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Tensor

Currently, support is only for contravariant Tensors of equal dimension basis vectors.
Also, all Tensors are assumed to use an orthonormal basis (Ex: Euclidean standard basis).

We use the following Tensor definition:

T'α..'β = ( ∂x'α / ∂xγ )..( ∂x'β / ∂xμ ) Tγ..μ

After assuming an orthonormal basis, we know that ( ∂x'α / ∂xγ ) will be zero for all cases α != γ.
and one for α = γ The same is true for other components such as ( ∂x'β / ∂xμ ) with regards to β != μ.

This allows a straight-forward calculation of the outer and inner products of Tensors.

The inner product between two Tensors is currently defined for all Tensor ranks, provided the ranks are equal, and the indices of both Tensors are all of equal dimension. We will gradually ease up on these restrictions.

Example

This code serves as a sketch.

// 3d Rank3 Tensor Examplelet t3 = Tensor::build(3,3,vec![1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);let t = t3.inner_product(&t3);
t.print();

The above code will perform the inner product between t3 and itself, and then print out each component of the final Tensor, t.

A more robust Tensor library is on the way.

Purpose

This library is meant to abstract Tensor math and allow high rank Tensor calculations (Rank > 2). Several individuals use the term 'Tensor' despite using only Vectors and Matrices. We do not encourage this technicality. Though Matrices and Vectors are special cases of Tensors, we do not aim to provide the highest performance for such low ranks. We recommend 'nalgebra', https://crates.io/crates/nalgebra, for high performance Vector and Matrix operations.

To Do

A list of additions and improvements:

  • Tensor Outer Product
  • Scalar Multiplication and Addition
  • Tensor Addition and Subtration
  • Tensor Conversion to nalgebra types

About

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all
 blocks\n(function() {\n function addCopyButtons() {\n document.querySelectorAll('pre code').forEach(function(codeBlock) {\n if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;\n codeBlock.parentElement.setAttribute('data-copy-added', 'true');\n \n var btn = document.createElement('button');\n btn.textContent = 'Copy';\n btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';\n btn.onmouseover = function() { this.style.opacity = '1'; };\n btn.onmouseout = function() { this.style.opacity = '0.7'; };\n btn.onclick = function() {\n navigator.clipboard.writeText(codeBlock.textContent).then(function() {\n btn.textContent = 'Copied!';\n setTimeout(function() { btn.textContent = 'Copy'; }, 1500);\n });\n };\n codeBlock.parentElement.style.position = 'relative';\n codeBlock.parentElement.appendChild(btn);\n });\n }\n \n addCopyButtons();\n \n // Re-run on dynamic content\n var observer = new MutationObserver(addCopyButtons);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Add Copy Buttons to Code Blocks");
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '
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Tensor

Currently, support is only for contravariant Tensors of equal dimension basis vectors.
Also, all Tensors are assumed to use an orthonormal basis (Ex: Euclidean standard basis).

We use the following Tensor definition:

T'α..'β = ( ∂x'α / ∂xγ )..( ∂x'β / ∂xμ ) Tγ..μ

After assuming an orthonormal basis, we know that ( ∂x'α / ∂xγ ) will be zero for all cases α != γ.
and one for α = γ The same is true for other components such as ( ∂x'β / ∂xμ ) with regards to β != μ.

This allows a straight-forward calculation of the outer and inner products of Tensors.

The inner product between two Tensors is currently defined for all Tensor ranks, provided the ranks are equal, and the indices of both Tensors are all of equal dimension. We will gradually ease up on these restrictions.

Example

This code serves as a sketch.

// 3d Rank3 Tensor Examplelet t3 = Tensor::build(3,3,vec![1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);let t = t3.inner_product(&t3);
t.print();

The above code will perform the inner product between t3 and itself, and then print out each component of the final Tensor, t.

A more robust Tensor library is on the way.

