From 8104aedb45fc4681114b4e448a911c3673d572d9 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Mon, 7 Apr 2025 08:25:21 +0000
Subject: [PATCH 01/11] feat: add base algorithm

---
 .../@stdlib/lapack/base/dppequ/lib/base.js    | 126 ++++++++++++++++++
 1 file changed, 126 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
new file mode 100644
index 000000000000..acacba60715b
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
@@ -0,0 +1,126 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 sqrt = require( '@stdlib/math/base/special/sqrt' );
+var max = require( '@stdlib/math/base/special/max' );
+var min = require( '@stdlib/math/base/special/min' );
+
+
+// MAIN //
+
+/**
+* Computes the row and column scalings intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
+*
+* @param {string} order - specifies whether `AP` is packed in row-major or column-major order
+* @param {string} uplo - 'Upper' or 'Lower' triangle of `A` is stored
+* @param {NonNegativeInteger} N - order of the matrix `A`
+* @param {Float64Array} AP - array containing the upper or lower triangle of `A` in packed form
+* @param {integer} strideAP - stride length for `AP`
+* @param {integer} offsetAP - starting index for `AP`
+* @param {Float64Array} S - array to store the scale factors of `A`
+* @param {integer} strideS - stride length for `S`
+* @param {integer} offsetS - starting index for `S`
+* @param {Float64Array} out - array to store the output
+* @param {integer} strideOut - stride length for `out`
+* @param {integer} offsetOut - starting index for `out`
+* @returns {integer} status code
+*/
+function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, out, strideOut, offsetOut ) { // eslint-disable-line max-len, max-params
+	var info;
+	var smin;
+	var amax;
+	var jj;
+	var i;
+
+	if ( N === 0 ) {
+		out[ offsetOut ] = 1.0; // scond
+		out[ offsetOut + strideOut ] = 0.0; // amax
+		return 0; // info
+	}
+
+	S[ offsetAP ] = AP[ offsetAP ];
+	smin = S[ offsetAP ];
+	amax = S[ offsetAP ];
+
+	if ( order === 'row-major' ) {
+		if ( uplo === 'U' ) { // uplo === 'U'
+			jj = 0;
+			for ( i = 1; i < N; i++ ) {
+				jj += N - i + 1;
+				S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
+				smin = min( smin, S[ offsetS + (i * strideS) ] );
+				amax = max( amax, S[ offsetS + (i * strideS) ] );
+			}
+		} else { // uplo === 'L'
+			jj = 0;
+			for ( i = 1; i < N; i++ ) {
+				jj += i + 1;
+				S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
+				smin = min( smin, S[ offsetS + (i * strideS) ] );
+				amax = max( amax, S[ offsetS + (i * strideS) ] );
+			}
+		}
+	} else { // order === 'col-major'
+		if ( uplo === 'U' ) { // uplo === 'U'
+			jj = 0;
+			for ( i = 1; i < N; i++ ) {
+				jj += i + 1;
+				S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
+				smin = min( smin, S[ offsetS + (i * strideS) ] );
+				amax = max( amax, S[ offsetS + (i * strideS) ] );
+			}
+		} else { // uplo === 'L'
+			jj = 0;
+			for ( i = 1; i < N; i++ ) {
+				jj += N - i + 1;
+				S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
+				smin = min( smin, S[ offsetS + (i * strideS) ] );
+				amax = max( amax, S[ offsetS + (i * strideS) ] );
+			}
+		}
+	}
+
+	if ( smin <= 0.0 ) {
+		for ( i = 0; i < N; i++ ) {
+			if ( S[ offsetS + (i * strideS) ] <= 0.0 ) {
+				out[ offsetOut ] = 0.0; // scond
+				out[ offsetOut + strideOut ] = amax; // amax
+				info = i;
+				return info;
+			}
+		}
+	} else {
+		for ( i = 0; i < N; i++ ) {
+			S[ offsetS + (i * strideS) ] = 1.0 / sqrt( S[ offsetS + (i * strideS) ] ); // eslint-disable-line max-len
+		}
+	}
+
+	out[ offsetOut ] = sqrt( smin ) / sqrt( amax ); // scond
+	out[ offsetOut + strideOut ] = amax; // amax
+	info = 0;
+	return info;
+}
+
+
+// EXPORTS //
+
+module.exports = dppequ;

From b5618f14d4ee1e4d69a1757f259a763f480d5e9b Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Mon, 7 Apr 2025 09:39:01 +0000
Subject: [PATCH 02/11] feat: add exports

