feat: add base algorithm

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: passed
  - task: lint_markdown
    status: na
  - task: lint_package_json
    status: na
  - task: lint_repl_help
    status: na
  - task: lint_javascript_src
    status: passed
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: na
  - task: lint_javascript_benchmarks
    status: na
  - task: lint_python
    status: na
  - task: lint_r
    status: na
  - task: lint_c_src
    status: na
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: na
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: na
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---

Author: aayush0325

lib/node_modules/@stdlib/lapack/base/dgttrf/lib/base.js

@@ -0,0 +1,146 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 abs = require( '@stdlib/math/base/special/abs' );
+
+
+// MAIN //
+
+/**
+* Computes an LU factorization of a real tri diagonal matrix A using elimination with partial pivoting and row interchanges.
+*
+* @private
+* @param {NonNegativeInteger} N - order of `A`
+* @param {Float64Array} DL - sub diagonal elements of `A`
+* @param {integer} strideDL - stride of the sub diagonal elements of `A`
+* @param {NonNegativeInteger} offsetDL - offset of the sub diagonal elements of `A`
+* @param {Float64Array} D - diagonal elements of `A`
+* @param {integer} strideD - stride of the diagonal elements of `A`
+* @param {NonNegativeInteger} offsetD - offset of the diagonal elements of `A`
+* @param {Float64Array} DU - diagonal elements of `A`
+* @param {integer} strideDU - stride of the first super diagonal elements of `A`
+* @param {NonNegativeInteger} offsetDU - offset of the first super diagonal elements of `A`
+* @param {Float64Array} DU2 - diagonal elements of `A`
+* @param {integer} strideDU2 - stride of the second super diagonal elements of `A`
+* @param {NonNegativeInteger} offsetDU2 - offset of the second super diagonal elements of `A`
+* @param {Int32Array} IPIV - vector of pivot indices
+* @param {integer} strideIPIV - `IPIV` stride length
+* @param {NonNegativeInteger} offsetIPIV - index offset for `IPIV`
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var DL = new Float64Array( [ 1.0, 1.0 ] );
+* var D = new Float64Array( [ 2.0, 3.0, 1.0 ] );
+* var DU = new Float64Array( [ 1.0, 1.0 ] );
+* var DU2 = new Float64Array( [ 0.0 ] );
+* var IPIV = new Int32Array( [ 0, 1, 2 ] );
+*
+* dgttrf( 3, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0 );
+* // DL => <Float64Array>[ 0.5, 0.4 ]
+* // D => <Float64Array>[ 2, 2.5, 0.6 ]
+* // DU => <Float64Array>[ 1, 1 ]
+* // DU2 => <Float64Array>[ 0 ]
+*/
+function dgttrf( N, DL, strideDL, offsetDL, D, strideD, offsetD, DU, strideDU, offsetDU, DU2, strideDU2, offsetDU2, IPIV, strideIPIV, offsetIPIV ) { // eslint-disable-line max-len, max-params
+	var fact;
+	var temp;
+	var idu2;
+	var idu;
+	var idl;
+	var id;
+	var ip;
+	var i;
+
+	if ( N === 0 ) {
+		return 0;
+	}
+
+	idl = offsetDL;
+	idu2 = offsetDU2;
+
+	ip = offsetIPIV;
+	for ( i = 0; i < N; i++ ) {
+		IPIV[ ip + (strideIPIV*i) ] = i;
+	}
+
+	idu = offsetDU;
+	for ( i = 0; i < N-2; i++ ) {
+		DU2[ idu + (strideDU*i) ] = 0;
+	}
+
+	idl = offsetDL;
+	idu2 = offsetDU2;
+	id = offsetD;
+	for ( i = 0; i < N-2; i++ ) {
+		if ( abs( D[ id + (strideD*i) ] ) >= abs( DL[ idl + (strideDL*i) ] ) ) { // no row interchange required
+			if ( D[ id ] !== 0.0 ) {
+				fact = DL[ idl + (strideDL*i) ] / D[ id + (strideD*i) ];
+				DL[ idl + (strideDL*i) ] = fact;
+				D[ id + (strideD*(i+1)) ] = D[ id + (strideD*(i+1)) ] - ( fact*DU[ idu + (strideDU*i) ] ); // eslint-disable-line max-len
+			}
+		} else {
+			fact = D[ id+(strideD*i) ] / DL[ idl+(strideDL*i) ];
+			D[ id+(strideD*i) ] = DL[ idl+(strideDL*i) ];
+			DL[ idl+(strideDL*i) ] = fact;
+			temp = DU[ idu+(strideDU*i) ];
+			DU[ idu+(strideDU*i) ] = D[ id + (strideD*(i+1)) ];
+			D[ id+(strideD*(i+1)) ] = temp - ( fact*D[ id+(strideD*(i+1)) ] );
+			DU2[ idu2+(strideDU2*i) ] = DU[ idu+(strideDU*(i+1)) ];
+			DU[ idu+(strideDU*(i+1)) ] = -fact*DU[ idu+(strideDU*(i+1)) ];
+			IPIV[ ip+(strideIPIV*i) ] = i + 1;
+		}
+	}
+
+	if ( N > 1 ) {
+		i = N - 2;
+		if ( abs( D[ id + (strideD*i) ] ) >= abs( DL[ idl + (strideDL*i) ] ) ) {
+			if ( D[ id + (strideD*i) ] !== 0 ) {
+				fact = DL[ idl + (strideDL*i) ] / D[ id + (strideD*i) ];
+				DL[ idl + (strideDL*i) ] = fact;
+				D[ id + (strideD*(i+1)) ] = D[ id + (strideD*(i+1)) ] - (fact*DU[ idu + (strideDU*i) ]); // eslint-disable-line max-len
+			}
+		} else {
+			fact = D[ id+(strideD*i) ] / DL[ idl+(strideDL*i) ];
+			D[ id+(strideD*i) ] = DL[ idl+(strideDL*i) ];
+			DL[ idl+(strideDL*i) ] = fact;
+			temp = DU[ idu+(strideDU*i) ];
+			DU[ idu+(strideDU*i) ] = D[ id + (strideD*(i+1)) ];
+			D[ id+(strideD*(i+1)) ] = temp - ( fact*D[ id+(strideD*(i+1)) ] );
+			IPIV[ ip+(strideIPIV*i) ] = i + 1;
+		}
+	}
+
+	for ( i = 0; i < N; i++ ) {
+		if ( D[ id+(strideD*i) ] === 0.0 ) {
+			return i;
+		}
+	}
+
+	return 0;
+}
+
+
+// EXPORTS //
+
+module.exports = dgttrf;