daxpy

Multiply x by a constant alpha and add the result to y.

Usage

var daxpy = require( '@stdlib/math/base/blas/daxpy' );

daxpy( N, alpha, x, strideX, y, strideY )

Multiplies x by a constant alpha and adds the result to y.

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = 5.0;

daxpy( x.length, alpha, x, 1, y, 1 );
// y => <Float64Array>[ 6.0, 11.0, 16.0, 21.0, 26.0 ]

The function accepts the following parameters:

• N: number of indexed elements.
• alpha: numeric constant.
• x: input Float64Array.
• strideX: index increment for x.
• y: input Float64Array.
• strideY: index increment for y.

The N and stride parameters determine which elements in x and y are accessed at runtime. For example, to multiply every other value in x by alpha and add the result to the first N elements of y in reverse order,

var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

var alpha = 5.0;
var N = floor( x.length / 2 );

daxpy( N, alpha, x, 2, y, -1 );
// y => <Float64Array>[ 26.0, 16.0, 6.0, 1.0, 1.0, 1.0 ]

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

var floor = require( '@stdlib/math/base/special/floor' );

// Initial arrays...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

var N = floor( x0.length / 2 );

daxpy( N, 5.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]

daxpy.ndarray( N, alpha, x, strideX, offsetX, y, strideY, offsetY )

Multiplies x by a constant alpha and adds the result to y, with alternative indexing semantics.

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = 5.0;

daxpy.ndarray( x.length, alpha, x, 1, 0, y, 1, 0 );
// y => <Float64Array>[ 6.0, 11.0, 16.0, 21.0, 26.0 ]

The function accepts the following additional parameters:

• offsetX: starting index for x.
• offsetY: starting index for y.

While typed array views mandate a view offset based on the underlying buffer, the offsetX and offsetY parameters support indexing semantics based on starting indices. For example, to multiply every other value in x by a constant alpha starting from the second value and add to the last N elements in y where x[i] -> y[n], x[i+2] -> y[n-1],...,

var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

var alpha = 5.0;
var N = floor( x.length / 2 );

daxpy.ndarray( N, alpha, x, 2, 1, y, -1, y.length-1 );
// y => <Float64Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]

daxpy.wasm( [options] )

Returns a memory managed function to multiply x by a constant alpha and add the result to y.

var wasm = daxpy.wasm();

// Number of data elements:
var N = 5;

// Allocate space on the heap:
var xbytes = wasm.malloc( N * 8 ); // 8 bytes per double
var ybytes = wasm.malloc( N * 8 );

// Create Float64Array views:
var x = new Float64Array( xbytes.buffer, xbytes.byteOffset, N );
var y = new Float64Array( ybytes.buffer, ybytes.byteOffset, N );

// Copy data to the heap:
x.set( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
y.set( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );

// Multiply and add:
var alpha = 5.0;
daxpy( N, alpha, xbytes, 1, ybytes, 1 );
// y => <Float64Array>[ 6.0, 11.0, 16.0, 21.0, 26.0 ]

// Extract the results from the heap:
var r = new Float64Array( y.length );
var i;
for ( i = 0; i < y.length; i++ ) {
    r[ i ] = y[ i ];
}

// Free the memory:
wasm.free( xbytes );
wasm.free( ybytes );

For externally defined typed arrays, data must be copied to the heap.

var wasm = daxpy.wasm();

// Externally defined data arrays:
var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );

// Allocate space on the heap:
var xbytes = wasm.malloc( x.length * x.BYTES_PER_ELEMENT );
var ybytes = wasm.malloc( y.length * y.BYTES_PER_ELEMENT );

// Copy data to the heap:
xbytes.set( new Uint8Array( x.buffer ) );
ybytes.set( new Uint8Array( y.buffer ) );

// Multiply and add:
var alpha = 5.0;
daxpy( N, alpha, xbytes, 1, ybytes, 1 );

// Extract the results from the heap:
var view = new Float64Array( ybytes.buffer, ybytes.byteOffset, y.length );
var i;
for ( i = 0; i < y.length; i++ ) {
    y[ i ] = view[ i ];
}
// y => <Float64Array>[ 6.0, 11.0, 16.0, 21.0, 26.0 ]

// Free the memory:
wasm.free( xbytes );
wasm.free( ybytes );

The method accepts the following options:

• memory: total memory. If not provided a buffer, setting the memory option instructs the returned function to allocate an internal memory store of the specified size.
• stack: total stack size. Must be less than the memory option and large enough for a program's needs. Default: 1024 bytes.
• buffer: ArrayBuffer serving as the underlying memory store. If not provided, each returned function will allocate and manage its own memory. If provided a memory option, the buffer byteLength must equal the specified total memory.