---
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
---
---
 .../@stdlib/lapack/base/dppequ/lib/base.js    | 43 +++++++-----
 .../@stdlib/lapack/base/dppequ/lib/dppequ.js  | 63 +++++++++++++++++
 .../@stdlib/lapack/base/dppequ/lib/main.js    | 35 ++++++++++
 .../@stdlib/lapack/base/dppequ/lib/ndarray.js | 69 +++++++++++++++++++
 4 files changed, 193 insertions(+), 17 deletions(-)
 create mode 100644 lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
 create mode 100644 lib/node_modules/@stdlib/lapack/base/dppequ/lib/main.js
 create mode 100644 lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
index acacba60715b..1959f700cb4a 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
@@ -43,6 +43,17 @@ var min = require( '@stdlib/math/base/special/min' );
 * @param {integer} strideOut - stride length for `out`
 * @param {integer} offsetOut - starting index for `out`
 * @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+* var S = new Float64Array( 3 );
+* var out = new Float64Array( 2 );
+*
+* dppequ( 'row-major', 'L', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+* // S => <Float64Array>[ 1, ~0.58, ~0.33 ]
+* // out => <Float64Array>[ ~0.33, 9 ]
 */
 function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, out, strideOut, offsetOut ) { // eslint-disable-line max-len, max-params
 	var info;
@@ -79,23 +90,21 @@ function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, ou
 				amax = max( amax, S[ offsetS + (i * strideS) ] );
 			}
 		}
-	} else { // order === 'col-major'
-		if ( uplo === 'U' ) { // uplo === 'U'
-			jj = 0;
-			for ( i = 1; i < N; i++ ) {
-				jj += i + 1;
-				S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
-				smin = min( smin, S[ offsetS + (i * strideS) ] );
-				amax = max( amax, S[ offsetS + (i * strideS) ] );
-			}
-		} else { // uplo === 'L'
-			jj = 0;
-			for ( i = 1; i < N; i++ ) {
-				jj += N - i + 1;
-				S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
-				smin = min( smin, S[ offsetS + (i * strideS) ] );
-				amax = max( amax, S[ offsetS + (i * strideS) ] );
-			}
+	} else if ( uplo === 'U' ) { // order === 'col-major'
+		jj = 0;
+		for ( i = 1; i < N; i++ ) {
+			jj += i + 1;
+			S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
+			smin = min( smin, S[ offsetS + (i * strideS) ] );
+			amax = max( amax, S[ offsetS + (i * strideS) ] );
+		}
+	} else { // uplo === 'L', order === 'col-major'
+		jj = 0;
+		for ( i = 1; i < N; i++ ) {
+			jj += N - i + 1;
+			S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
+			smin = min( smin, S[ offsetS + (i * strideS) ] );
+			amax = max( amax, S[ offsetS + (i * strideS) ] );
 		}
 	}
 
