randu()*20.0 ) - 10.0;
-	}
+	var x = uniform( len, -10.0, 10.0, options );
 	return benchmark;
 
 	function benchmark( b ) {

lib/node_modules/@stdlib/stats/base/dsempn/benchmark/benchmark.native.js

@@ -22,10 +22,9 @@
 
 var resolve = require( 'path' ).resolve;
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pow = require( '@stdlib/math/base/special/pow' );
-var Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 var pkg = require( './../package.json' ).name;
 
@@ -36,6 +35,9 @@ var dsempn = tryRequire( resolve( __dirname, './../lib/dsempn.native.js' ) );
 var opts = {
 	'skip': ( dsempn instanceof Error )
 };
+var options = {
+	'dtype': 'float64'
+};
 
 
 // FUNCTIONS //
@@ -48,13 +50,7 @@ var opts = {
 * @returns {Function} benchmark function
 */
 function createBenchmark( len ) {
-	var x;
-	var i;
-
-	x = new Float64Array( len );
-	for ( i = 0; i < x.length; i++ ) {
-		x[ i ] = ( randu()*20.0 ) - 10.0;
-	}
+	var x = uniform( len, -10.0, 10.0, options );
 	return benchmark;
 
 	function benchmark( b ) {

lib/node_modules/@stdlib/stats/base/dsempn/benchmark/benchmark.ndarray.js

@@ -21,14 +21,20 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pow = require( '@stdlib/math/base/special/pow' );
-var Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var pkg = require( './../package.json' ).name;
 var dsempn = require( './../lib/ndarray.js' );
 
 
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
 // FUNCTIONS //
 
 /**
@@ -39,13 +45,7 @@ var dsempn = require( './../lib/ndarray.js' );
 * @returns {Function} benchmark function
 */
 function createBenchmark( len ) {
-	var x;
-	var i;
-
-	x = new Float64Array( len );
-	for ( i = 0; i < x.length; i++ ) {
-		x[ i ] = ( randu()*20.0 ) - 10.0;
-	}
+	var x = uniform( len, -10.0, 10.0, options );
 	return benchmark;
 
 	function benchmark( b ) {

lib/node_modules/@stdlib/stats/base/dsempn/benchmark/benchmark.ndarray.native.js

@@ -22,10 +22,9 @@
 
 var resolve = require( 'path' ).resolve;
 var bench = require( '@stdlib/bench' );
-var randu = require( '@stdlib/random/base/randu' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var pow = require( '@stdlib/math/base/special/pow' );
-var Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/array/uniform' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 var pkg = require( './../package.json' ).name;
 
@@ -36,6 +35,9 @@ var dsempn = tryRequire( resolve( __dirname, './../lib/ndarray.native.js' ) );
 var opts = {
 	'skip': ( dsempn instanceof Error )
 };
+var options = {
+	'dtype': 'float64'
+};
 
 
 // FUNCTIONS //
@@ -48,13 +50,7 @@ var opts = {
 * @returns {Function} benchmark function
 */
 function createBenchmark( len ) {
-	var x;
-	var i;
-
-	x = new Float64Array( len );
-	for ( i = 0; i < x.length; i++ ) {
-		x[ i ] = ( randu()*20.0 ) - 10.0;
-	}
+	var x = uniform( len, -10.0, 10.0, options );
 	return benchmark;
 
 	function benchmark( b ) {