Purpose

This library is meant to abstract Tensor math and allow high rank Tensor calculations (Rank > 2). Several individuals use the term 'Tensor' despite using only Vectors and Matrices. We do not encourage this technicality. Though Matrices and Vectors are special cases of Tensors, we do not aim to provide the highest performance for such low ranks. We recommend 'nalgebra', https://crates.io/crates/nalgebra, for high performance Vector and Matrix operations.

To Do

A list of additions and improvements:

  • Tensor Outer Product
  • Scalar Multiplication and Addition
  • Tensor Addition and Subtration
  • Tensor Conversion to nalgebra types

About

A tensor library for Rust

Resources

Stars

16 stars

Watchers

2 watching

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Used by

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Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix"); } } catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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Tensor

Currently, support is only for contravariant Tensors of equal dimension basis vectors.
Also, all Tensors are assumed to use an orthonormal basis (Ex: Euclidean standard basis).

We use the following Tensor definition:

T'α..'β = ( ∂x'α / ∂xγ )..( ∂x'β / ∂xμ ) Tγ..μ

After assuming an orthonormal basis, we know that ( ∂x'α / ∂xγ ) will be zero for all cases α != γ.
and one for α = γ The same is true for other components such as ( ∂x'β / ∂xμ ) with regards to β != μ.

This allows a straight-forward calculation of the outer and inner products of Tensors.

The inner product between two Tensors is currently defined for all Tensor ranks, provided the ranks are equal, and the indices of both Tensors are all of equal dimension. We will gradually ease up on these restrictions.

Example

This code serves as a sketch.

// 3d Rank3 Tensor Examplelet t3 = Tensor::build(3,3,vec![1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);let t = t3.inner_product(&t3);
t.print();

The above code will perform the inner product between t3 and itself, and then print out each component of the final Tensor, t.

A more robust Tensor library is on the way.

Purpose

This library is meant to abstract Tensor math and allow high rank Tensor calculations (Rank > 2). Several individuals use the term 'Tensor' despite using only Vectors and Matrices. We do not encourage this technicality. Though Matrices and Vectors are special cases of Tensors, we do not aim to provide the highest performance for such low ranks. We recommend 'nalgebra', https://crates.io/crates/nalgebra, for high performance Vector and Matrix operations.

To Do

A list of additions and improvements:

  • Tensor Outer Product
  • Scalar Multiplication and Addition
  • Tensor Addition and Subtration
  • Tensor Conversion to nalgebra types

About

A tensor library for Rust

Resources

Stars

16 stars

Watchers

2 watching

Forks

Releases

Packages

Used by

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms"); } } catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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Tensor

Currently, support is only for contravariant Tensors of equal dimension basis vectors.
Also, all Tensors are assumed to use an orthonormal basis (Ex: Euclidean standard basis).

We use the following Tensor definition:

T'α..'β = ( ∂x'α / ∂xγ )..( ∂x'β / ∂xμ ) Tγ..μ

After assuming an orthonormal basis, we know that ( ∂x'α / ∂xγ ) will be zero for all cases α != γ.
and one for α = γ The same is true for other components such as ( ∂x'β / ∂xμ ) with regards to β != μ.

This allows a straight-forward calculation of the outer and inner products of Tensors.

The inner product between two Tensors is currently defined for all Tensor ranks, provided the ranks are equal, and the indices of both Tensors are all of equal dimension. We will gradually ease up on these restrictions.

Example

This code serves as a sketch.

// 3d Rank3 Tensor Examplelet t3 = Tensor::build(3,3,vec![1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);let t = t3.inner_product(&t3);
t.print();

The above code will perform the inner product between t3 and itself, and then print out each component of the final Tensor, t.

A more robust Tensor library is on the way.

Purpose

This library is meant to abstract Tensor math and allow high rank Tensor calculations (Rank > 2). Several individuals use the term 'Tensor' despite using only Vectors and Matrices. We do not encourage this technicality. Though Matrices and Vectors are special cases of Tensors, we do not aim to provide the highest performance for such low ranks. We recommend 'nalgebra', https://crates.io/crates/nalgebra, for high performance Vector and Matrix operations.