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
new file mode 100644
index 000000000000..6cf26fb0f45e
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
@@ -0,0 +1,63 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 isLayout = require( '@stdlib/blas/base/assert/is-layout' );
+var format = require( '@stdlib/string/format' );
+var base = require( './base.js' );
+
+
+// MAIN //
+
+/**
+* Computes the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
+*
+* @param {string} order - specifies whether `AP` is packed in row-major or column-major order
+* @param {string} uplo - 'Upper' or 'Lower' triangle of `A` is stored
+* @param {NonNegativeInteger} N - order of the matrix `A`
+* @param {Float64Array} AP - array containing the upper or lower triangle of `A` in packed form
+* @param {Float64Array} S - array to store the scale factors of `A`
+* @param {Float64Array} out - array to store the output
+* @throws {TypeError} first argument must be a valid order
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+* var S = new Float64Array( 3 );
+* var out = new Float64Array( 2 );
+*
+* dppequ( 'row-major', 'L', 3, AP, S, out );
+* // S => <Float64Array>[ 1, ~0.58, ~0.33 ]
+* // out => <Float64Array>[ ~0.33, 9 ]
+*/
+function dppequ( order, uplo, N, AP, S, out ) {
+	if ( !isLayout( order ) ) {
+		throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
+	}
+	return base( order, uplo, N, AP, 1, 0, S, 1, 0, out, 1, 0 );
+}
+
+
+// EXPORTS //
+
+module.exports = dppequ;
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/main.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/main.js
new file mode 100644
index 000000000000..d40caa8fc3f4
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/main.js
@@ -0,0 +1,35 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
+var dppequ = require( './dppequ.js' );
+var ndarray = require( './ndarray.js' );
+
+
+// MAIN //
+
+setReadOnly( dppequ, 'ndarray', ndarray );
+
+
+// EXPORTS //
+
+module.exports = dppequ;
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js
new file mode 100644
index 000000000000..f8f6486b3470
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js
@@ -0,0 +1,69 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 isLayout = require( '@stdlib/blas/base/assert/is-layout' );
+var format = require( '@stdlib/string/format' );
+var base = require( './base.js' );
+
+
+// MAIN //
+
+/**
+* Computes the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
+*
+* @param {string} order - specifies whether `AP` is packed in row-major or column-major order
+* @param {string} uplo - 'Upper' or 'Lower' triangle of `A` is stored
+* @param {NonNegativeInteger} N - order of the matrix `A`
+* @param {Float64Array} AP - array containing the upper or lower triangle of `A` in packed form
+* @param {integer} strideAP - stride length for `AP`
+* @param {integer} offsetAP - starting index for `AP`
+* @param {Float64Array} S - array to store the scale factors of `A`
+* @param {integer} strideS - stride length for `S`
+* @param {integer} offsetS - starting index for `S`
+* @param {Float64Array} out - array to store the output
+* @param {integer} strideOut - stride length for `out`
+* @param {integer} offsetOut - starting index for `out`
+* @throws {TypeError} first argument must be a valid order
+* @returns {integer} status code
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+* var S = new Float64Array( 3 );
+* var out = new Float64Array( 2 );
+*
+* dppequ( 'row-major', 'L', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+* // S => <Float64Array>[ 1, ~0.58, ~0.33 ]
+* // out => <Float64Array>[ ~0.33, 9 ]
+*/
+function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, out, strideOut, offsetOut ) { // eslint-disable-line max-len, max-params
+	if ( !isLayout( order ) ) {
+		throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
+	}
+	return base( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, out, strideOut, offsetOut ); // eslint-disable-line max-len
+}
+
+
+// EXPORTS //
+
+module.exports = dppequ;

From b7e80ebf8668773d0f820d8c8af4171dda632a95 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Mon, 7 Apr 2025 09:46:14 +0000
Subject: [PATCH 03/11] feat: merge loops

---
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
---
---
 .../@stdlib/lapack/base/dppequ/lib/base.js    | 34 +++++++------------
 1 file changed, 12 insertions(+), 22 deletions(-)

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
index 1959f700cb4a..63a8e19ec4d7 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
@@ -28,7 +28,7 @@ var min = require( '@stdlib/math/base/special/min' );
 // MAIN //
 
 /**
-* Computes the row and column scalings intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
+* Computes the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
 *
 * @param {string} order - specifies whether `AP` is packed in row-major or column-major order
 * @param {string} uplo - 'Upper' or 'Lower' triangle of `A` is stored
@@ -72,36 +72,26 @@ function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, ou
 	smin = S[ offsetAP ];
 	amax = S[ offsetAP ];
 
-	if ( order === 'row-major' ) {
-		if ( uplo === 'U' ) { // uplo === 'U'
-			jj = 0;
-			for ( i = 1; i < N; i++ ) {
+	if ( uplo === 'U' ) { // uplo === 'U'
+		jj = 0;
+		for ( i = 1; i < N; i++ ) {
+			if ( order === 'row-major' ) {
 				jj += N - i + 1;
-				S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
-				smin = min( smin, S[ offsetS + (i * strideS) ] );
-				amax = max( amax, S[ offsetS + (i * strideS) ] );
-			}
-		} else { // uplo === 'L'
-			jj = 0;
-			for ( i = 1; i < N; i++ ) {
+			} else { // order === 'column-major'
 				jj += i + 1;
-				S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
-				smin = min( smin, S[ offsetS + (i * strideS) ] );
-				amax = max( amax, S[ offsetS + (i * strideS) ] );
 			}
-		}
-	} else if ( uplo === 'U' ) { // order === 'col-major'
-		jj = 0;
-		for ( i = 1; i < N; i++ ) {
-			jj += i + 1;
 			S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
 			smin = min( smin, S[ offsetS + (i * strideS) ] );
 			amax = max( amax, S[ offsetS + (i * strideS) ] );
 		}
-	} else { // uplo === 'L', order === 'col-major'
+	} else { // uplo === 'L'
 		jj = 0;
 		for ( i = 1; i < N; i++ ) {
-			jj += N - i + 1;
+			if ( order === 'row-major' ) {
+				jj += i + 1;
+			} else { // order === 'column-major'
+				jj += N - i + 1;
+			}
 			S[ offsetS + (i * strideS) ] = AP[ offsetAP + (jj * strideAP) ];
 			smin = min( smin, S[ offsetS + (i * strideS) ] );
 			amax = max( amax, S[ offsetS + (i * strideS) ] );

