snrm2

Calculate the L2-norm of a single-precision floating-point vector.

The L2-norm is defined as

Installation

npm install @stdlib/blas-base-snrm2

Usage

var snrm2 = require( '@stdlib/blas-base-snrm2' );

snrm2( N, x, stride )

Computes the L2-norm of a single-precision floating-point vector x.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var z = snrm2( x.length, x, 1 );
// returns 3.0

The function has the following parameters:

• N: number of indexed elements.
• x: input Float32Array.
• stride: index increment for x.

The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the L2-norm of every other element in x,

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var z = snrm2( 4, x, 2 );
// returns 5.0

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float32Array = require( '@stdlib/array-float32' );

var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var z = snrm2( 4, x1, 2 );
// returns 5.0

If N is less than or equal to 0, the function returns 0.

snrm2.ndarray( N, x, stride, offset )

Computes the L2-norm of a single-precision floating-point vector using alternative indexing semantics.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var z = snrm2.ndarray( x.length, x, 1, 0 );
// returns 3.0

The function has the following additional parameters:

• offset: starting index for x.

While 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 L2-norm for every other value in x starting from the second value

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var z = snrm2.ndarray( 4, x, 2, 1 );
// returns 5.0

Notes

• If N <= 0, both functions return 0.0.
• snrm2() corresponds to the BLAS level 1 function snrm2.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var snrm2 = require( '@stdlib/blas-base-snrm2' );

var opts = {
    'dtype': 'float32'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );

var out = snrm2( x.length, x, 1 );
console.log( out );

C APIs

Usage

#include "stdlib/blas/base/snrm2.h"

c_snrm2( N, *X, stride )

Computes the L2-norm of a single-precision floating-point vector.

const float x[] = { 1.0f, 2.0f, 2.0f, -7.0f, -2.0f, 3.0f, 4.0f, 2.0f };

float norm = c_snrm2( 4, x, 2 );
// returns 5.0f

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] float* input array.
• stride: [in] CBLAS_INT index increment for X.

float c_snrm2( const CBLAS_INT N, const float *X, const CBLAS_INT stride );

c_snrm2_ndarray( N, *X, stride, offset )

Computes the L2-norm of a single-precision floating-point vector using alternative indexing semantics.

const float x[] = { 1.0f, 2.0f, 2.0f, -7.0f, -2.0f, 3.0f, 4.0f, 2.0f };

float norm = c_snrm2_ndarray( 4, x, 2, 0 );
// returns 5.0f

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] float* input array.
• stride: [in] CBLAS_INT index increment for X.
• offset: [in] CBLAS_INT starting index for X.

float c_snrm2_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT stride, const CBLAS_INT offset );

Examples

#include "stdlib/blas/base/snrm2.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };

    // Specify the number of indexed elements:
    const int N = 8;

    // Specify a stride:
    const int strideX = 1;

    // Compute the L2-norm:
    float l2 = c_snrm2( N, x, strideX );

    // Print the result:
    printf( "L2-norm: %f\n", l2 );

    // Compute the L2-norm:
    l2 = c_snrm2_ndarray( N, x, -strideX, 7 );

    // Print the result:
    printf( "L2-norm: %f\n", l2 );
}

References

• Blue, James L. 1978. "A Portable Fortran Program to Find the Euclidean Norm of a Vector." ACM Transactions on Mathematical Software 4 (1). New York, NY, USA: Association for Computing Machinery: 15–23. doi:10.1145/355769.355771.
• Anderson, Edward. 2017. "Algorithm 978: Safe Scaling in the Level 1 BLAS." ACM Transactions on Mathematical Software 44 (1). New York, NY, USA: Association for Computing Machinery: 1–28. doi:10.1145/3061665.

See Also

• @stdlib/blas-base/dnrm2: calculate the L2-norm of a double-precision floating-point vector.
• @stdlib/blas-base/gnrm2: calculate the L2-norm of a vector.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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License

See LICENSE.

Copyright

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