feat: add C and fortran implmentation of blas/base/dgemm

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

@@ -2,7 +2,7 @@
 
 @license Apache-2.0
 
-Copyright (c) 2024 The Stdlib Authors.
+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.
@@ -22,6 +22,12 @@ limitations under the License.
 
 > Perform the matrix-matrix operation `C = α*op(A)*op(B) + β*C` where `op(X)` is one of the `op(X) = X`, or `op(X) = X^T`.
 
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -62,7 +68,7 @@ The function has the following parameters:
 -   **C**: third input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
 -   **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
+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 Float64Array = require( '@stdlib/array/float64' );
@@ -75,6 +81,27 @@ dgemm( 'row-major', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 4, B, 4, 1.
 // C => <Float64Array>[ 2.0, 5.0, 6.0, 11.0 ]
 ```
 
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays (with extra leading element to be skipped):
+var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+var B0 = new Float64Array( [ 0.0, 1.0, 1.0, 0.0, 1.0 ] );
+var C0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+
+// Create offset views...
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var B1 = new Float64Array( B0.buffer, B0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var C1 = new Float64Array( C0.buffer, C0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dgemm( 'row-major', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A1, 2, B1, 2, 1.0, C1, 2 );
+// C0 => <Float64Array>[ 0.0, 2.0, 5.0, 6.0, 11.0 ]
+```
+
 <!-- lint disable maximum-heading-length -->
 
 #### dgemm.ndarray( ta, tb, M, N, K, α, A, sa1, sa2, oa, B, sb1, sb2, ob, β, C, sc1, sc2, oc )
@@ -190,18 +217,99 @@ console.log( C );
 #include "stdlib/blas/base/dgemm.h"
 ```
 
-#### TODO
+#### c_dgemm( layout, transA, transB, M, N, K, alpha, \*A, LDA, \*B, LDB, beta, \*C, LDC )
 
-TODO.
+Performs the matrix-matrix operation `C = alpha*op(A)*op(B) + beta*C`, where `op(X)` is either `op(X) = X` or `op(X) = X^T`, `alpha` and `beta` are scalars, and `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.
 
 ```c
-TODO
+#include "stdlib/blas/base/shared.h"
+
+double A[ 2*3 ] = {
+    1.0, 2.0, 3.0,
+    4.0, 5.0, 6.0
+};
+double B[ 3*2 ] = {
+    7.0,  8.0,
+    9.0,  10.0,
+    11.0, 12.0
+};
+double C[ 2*2 ] = {
+    0.0, 0.0,
+    0.0, 0.0
+};
+
+c_dgemm( CblasRowMajor, CblasNoTrans, CblasNoTrans, 2, 2, 3, 1.0, A, 3, B, 2, 0.0, C, 2 );
 ```
 