To Do

A list of additions and improvements:

  • Tensor Outer Product
  • Scalar Multiplication and Addition
  • Tensor Addition and Subtration
  • Tensor Conversion to nalgebra types

About

A tensor library for Rust

Resources

Stars

16 stars

Watchers

2 watching

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Releases

Packages

Used by

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Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links"); } } catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); } })(); (function(){ try { var __m = "youtube.com"; var __re = new RegExp('^' + "youtube\\.com" + '
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Tensor

Currently, support is only for contravariant Tensors of equal dimension basis vectors.
Also, all Tensors are assumed to use an orthonormal basis (Ex: Euclidean standard basis).

We use the following Tensor definition:

T'α..'β = ( ∂x'α / ∂xγ )..( ∂x'β / ∂xμ ) Tγ..μ

After assuming an orthonormal basis, we know that ( ∂x'α / ∂xγ ) will be zero for all cases α != γ.
and one for α = γ The same is true for other components such as ( ∂x'β / ∂xμ ) with regards to β != μ.

This allows a straight-forward calculation of the outer and inner products of Tensors.

The inner product between two Tensors is currently defined for all Tensor ranks, provided the ranks are equal, and the indices of both Tensors are all of equal dimension. We will gradually ease up on these restrictions.

Example

This code serves as a sketch.

// 3d Rank3 Tensor Examplelet t3 = Tensor::build(3,3,vec![1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);let t = t3.inner_product(&t3);
t.print();

The above code will perform the inner product between t3 and itself, and then print out each component of the final Tensor, t.

A more robust Tensor library is on the way.

Purpose

This library is meant to abstract Tensor math and allow high rank Tensor calculations (Rank > 2). Several individuals use the term 'Tensor' despite using only Vectors and Matrices. We do not encourage this technicality. Though Matrices and Vectors are special cases of Tensors, we do not aim to provide the highest performance for such low ranks. We recommend 'nalgebra', https://crates.io/crates/nalgebra, for high performance Vector and Matrix operations.

To Do

A list of additions and improvements:

  • Tensor Outer Product
  • Scalar Multiplication and Addition
  • Tensor Addition and Subtration
  • Tensor Conversion to nalgebra types

About

A tensor library for Rust

Resources

Stars

16 stars

Watchers

2 watching

Forks

Releases

Packages

Used by

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default"); } } catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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Tensor

Currently, support is only for contravariant Tensors of equal dimension basis vectors.
Also, all Tensors are assumed to use an orthonormal basis (Ex: Euclidean standard basis).

We use the following Tensor definition:

T'α..'β = ( ∂x'α / ∂xγ )..( ∂x'β / ∂xμ ) Tγ..μ

After assuming an orthonormal basis, we know that ( ∂x'α / ∂xγ ) will be zero for all cases α != γ.
and one for α = γ The same is true for other components such as ( ∂x'β / ∂xμ ) with regards to β != μ.

This allows a straight-forward calculation of the outer and inner products of Tensors.

The inner product between two Tensors is currently defined for all Tensor ranks, provided the ranks are equal, and the indices of both Tensors are all of equal dimension. We will gradually ease up on these restrictions.

Example

This code serves as a sketch.

// 3d Rank3 Tensor Examplelet t3 = Tensor::build(3,3,vec![1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);let t = t3.inner_product(&t3);
t.print();

The above code will perform the inner product between t3 and itself, and then print out each component of the final Tensor, t.

A more robust Tensor library is on the way.

Purpose

This library is meant to abstract Tensor math and allow high rank Tensor calculations (Rank > 2). Several individuals use the term 'Tensor' despite using only Vectors and Matrices. We do not encourage this technicality. Though Matrices and Vectors are special cases of Tensors, we do not aim to provide the highest performance for such low ranks. We recommend 'nalgebra', https://crates.io/crates/nalgebra, for high performance Vector and Matrix operations.

