feat(blas/base/sgemmtr): adding lib, test, docs, examples, benchmark

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# sgemmtr
+
+> Perform the matrix-matrix operation `uplo(C) = uplo(α*op(A)*op(B) + β*C)` where `op(X)` is one of the `op(X) = X`, or `op(X) = X^T`, and update only the upper or lower triangular part of `C`.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var sgemmtr = require( '@stdlib/blas/base/sgemmtr' );
+```
+
+#### sgemmtr( ord, uplo, ta, tb, M, N, K, α, A, lda, B, ldb, β, C, ldc )
+
+Performs the matrix-matrix operation `uplo(C) = uplo(α*op(A)*op(B) + β*C)` where `op(X)` is either `op(X) = X` or `op(X) = X^T`, `α` and `β` are scalars, `A`, `B`, and `C` are matrices, with `op(A)` an `M` by `K` matrix, `op(B)` a `K` by `N` matrix, and `C` an `M` by `N` matrix, and only the elements in the upper or lower triangle of `C` are updated.
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var A = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var B = new Float32Array( [ 1.0, 1.0, 0.0, 1.0 ] );
+var C = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+sgemmtr( 'row-major', 'upper', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 2, B, 2, 1.0, C, 2 );
+// C => <Float32Array>[ 2.0, 5.0, 3.0, 11.0 ]
+```
+
+The function has the following parameters:
+
+-   **ord**: storage layout.
+-   **uplo**: specifies whether to update the upper or lower triangular part of `C`.
+-   **ta**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
+-   **tb**: specifies whether `B` should be transposed, conjugate-transposed, or not transposed.
+-   **M**: number of rows in the matrix `op(A)` and in the matrix `C`.
+-   **N**: number of columns in the matrix `op(B)` and in the matrix `C`.
+-   **K**: number of columns in the matrix `op(A)` and number of rows in the matrix `op(B)`.
+-   **α**: scalar constant.
+-   **A**: first input matrix stored in linear memory as a [`Float32Array`][mdn-float32array].
+-   **lda**: stride of the first dimension of `A` (leading dimension of `A`).
+-   **B**: second input matrix stored in linear memory as a [`Float32Array`][mdn-float32array].
+-   **ldb**: stride of the first dimension of `B` (leading dimension of `B`).
+-   **β**: scalar constant.
+-   **C**: third input matrix stored in linear memory as a [`Float32Array`][mdn-float32array].
+-   **ldc**: stride of the first dimension of `C` (leading dimension of `C`).
+
+The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to perform matrix multiplication of two subarrays
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var A = new Float32Array( [ 1.0, 2.0, 0.0, 0.0, 3.0, 4.0, 0.0, 0.0 ] );
+var B = new Float32Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0 ] );
+var C = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+sgemmtr( 'row-major', 'upper', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 4, B, 4, 1.0, C, 2 );
+// C => <Float32Array>[ 2.0, 5.0, 3.0, 11.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### sgemmtr.ndarray( uplo, ta, tb, M, N, K, α, A, sa1, sa2, oa, B, sb1, sb2, ob, β, C, sc1, sc2, oc )
+
+Performs the matrix-matrix operation `uplo(C) = uplo(α*op(A)*op(B) + β*C)`, using alternative indexing semantics and where `op(X)` is either `op(X) = X` or `op(X) = X^T`, `α` and `β` are scalars, `A`, `B`, and `C` are matrices, with `op(A)` an `M` by `K` matrix, `op(B)` a `K` by `N` matrix, and `C` an `M` by `N` matrix, and only the elements in the upper or lower triangle of `C` are updated.
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var A = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var B = new Float32Array( [ 1.0, 1.0, 0.0, 1.0 ] );
+var C = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+sgemmtr.ndarray( 'upper', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 2, 1, 0, B, 2, 1, 0, 1.0, C, 2, 1, 0 );
+// C => <Float32Array>[ 2.0, 5.0, 3.0, 11.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **sa1**: stride of the first dimension of `A`.
+-   **sa2**: stride of the second dimension of `A`.
+-   **oa**: starting index for `A`.
+-   **sb1**: stride of the first dimension of `B`.
+-   **sb2**: stride of the second dimension of `B`.
+-   **ob**: starting index for `B`.
+-   **sc1**: stride of the first dimension of `C`.
+-   **sc2**: stride of the second dimension of `C`.
+-   **oc**: starting index for `C`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
+
+```javascript
+var Float32Array = require( '@stdlib/array/float32' );
+
+var A = new Float32Array( [ 0.0, 0.0, 1.0, 3.0, 2.0, 4.0 ] );
+var B = new Float32Array( [ 0.0, 1.0, 0.0, 1.0, 1.0 ] );
+var C = new Float32Array( [ 0.0, 0.0, 0.0, 1.0, 3.0, 2.0, 4.0 ] );
+
+sgemmtr.ndarray( 'upper', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 1, 2, 2, B, 1, 2, 1, 1.0, C, 1, 2, 3 );
+// C => <Float32Array>[ 0.0, 0.0, 0.0, 2.0, 3.0, 5.0, 11.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `sgemmtr()` is an extension of the standard [BLAS][blas] level 3 `gemm` routine—provided by optimized BLAS libraries, such as Intel MKL and OpenBLAS, as [`?gemmt`][mkl-gemmt]—which updates only the upper or lower triangular part of `C`, avoiding unnecessary computation and writes when `C` is known to be symmetric or triangular.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var sgemmtr = require( '@stdlib/blas/base/sgemmtr' );
+
+var opts = {
+    'dtype': 'float32'
+};
+
+var M = 3;
+var N = 4;
+var K = 2;
+
+var A = discreteUniform( M*K, 0, 10, opts ); // 3x2
+var B = discreteUniform( K*N, 0, 10, opts ); // 2x4
+var C = discreteUniform( M*N, 0, 10, opts ); // 3x4
+
+sgemmtr( 'row-major', 'upper', 'no-transpose', 'no-transpose', M, N, K, 1.0, A, K, B, N, 1.0, C, N );
+console.log( C );
+
+sgemmtr.ndarray( 'lower', 'no-transpose', 'no-transpose', M, N, K, 1.0, A, K, 1, 0, B, N, 1, 0, 1.0, C, N, 1, 0 );
+console.log( C );
+```
+
+</section>
+
+<!-- /.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/blas/base/sgemmtr.h"
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</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
+TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[blas]: http://www.netlib.org/blas
+
+[mkl-gemmt]: https://www.intel.com/content/www/us/en/docs/onemkl/developer-reference-c/2023-2/cblas-gemmt.html
+
+[mdn-float32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float32Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/base/sgemmtr/benchmark/benchmark_ca_cb_cc_nta_ntb.ndarray.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var sgemmtr = require( './../lib/ndarray.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float32'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - array dimension size
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var A = uniform( N*N, -10.0, 10.0, options );
+	var B = uniform( N*N, -10.0, 10.0, options );
+	var C = uniform( N*N, -10.0, 10.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var z;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			z = sgemmtr( 'upper', 'no-transpose', 'no-transpose', N, N, N, 1.0, A, 1, N, 0, B, 1, N, 0, 1.0, C, 1, N, 0 );
+			if ( isnanf( z[ i%z.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnanf( z[ i%z.length ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 4; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+		f = createBenchmark( len );
+		bench( format( '%s:ndarray:uplo=upper,order(A)=column-major,order(B)=column-major,order(C)=column-major,trans(A)=false,trans(B)=false,size=%d', pkg, (len*len) ), f );
+	}
+}
+
+main();