-TODO
+The function accepts the following arguments:
+
+-   **layout**: `[in] CBLAS_LAYOUT` storage layout.
+-   **transA**: `[in] CBLAS_TRANSPOSE` specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
+-   **transB**: `[in] CBLAS_TRANSPOSE` specifies whether `B` should be transposed, conjugate-transposed, or not transposed.
+-   **M**: `[in] CBLAS_INT` number of rows in the matrix `op(A)` and in the matrix `C`.
+-   **N**: `[in] CBLAS_INT` number of columns in the matrix `op(B)` and in the matrix `C`.
+-   **K**: `[in] CBLAS_INT` number of columns in the matrix `op(A)` and number of rows in the matrix `op(B)`.
+-   **alpha**: `[in] double` scalar constant.
+-   **A**: `[in] double*` first input matrix.
+-   **LDA**: `[in] CBLAS_INT` stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **B**: `[in] double*` second input matrix.
+-   **LDB**: `[in] CBLAS_INT` stride of the first dimension of `B` (a.k.a., leading dimension of the matrix `B`).
+-   **beta**: `[in] double` scalar constant.
+-   **C**: `[inout] double*` result matrix.
+-   **LDC**: `[in] CBLAS_INT` stride of the first dimension of `C` (a.k.a., leading dimension of the matrix `C`).
 
 ```c
-TODO
+void c_dgemm( const CBLAS_LAYOUT layout, const CBLAS_TRANSPOSE transA, const CBLAS_TRANSPOSE transB, const CBLAS_INT M, const CBLAS_INT N, const CBLAS_INT K, const double alpha, const double *A, const CBLAS_INT LDA, const double *B, const CBLAS_INT LDB, const double beta, double *C, const CBLAS_INT LDC );
+```
+
+#### c_dgemm_ndarray( transA, transB, M, N, K, alpha, \*A, sa1, sa2, oa, \*B, sb1, sb2, ob, beta, \*C, sc1, sc2, oc )
+
+Performs the matrix-matrix operation `C = alpha*op(A)*op(B) + beta*C`, using alternative indexing semantics and where `op(X)` is either `op(X) = X` or `op(X) = X^T`, `alpha` and `beta` are scalars, and `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.
+
+```c
+#include "stdlib/blas/base/shared.h"
+
+double A[ 2*3 ] = {
+    1.0, 2.0, 3.0,
+    4.0, 5.0, 6.0
+};
+double B[ 3*2 ] = {
+    7.0,  8.0,
+    9.0,  10.0,
+    11.0, 12.0
+};
+double C[ 2*2 ] = {
+    0.0, 0.0,
+    0.0, 0.0
+};
+
+c_dgemm_ndarray( CblasNoTrans, CblasNoTrans, 2, 2, 3, 1.0, A, 3, 1, 0, B, 2, 1, 0, 0.0, C, 2, 1, 0 );
+```
+
+The function accepts the following arguments:
+
+-   **transA**: `[in] CBLAS_TRANSPOSE` specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
+-   **transB**: `[in] CBLAS_TRANSPOSE` specifies whether `B` should be transposed, conjugate-transposed, or not transposed.
+-   **M**: `[in] CBLAS_INT` number of rows in the matrix `op(A)` and in the matrix `C`.
+-   **N**: `[in] CBLAS_INT` number of columns in the matrix `op(B)` and in the matrix `C`.
+-   **K**: `[in] CBLAS_INT` number of columns in the matrix `op(A)` and number of rows in the matrix `op(B)`.
+-   **alpha**: `[in] double` scalar constant.
+-   **A**: `[in] double*` first input matrix.
+-   **sa1**: `[in] CBLAS_INT` stride of the first dimension of `A`.
+-   **sa2**: `[in] CBLAS_INT` stride of the second dimension of `A`.
+-   **oa**: `[in] CBLAS_INT` starting index for `A`.
+-   **B**: `[in] double*` second input matrix.
+-   **sb1**: `[in] CBLAS_INT` stride of the first dimension of `B`.
+-   **sb2**: `[in] CBLAS_INT` stride of the second dimension of `B`.
+-   **ob**: `[in] CBLAS_INT` starting index for `B`.
+-   **beta**: `[in] double` scalar constant.
+-   **C**: `[inout] double*` result matrix.
+-   **sc1**: `[in] CBLAS_INT` stride of the first dimension of `C`.
+-   **sc2**: `[in] CBLAS_INT` stride of the second dimension of `C`.
+-   **oc**: `[in] CBLAS_INT` starting index for `C`.
+
+```c
+void c_dgemm_ndarray( const CBLAS_TRANSPOSE transA, const CBLAS_TRANSPOSE transB, const CBLAS_INT M, const CBLAS_INT N, const CBLAS_INT K, const double alpha, const double *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA, const double *B, const CBLAS_INT strideB1, const CBLAS_INT strideB2, const CBLAS_INT offsetB, const double beta, double *C, const CBLAS_INT strideC1, const CBLAS_INT strideC2, const CBLAS_INT offsetC );
 ```
 
 </section>
@@ -223,7 +331,45 @@ TODO
 ### Examples
 
 ```c
-TODO
+#include "stdlib/blas/base/dgemm.h"
+#include "stdlib/blas/base/shared.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Define a 2x2 output matrix stored in row-major order:
+    double C[ 2*2 ] = {
+        0.0, 0.0,
+        0.0, 0.0
+    };
+
+    // Define a 2x3 matrix `A` stored in row-major order:
+    const double A[ 2*3 ] = {
+        1.0, 2.0, 3.0,
+        4.0, 5.0, 6.0
+    };
+
+    // Define a 3x2 matrix `B` stored in row-major order:
+    const double B[ 3*2 ] = {
+        7.0,  8.0,
+        9.0,  10.0,
+        11.0, 12.0
+    };
+
+    // Specify matrix dimensions:
+    const int M = 2; // rows of op(A) and C
+    const int N = 2; // columns of op(B) and C
+    const int K = 3; // columns of op(A) and rows of op(B)
+
+    // Perform operation: C = 1.0*A*B + 0.0*C
+    c_dgemm( CblasRowMajor, CblasNoTrans, CblasNoTrans, M, N, K, 1.0, A, K, B, N, 0.0, C, N );
+
+    // Print the result:
+    for ( int i = 0; i < M; i++ ) {
+        for ( int j = 0; j < N; j++ ) {
+            printf( "C[%i,%i] = %lf\n", i, j, C[ (i*N)+j ] );
+        }
+    }
+}
 ```
 
 </section>

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

@@ -0,0 +1,111 @@
+/**
+* @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 resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var format = require( '@stdlib/string/format' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var dgemm = tryRequire( resolve( __dirname, './../lib/ndarray.native.js' ) );
+var opts = {
+	'skip': ( dgemm instanceof Error )
+};
+var options = {
+	'dtype': 'float64'
+};
+
+
+// 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 = dgemm( 'no-transpose', 'no-transpose', N, N, N, 1.0, A, 1, N, 0, B, 1, N, 0, 1.0, C, 1, N, 0 );
+			if ( isnan( z[ i%z.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( 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 = 5; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+		f = createBenchmark( len );
+		bench( format( '%s::native:ndarray:order(A)=column-major,order(B)=column-major,order(C)=column-major,trans(A)=false,trans(B)=false,size=%d', pkg, len*len ), opts, f );
+	}
+}
+
+main();