From 9bb5c3897a7135c15581792eaf218f8a6cdec575 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Mon, 7 Apr 2025 09:50:37 +0000
Subject: [PATCH 04/11] feat: add main export

---
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
---
---
 .../@stdlib/lapack/base/dppequ/lib/base.js    |  2 +-
 .../@stdlib/lapack/base/dppequ/lib/dppequ.js  |  2 +-
 .../@stdlib/lapack/base/dppequ/lib/index.js   | 72 +++++++++++++++++++
 .../@stdlib/lapack/base/dppequ/lib/main.js    |  2 +-
 .../@stdlib/lapack/base/dppequ/lib/ndarray.js |  4 +-
 5 files changed, 77 insertions(+), 5 deletions(-)
 create mode 100644 lib/node_modules/@stdlib/lapack/base/dppequ/lib/index.js

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
index 63a8e19ec4d7..ff622f664b59 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2024 The Stdlib Authors.
+* 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.
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
index 6cf26fb0f45e..6859e71eaa25 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2024 The Stdlib Authors.
+* 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.
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/index.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/index.js
new file mode 100644
index 000000000000..40790ac7c266
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/index.js
@@ -0,0 +1,72 @@
+/**
+* @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';
+
+/**
+* LAPACK routine to compute the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
+*
+* @module @stdlib/lapack/base/dppequ
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var dppequ = require( '@stdlib/lapack/base/dppequ' );
+*
+* var AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+* var S = new Float64Array( 3 );
+* var out = new Float64Array( 2 );
+*
+* dppequ( 'row-major', 'L', 3, AP, S, out );
+* // S => <Float64Array>[ 1, ~0.58, ~0.33 ]
+* // out => <Float64Array>[ ~0.33, 9 ]
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var dppequ = require( '@stdlib/lapack/base/dppequ' );
+*
+* var AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+* var S = new Float64Array( 3 );
+* var out = new Float64Array( 2 );
+*
+* dppequ.ndarray( 'row-major', 'L', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+* // S => <Float64Array>[ 1, ~0.58, ~0.33 ]
+* // out => <Float64Array>[ ~0.33, 9 ]
+*/
+
+// MODULES //
+
+var join = require( 'path' ).join;
+var tryRequire = require( '@stdlib/utils/try-require' );
+var isError = require( '@stdlib/assert/is-error' );
+var main = require( './main.js' );
+
+
+// MAIN //
+
+var dppequ;
+var tmp = tryRequire( join( __dirname, './native.js' ) );
+if ( isError( tmp ) ) {
+	dppequ = main;
+} else {
+	dppequ = tmp;
+}
+
+
+// EXPORTS //
+
+module.exports = dppequ;
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/main.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/main.js
index d40caa8fc3f4..7b6ee1e50424 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/main.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/main.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2024 The Stdlib Authors.
+* 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.
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js
index f8f6486b3470..44f98b80b569 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2024 The Stdlib Authors.
+* 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.
@@ -28,7 +28,7 @@ var base = require( './base.js' );
 // MAIN //
 
 /**
-* Computes the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
+* Computes the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm) using alternative indexing semantics.
 *
 * @param {string} order - specifies whether `AP` is packed in row-major or column-major order
 * @param {string} uplo - 'Upper' or 'Lower' triangle of `A` is stored

From fab8873dea994afefe5a08b27595bbf6702c32f3 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Wed, 16 Apr 2025 18:15:54 +0000
Subject: [PATCH 05/11] test: add initial tests

---
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: passed
  - 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
---
---
 .../@stdlib/lapack/base/dppequ/lib/dppequ.js  |   4 +
 .../lapack/base/dppequ/test/test.dppequ.js    | 109 ++++++++++++++++++
 .../@stdlib/lapack/base/dppequ/test/test.js   |  82 +++++++++++++
 3 files changed, 195 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
 create mode 100644 lib/node_modules/@stdlib/lapack/base/dppequ/test/test.js

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
index 6859e71eaa25..947507c94276 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/dppequ.js
@@ -37,6 +37,7 @@ var base = require( './base.js' );
 * @param {Float64Array} S - array to store the scale factors of `A`
 * @param {Float64Array} out - array to store the output
 * @throws {TypeError} first argument must be a valid order
+* @throws {RangeError} third argument must be a nonnegative integer
 * @returns {integer} status code
 *
 * @example
@@ -54,6 +55,9 @@ function dppequ( order, uplo, N, AP, S, out ) {
 	if ( !isLayout( order ) ) {
 		throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
 	}
+	if ( N < 0 ) {
+		throw new RangeError( format( 'invalid argument. First argument must be a nonnegative integer. Value: `%d`.', N ) );
+	}
 	return base( order, uplo, N, AP, 1, 0, S, 1, 0, out, 1, 0 );
 }
 
