feat!: add support for specifying the index offset for AP

BREAKING CHANGE: add offset parameter to `ndarray` method

To migrate, users should set the `offsetAP` parameter. For most cases,
this parameter will be zero, but supporting this parameter allows
users to specify alternative starting indices, such as needed when
working with ndarray views.

lib/node_modules/@stdlib/blas/base/dspmv/README.md

@@ -91,7 +91,7 @@ dspmv( 'row-major', 'upper', 2, 1.0, AP, x1, -1, 1.0, y1, -1 );
 // y0 => <Float64Array>[ 6.0, 4.0 ]
 ```
 
-#### dspmv.ndarray( order, uplo, N, α, AP, x, sx, ox, β, y, sy, oy )
+#### dspmv.ndarray( order, uplo, N, α, AP, oa, x, sx, ox, β, y, sy, oy )
 
 Performs the matrix-vector operation `y = α*A*x + β*y` using alternative indexing semantics and where `α` and `β` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix supplied in packed form `AP`.
 
@@ -102,12 +102,13 @@ var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
 var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
 var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );
 
-dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 );
+dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 );
 // y => <Float64Array>[ 7.0, 12.0, 15.0 ]
 ```
 
 The function has the following additional parameters:
 
+- **oa**: starting index for `AP`.
 - **ox**: starting index for `x`.
 - **oy**: starting index for `y`.
 
@@ -116,11 +117,11 @@ While [`typed array`][mdn-typed-array] views mandate a view offset based on the
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 
-var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var AP = new Float64Array( [ 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
 var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
 var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );
 
-dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, x, 1, 0, 1.0, y, -1, 2 );
+dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, 2, x, 1, 0, 1.0, y, -1, 2 );
 // y => <Float64Array>[ 15.0, 12.0, 7.0 ]
 ```
 
@@ -158,7 +159,7 @@ var AP = discreteUniform( N * ( N + 1 ) / 2, -10, 10, opts );
 var x = discreteUniform( N, -10, 10, opts );
 var y = discreteUniform( N, -10, 10, opts );
 
-dspmv.ndarray( 'row-major', 'upper', N, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 );
+dspmv.ndarray( 'row-major', 'upper', N, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 );
 console.log( y );
 ```
 

lib/node_modules/@stdlib/blas/base/dspmv/benchmark/benchmark.ndarray.js

@@ -63,7 +63,7 @@ function createBenchmark( len ) {
 
  b.tic();
  for ( i = 0; i < b.iterations; i++ ) {
- z = dspmv( 'row-major', 'upper', len, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 );
+ z = dspmv( 'row-major', 'upper', len, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 );
  if ( isnan( z[ i%z.length ] ) ) {
  b.fail( 'should not return NaN' );
  }

lib/node_modules/@stdlib/blas/base/dspmv/docs/repl.txt

@@ -77,7 +77,7 @@
  <Float64Array>[ ~6.0, ~4.0 ]
 
 
-{{alias}}.ndarray( ord, uplo, N, α, AP, x, sx, ox, β, y, sy, oy )
+{{alias}}.ndarray( ord, uplo, N, α, AP, oa, x, sx, ox, β, y, sy, oy )
  Performs the matrix-vector operation `y = α*A*x + β*y` using alternative
  indexing semantics and where `α` and `β` are scalars, `x` and `y` are `N`
  element vectors, and `A` is an `N` by `N` symmetric matrix supplied in
@@ -106,6 +106,9 @@
  AP: Float64Array
  Matrix in packed form.
 
+ oa: integer
+ Starting index for `AP`.
+
  x: Float64Array
  Input vector `x`.
 
@@ -140,14 +143,14 @@
  > var AP = new {{alias:@stdlib/array/float64}}( [ 1.0, 2.0, 3.0, 4.0 ] );
  > var ord = 'row-major';
  > var uplo = 'upper';
- > {{alias}}.ndarray( ord, uplo, 2, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 )
+ > {{alias}}.ndarray( ord, uplo, 2, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 )
  <Float64Array>[ ~4.0, ~6.0 ]
 
  // Advanced indexing:
  > x = new {{alias:@stdlib/array/float64}}( [ 1.0, 1.0 ] );
  > y = new {{alias:@stdlib/array/float64}}( [ 1.0, 1.0 ] );
  > AP = new {{alias:@stdlib/array/float64}}( [ 1.0, 2.0, 3.0, 4.0 ] );
- > {{alias}}.ndarray( ord, uplo, 2, 1.0, AP, x, -1, 1, 1.0, y, -1, 1 )
+ > {{alias}}.ndarray( ord, uplo, 2, 1.0, AP, 0, x, -1, 1, 1.0, y, -1, 1 )
  <Float64Array>[ ~6.0, ~4.0 ]
 
  See Also

lib/node_modules/@stdlib/blas/base/dspmv/docs/types/index.d.ts

@@ -61,6 +61,7 @@ interface Routine {
  * @param N - number of columns in the matrix `A`
  * @param alpha - scalar constant
  * @param AP - packed form of a symmetric matrix `A`
+ * @param offsetAP - starting `AP` index
  * @param x - first input array
  * @param strideX - `x` stride length
  * @param offsetX - starting `x` index
@@ -77,10 +78,10 @@ interface Routine {
  * var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
  * var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );
  *
- * dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 );
+ * dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 );
  * // y => <Float64Array>[ 7.0, 12.0, 15.0 ]
  */
- ndarray( order: Layout, uplo: MatrixTriangle, N: number, alpha: number, AP: Float64Array, x: Float64Array, strideX: number, offsetX: number, beta: number, y: Float64Array, strideY: number, offsetY: number ): Float64Array;
+ ndarray( order: Layout, uplo: MatrixTriangle, N: number, alpha: number, AP: Float64Array, offsetAP: number, x: Float64Array, strideX: number, offsetX: number, beta: number, y: Float64Array, strideY: number, offsetY: number ): Float64Array;
 }
 
 /**
@@ -115,7 +116,7 @@ interface Routine {
 * var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
 * var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );
 *
-* dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, x, 1, 0, 1.0, y, -1, 2 );
+* dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, 0, x, 1, 0, 1.0, y, -1, 2 );
 * // y => <Float64Array>[ 15.0, 12.0, 7.0 ]
 */
 declare var dspmv: Routine;