To create a function using an externally defined memory buffer, set the buffer option.

var buffer = new ArrayBuffer( 16777216 ); // ~16MB

var wasm = daxpy.wasm({
    'buffer': buffer
});

Providing external memory can be advantageous when wanting to a) centrally manage memory allocation, b) share memory between multiple memory managed functions, and/or c) limit the total amount of allocated memory within an application or library.

wasm.malloc( nbytes )

Allocates space on the heap and returns a bytes-wise typed array view (Uint8Array).

var wasm = daxpy.wasm();

// Allocate 64 bytes:
var bytes = wasm.malloc( 64 );

bytes.getValue( ptr[, type] )

Returns a value at a specific memory address (represented by a byte index). By default, the function returns a double. Possible types include: 'i8', 'i16', 'i32', 'i64', 'float', and 'double'.

var wasm = daxpy.wasm();

var N = 3;

var bytes = wasm.malloc( N * 8 );
var view = new Float64Array( bytes.buffer, bytes.byteOffset, N );

view.set( [ 1.0, -2.0, 3.0 ] );

var ptr = 1 * 8; // 8 bytes per double
var y = bytes.getValue( ptr );
// returns -2.0

wasm.free( bytes );

While this method may be convenient when interacting with the bytes view directly, using a typed array view is likely to be more performant.

var wasm = daxpy.wasm();

var N = 3;

var bytes = wasm.malloc( N * 8 );
var view = new Float64Array( bytes.buffer, bytes.byteOffset, N );

view.set( [ 1.0, -2.0, 3.0 ] );

var y = view[ 1 ];
// returns -2.0

wasm.free( bytes );

bytes.setValue( ptr, value[, type] )

Sets a value at a specific memory address (represented by a byte index). By default, the function sets a double. Possible types include: 'i8', 'i16', 'i32', 'i64', 'float', and 'double'.

var wasm = daxpy.wasm();

var N = 3;

var bytes = wasm.malloc( N * 8 );
var view = new Float64Array( bytes.buffer, bytes.byteOffset, N );

view.set( [ 1.0, -2.0, 3.0 ] );

var ptr = 1 * 8; // 8 bytes per double
var y = bytes.getValue( ptr );
// returns -2.0

bytes.setValue( ptr, -10.0 );

y = bytes.getValue( ptr );
// returns -10.0

wasm.free( bytes );

While this method may be convenient when interacting with the bytes view directly, using a typed array view is likely to be more performant.

var wasm = daxpy.wasm();

var N = 3;

var bytes = wasm.malloc( N * 8 );
var view = new Float64Array( bytes.buffer, bytes.byteOffset, N );

view.set( [ 1.0, -2.0, 3.0 ] );

var y = view[ 1 ];
// returns -2.0

view[ 1 ] = -10.0;

y = view[ 1 ];
// returns -10.0

wasm.free( bytes );

wasm.free( heap )

Frees allocated space.

var wasm = daxpy.wasm();

var bytes = wasm.malloc( 64 );

// ...

// Free the space and allow reallocation:
wasm.free( bytes );

Notes

• If N <= 0 or alpha == 0, both functions return y unchanged.
• daxpy() corresponds to the BLAS level 1 function daxpy.

Examples

var randu = require( '@stdlib/math/base/random/randu' );
var round = require( '@stdlib/math/base/special/round' );
var daxpy = require( '@stdlib/math/base/blas/daxpy' ).ndarray;

var x;
var y;
var i;

x = new Float64Array( 10 );
y = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( randu() * 100.0 );
    y[ i ] = round( randu() * 10.0 );
}
console.log( x );
console.log( y );

daxpy( x.length, 5.0, x, 1, 0, y, -1, y.length-1 );
console.log( y );