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
new file mode 100644
index 000000000000..61737e4d2de4
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
@@ -0,0 +1,109 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 tape = require( 'tape' );
+var Float64Array = require( '@stdlib/array/float64' );
+var dppequ = require( './../lib/dppequ.js' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof dppequ, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'the function has an arity of 6', function test( t ) {
+	t.strictEqual( dppequ.length, 6, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function throws an error if provided an invalid third argument', function test( t ) {
+	var values;
+	var out;
+	var AP;
+	var S;
+	var i;
+
+	values = [
+		-1,
+		-2,
+		-3,
+		-4,
+		-5
+	];
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			dppequ( 'row-major', 'L', value, AP, S, out );
+		};
+	}
+});
+
+tape( 'the function throws an error if provided a first argument which is not a valid order', function test( t ) {
+	var values;
+	var out;
+	var AP;
+	var S;
+	var i;
+
+	values = [
+		'foo',
+		'bar',
+		'beep',
+		'boop',
+		-5,
+		NaN,
+		true,
+		false,
+		null,
+		void 0,
+		[],
+		{},
+		function noop() {}
+	];
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			dppequ( value, 'L', 3, AP, S, out );
+		};
+	}
+});
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.js
new file mode 100644
index 000000000000..96853273fab0
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.js
@@ -0,0 +1,82 @@
+/**
+* @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 tape = require( 'tape' );
+var proxyquire = require( 'proxyquire' );
+var IS_BROWSER = require( '@stdlib/assert/is-browser' );
+var dppequ = require( './../lib' );
+
+
+// VARIABLES //
+
+var opts = {
+	'skip': IS_BROWSER
+};
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof dppequ, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'attached to the main export is a method providing an ndarray interface', function test( t ) {
+	t.strictEqual( typeof dppequ.ndarray, 'function', 'method is a function' );
+	t.end();
+});
+
+tape( 'if a native implementation is available, the main export is the native implementation', opts, function test( t ) {
+	var dppequ = proxyquire( './../lib', {
+		'@stdlib/utils/try-require': tryRequire
+	});
+
+	t.strictEqual( dppequ, mock, 'returns expected value' );
+	t.end();
+
+	function tryRequire() {
+		return mock;
+	}
+
+	function mock() {
+		// Mock...
+	}
+});
+
+tape( 'if a native implementation is not available, the main export is a JavaScript implementation', opts, function test( t ) {
+	var dppequ;
+	var main;
+
+	main = require( './../lib/dppequ.js' );
+
+	dppequ = proxyquire( './../lib', {
+		'@stdlib/utils/try-require': tryRequire
+	});
+
+	t.strictEqual( dppequ, main, 'returns expected value' );
+	t.end();
+
+	function tryRequire() {
+		return new Error( 'Cannot find module' );
+	}
+});

From 51ad33f0297c29ecc236750e33127d68c0922b03 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Wed, 16 Apr 2025 18:23:51 +0000
Subject: [PATCH 06/11] test: add initial ndarray tests

---
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: passed
  - 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
---
---
 .../@stdlib/lapack/base/dppequ/lib/ndarray.js |   4 +
 .../lapack/base/dppequ/test/test.ndarray.js   | 109 ++++++++++++++++++
 2 files changed, 113 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js
index 44f98b80b569..8c264abd01f4 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/ndarray.js
@@ -43,6 +43,7 @@ var base = require( './base.js' );
 * @param {integer} strideOut - stride length for `out`
 * @param {integer} offsetOut - starting index for `out`
 * @throws {TypeError} first argument must be a valid order
+* @throws {RangeError} third argument must be a nonnegative integer
 * @returns {integer} status code
 *
 * @example
@@ -60,6 +61,9 @@ function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, ou
 	if ( !isLayout( order ) ) {
 		throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
 	}
+	if ( N < 0 ) {
+		throw new RangeError( format( 'invalid argument. First argument must be a nonnegative integer. Value: `%d`.', N ) );
+	}
 	return base( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, out, strideOut, offsetOut ); // eslint-disable-line max-len
 }
 