To Do

A list of additions and improvements:

  • Tensor Outer Product
  • Scalar Multiplication and Addition
  • Tensor Addition and Subtration
  • Tensor Conversion to nalgebra types

About

A tensor library for Rust

Resources

Stars

16 stars

Watchers

2 watching

Forks

Releases

Packages

Used by

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers"); } } catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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Tensor

Currently, support is only for contravariant Tensors of equal dimension basis vectors.
Also, all Tensors are assumed to use an orthonormal basis (Ex: Euclidean standard basis).

We use the following Tensor definition:

T'α..'β = ( ∂x'α / ∂xγ )..( ∂x'β / ∂xμ ) Tγ..μ

After assuming an orthonormal basis, we know that ( ∂x'α / ∂xγ ) will be zero for all cases α != γ.
and one for α = γ The same is true for other components such as ( ∂x'β / ∂xμ ) with regards to β != μ.

This allows a straight-forward calculation of the outer and inner products of Tensors.

The inner product between two Tensors is currently defined for all Tensor ranks, provided the ranks are equal, and the indices of both Tensors are all of equal dimension. We will gradually ease up on these restrictions.

Example

This code serves as a sketch.

// 3d Rank3 Tensor Examplelet t3 = Tensor::build(3,3,vec![1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);let t = t3.inner_product(&t3);
t.print();

The above code will perform the inner product between t3 and itself, and then print out each component of the final Tensor, t.

A more robust Tensor library is on the way.

Purpose

This library is meant to abstract Tensor math and allow high rank Tensor calculations (Rank > 2). Several individuals use the term 'Tensor' despite using only Vectors and Matrices. We do not encourage this technicality. Though Matrices and Vectors are special cases of Tensors, we do not aim to provide the highest performance for such low ranks. We recommend 'nalgebra', https://crates.io/crates/nalgebra, for high performance Vector and Matrix operations.

To Do

A list of additions and improvements:

  • Tensor Outer Product
  • Scalar Multiplication and Addition
  • Tensor Addition and Subtration
  • Tensor Conversion to nalgebra types

About

A tensor library for Rust

Resources

Stars

16 stars

Watchers

2 watching

Forks

Releases

Packages

Used by

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode"); } } catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); } })(); })();
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Tensor

Currently, support is only for contravariant Tensors of equal dimension basis vectors.
Also, all Tensors are assumed to use an orthonormal basis (Ex: Euclidean standard basis).

We use the following Tensor definition:

T'α..'β = ( ∂x'α / ∂xγ )..( ∂x'β / ∂xμ ) Tγ..μ

After assuming an orthonormal basis, we know that ( ∂x'α / ∂xγ ) will be zero for all cases α != γ.
and one for α = γ The same is true for other components such as ( ∂x'β / ∂xμ ) with regards to β != μ.

This allows a straight-forward calculation of the outer and inner products of Tensors.

The inner product between two Tensors is currently defined for all Tensor ranks, provided the ranks are equal, and the indices of both Tensors are all of equal dimension. We will gradually ease up on these restrictions.

Example

This code serves as a sketch.

// 3d Rank3 Tensor Examplelet t3 = Tensor::build(3,3,vec![1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);let t = t3.inner_product(&t3);
t.print();

The above code will perform the inner product between t3 and itself, and then print out each component of the final Tensor, t.

A more robust Tensor library is on the way.

Purpose

This library is meant to abstract Tensor math and allow high rank Tensor calculations (Rank > 2). Several individuals use the term 'Tensor' despite using only Vectors and Matrices. We do not encourage this technicality. Though Matrices and Vectors are special cases of Tensors, we do not aim to provide the highest performance for such low ranks. We recommend 'nalgebra', https://crates.io/crates/nalgebra, for high performance Vector and Matrix operations.

To Do

A list of additions and improvements:

  • Tensor Outer Product
  • Scalar Multiplication and Addition
  • Tensor Addition and Subtration
  • Tensor Conversion to nalgebra types

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A tensor library for Rust

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