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js
new file mode 100644
index 000000000000..acdac90d5b17
--- /dev/null
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js
@@ -0,0 +1,109 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 tape = require( 'tape' );
+var Float64Array = require( '@stdlib/array/float64' );
+var dppequ = require( './../lib/ndarray.js' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof dppequ, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'the function has an arity of 12', function test( t ) {
+	t.strictEqual( dppequ.length, 12, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function throws an error if provided an invalid third argument', function test( t ) {
+	var values;
+	var out;
+	var AP;
+	var S;
+	var i;
+
+	values = [
+		-1,
+		-2,
+		-3,
+		-4,
+		-5
+	];
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			dppequ( 'row-major', 'L', value, AP, 1, 0, S, 1, 0, out, 1, 0 );
+		};
+	}
+});
+
+tape( 'the function throws an error if provided a first argument which is not a valid order', function test( t ) {
+	var values;
+	var out;
+	var AP;
+	var S;
+	var i;
+
+	values = [
+		'foo',
+		'bar',
+		'beep',
+		'boop',
+		-5,
+		NaN,
+		true,
+		false,
+		null,
+		void 0,
+		[],
+		{},
+		function noop() {}
+	];
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			dppequ( value, 'L', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+		};
+	}
+});

From ccda72f9235a6bada4603ab69136db4d66546723 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Wed, 16 Apr 2025 18:24:44 +0000
Subject: [PATCH 07/11] test: add initial ndarray tests

---
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: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: passed
  - 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
---
---
 lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js | 2 +-
 .../@stdlib/lapack/base/dppequ/test/test.ndarray.js             | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
index 61737e4d2de4..7cfe9d30c9e9 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2024 The Stdlib Authors.
+* 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.
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js
index acdac90d5b17..3bce838fa53d 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2024 The Stdlib Authors.
+* 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.

From dc0dfd0793a65bc3708fcdc8ee1676fa184da600 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Fri, 18 Apr 2025 13:08:17 +0000
Subject: [PATCH 08/11] test: add tests

---
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: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: passed
  - 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
---
---
 .../lapack/base/dppequ/test/test.dppequ.js    | 86 +++++++++++++++++++
 1 file changed, 86 insertions(+)

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
index 7cfe9d30c9e9..83f3b97d6447 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
@@ -18,6 +18,8 @@
 
 'use strict';
 
+/* eslint-disable max-len */
+
 // MODULES //
 
 var tape = require( 'tape' );
@@ -107,3 +109,87 @@ tape( 'the function throws an error if provided a first argument which is not a
 		};
 	}
 });
+
+tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (lower-triangular) (row-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	dppequ( 'row-major', 'L', 3, AP, S, out );
+
+	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.57735026918962584, 0.33333333333333331 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (lower-triangular) (column-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 5.0, 3.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	dppequ( 'column-major', 'L', 3, AP, S, out );
+
+	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.57735026918962584, 0.33333333333333331 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (upper-triangular) (row-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	dppequ( 'row-major', 'U', 3, AP, S, out );
+
+	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.44721359549995793, 0.33333333333333331 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (upper-triangular) (column-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 5.0, 3.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	dppequ( 'column-major', 'U', 3, AP, S, out );
+
+	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.44721359549995793, 0.33333333333333331 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+
+	t.end();
+});

From 7ac07fd5f14ff7c20e50b13974db31860680d945 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Fri, 18 Apr 2025 13:37:09 +0000
Subject: [PATCH 09/11] test: add N=0 case

---
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: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: passed
  - 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
---
---
 .../lapack/base/dppequ/test/test.dppequ.js    | 39 +++++++++++++++++--
 1 file changed, 35 insertions(+), 4 deletions(-)

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
index 83f3b97d6447..70231f398d9d 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
@@ -110,9 +110,33 @@ tape( 'the function throws an error if provided a first argument which is not a
 	}
 });
 
+tape( 'the function leaves the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage unchanged if N is equal to 0', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'row-major', 'L', 0, AP, S, out );
+
+	expectedOut = new Float64Array( [ 1.0, 0.0 ] );
+	expectedS = new Float64Array( 3 );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
+
+	t.end();
+});
+
 tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (lower-triangular) (row-major)', function test( t ) {
 	var expectedOut;
 	var expectedS;
+	var info;
 	var out;
 	var AP;
 	var S;
@@ -121,12 +145,13 @@ tape( 'the function calculates the row and column scaling factors intended to eq
 	S = new Float64Array( 3 );
 	out = new Float64Array( 2 );
 
-	dppequ( 'row-major', 'L', 3, AP, S, out );
+	info = dppequ( 'row-major', 'L', 3, AP, S, out );
 
 	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
 	expectedS = new Float64Array( [ 1.0, 0.57735026918962584, 0.33333333333333331 ] );
 	t.deepEqual( S, expectedS, 'returns expected value' );
 	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
 
 	t.end();
 });
@@ -134,6 +159,7 @@ tape( 'the function calculates the row and column scaling factors intended to eq
 tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (lower-triangular) (column-major)', function test( t ) {
 	var expectedOut;
 	var expectedS;
+	var info;
 	var out;
 	var AP;
 	var S;
@@ -142,12 +168,13 @@ tape( 'the function calculates the row and column scaling factors intended to eq
 	S = new Float64Array( 3 );
 	out = new Float64Array( 2 );
 
-	dppequ( 'column-major', 'L', 3, AP, S, out );
+	info = dppequ( 'column-major', 'L', 3, AP, S, out );
 
 	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
 	expectedS = new Float64Array( [ 1.0, 0.57735026918962584, 0.33333333333333331 ] );
 	t.deepEqual( S, expectedS, 'returns expected value' );
 	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
 
 	t.end();
 });
@@ -155,6 +182,7 @@ tape( 'the function calculates the row and column scaling factors intended to eq
 tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (upper-triangular) (row-major)', function test( t ) {
 	var expectedOut;
 	var expectedS;
+	var info;
 	var out;
 	var AP;
 	var S;
@@ -163,12 +191,13 @@ tape( 'the function calculates the row and column scaling factors intended to eq
 	S = new Float64Array( 3 );
 	out = new Float64Array( 2 );
 
-	dppequ( 'row-major', 'U', 3, AP, S, out );
+	info = dppequ( 'row-major', 'U', 3, AP, S, out );
 
 	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
 	expectedS = new Float64Array( [ 1.0, 0.44721359549995793, 0.33333333333333331 ] );
 	t.deepEqual( S, expectedS, 'returns expected value' );
 	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
 
 	t.end();
 });
@@ -176,6 +205,7 @@ tape( 'the function calculates the row and column scaling factors intended to eq
 tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (upper-triangular) (column-major)', function test( t ) {
 	var expectedOut;
 	var expectedS;
+	var info;
 	var out;
 	var AP;
 	var S;
@@ -184,12 +214,13 @@ tape( 'the function calculates the row and column scaling factors intended to eq
 	S = new Float64Array( 3 );
 	out = new Float64Array( 2 );
 
-	dppequ( 'column-major', 'U', 3, AP, S, out );
+	info = dppequ( 'column-major', 'U', 3, AP, S, out );
 
 	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
 	expectedS = new Float64Array( [ 1.0, 0.44721359549995793, 0.33333333333333331 ] );
 	t.deepEqual( S, expectedS, 'returns expected value' );
 	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
 
 	t.end();
 });

From 7ff79c80c46ba27deaeb696daa79aa74f849b4a1 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Sat, 19 Apr 2025 08:10:30 +0000
Subject: [PATCH 10/11] test: add non positive diagonal element tests

---
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: passed
  - 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
---
---
 .../@stdlib/lapack/base/dppequ/lib/base.js    |  4 +-
 .../lapack/base/dppequ/test/test.dppequ.js    | 92 +++++++++++++++++++
 2 files changed, 94 insertions(+), 2 deletions(-)

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
index ff622f664b59..3eb0daec7511 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/lib/base.js
@@ -72,7 +72,7 @@ function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, ou
 	smin = S[ offsetAP ];
 	amax = S[ offsetAP ];
 
-	if ( uplo === 'U' ) { // uplo === 'U'
+	if ( uplo === 'U' ) {
 		jj = 0;
 		for ( i = 1; i < N; i++ ) {
 			if ( order === 'row-major' ) {
@@ -101,7 +101,7 @@ function dppequ( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, ou
 	if ( smin <= 0.0 ) {
 		for ( i = 0; i < N; i++ ) {
 			if ( S[ offsetS + (i * strideS) ] <= 0.0 ) {
-				out[ offsetOut ] = 0.0; // scond
+				// Leave first element of `out` unchanged
 				out[ offsetOut + strideOut ] = amax; // amax
 				info = i;
 				return info;
diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
index 70231f398d9d..8476e0085adc 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.dppequ.js
@@ -224,3 +224,95 @@ tape( 'the function calculates the row and column scaling factors intended to eq
 
 	t.end();
 });
+
+tape( 'the function finds the first non-positive diagonal element and returns (upper-triangular) (column-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 0.0, -1.0, 0.0, 0.0, 1.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'column-major', 'U', 3, AP, S, out );
+
+	expectedOut = new Float64Array( [ 0.0, 1.0 ] );
+	expectedS = new Float64Array( [ 1.0, -1.0, 1.0 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 1, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function finds the first non-positive diagonal element and returns (upper-triangular) (row-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 0.0, 0.0, -1.0, 0.0, 1.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'row-major', 'U', 3, AP, S, out );
+
+	expectedOut = new Float64Array( [ 0.0, 1.0 ] );
+	expectedS = new Float64Array( [ 1.0, -1.0, 1.0 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 1, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function finds the first non-positive diagonal element and returns (lower-triangular) (column-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 0.0, -1.0, 0.0, 0.0, 1.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'column-major', 'L', 3, AP, S, out );
+
+	expectedOut = new Float64Array( [ 0.0, 1.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.0, 1.0 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 1, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function finds the first non-positive diagonal element and returns (lower-triangular) (row-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 0.0, 0.0, -1.0, 0.0, 1.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'row-major', 'L', 3, AP, S, out );
+
+	expectedOut = new Float64Array( [ 0.0, 1.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.0, 1.0 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 1, 'returns expected value' );
+
+	t.end();
+});

From 9de21b0cced56231c785c0a9bbd997624ba0d026 Mon Sep 17 00:00:00 2001
From: Aayush Khanna <ayush25khanna@gmail.com>
Date: Sat, 19 Apr 2025 08:16:26 +0000
Subject: [PATCH 11/11] test: add ndarray tests

---
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: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: passed
  - 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
---
---
 .../lapack/base/dppequ/test/test.ndarray.js   | 209 ++++++++++++++++++
 1 file changed, 209 insertions(+)

diff --git a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js
index 3bce838fa53d..9baeb9f25394 100644
--- a/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js
+++ b/lib/node_modules/@stdlib/lapack/base/dppequ/test/test.ndarray.js
@@ -18,6 +18,8 @@
 
 'use strict';
 
+/* eslint-disable max-len */
+
 // MODULES //
 
 var tape = require( 'tape' );
@@ -107,3 +109,210 @@ tape( 'the function throws an error if provided a first argument which is not a
 		};
 	}
 });
+
+tape( 'the function leaves the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage unchanged if N is equal to 0', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'row-major', 'L', 0, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 1.0, 0.0 ] );
+	expectedS = new Float64Array( 3 );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (lower-triangular) (row-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'row-major', 'L', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.57735026918962584, 0.33333333333333331 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (lower-triangular) (column-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 5.0, 3.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'column-major', 'L', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.57735026918962584, 0.33333333333333331 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (upper-triangular) (row-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'row-major', 'U', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.44721359549995793, 0.33333333333333331 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function calculates the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage (upper-triangular) (column-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 2.0, 5.0, 3.0, 6.0, 9.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'column-major', 'U', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 0.33333333333333331, 9.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.44721359549995793, 0.33333333333333331 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 0, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function finds the first non-positive diagonal element and returns (upper-triangular) (column-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 0.0, -1.0, 0.0, 0.0, 1.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'column-major', 'U', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 0.0, 1.0 ] );
+	expectedS = new Float64Array( [ 1.0, -1.0, 1.0 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 1, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function finds the first non-positive diagonal element and returns (upper-triangular) (row-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 0.0, 0.0, -1.0, 0.0, 1.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'row-major', 'U', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 0.0, 1.0 ] );
+	expectedS = new Float64Array( [ 1.0, -1.0, 1.0 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 1, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function finds the first non-positive diagonal element and returns (lower-triangular) (column-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 0.0, -1.0, 0.0, 0.0, 1.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'column-major', 'L', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 0.0, 1.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.0, 1.0 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 1, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function finds the first non-positive diagonal element and returns (lower-triangular) (row-major)', function test( t ) {
+	var expectedOut;
+	var expectedS;
+	var info;
+	var out;
+	var AP;
+	var S;
+
+	AP = new Float64Array( [ 1.0, 0.0, 0.0, -1.0, 0.0, 1.0 ] );
+	S = new Float64Array( 3 );
+	out = new Float64Array( 2 );
+
+	info = dppequ( 'row-major', 'L', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+
+	expectedOut = new Float64Array( [ 0.0, 1.0 ] );
+	expectedS = new Float64Array( [ 1.0, 0.0, 1.0 ] );
+	t.deepEqual( S, expectedS, 'returns expected value' );
+	t.deepEqual( out, expectedOut, 'returns expected value' );
+	t.deepEqual( info, 1, 'returns expected value' );
+
+	t.end();
+});