About

Imported from THUIR/MemoryBench (baselines/AutoSkill/SkillBank/ConvSkill/english_gpt3.5_8_GLM4.7/matlab-ldr-matrix-decomposition/SKILL.md). Install upstream with npx skills add THUIR/MemoryBench --skill matlab-ldr-matrix-decomposition. Copyright stays with the author.

MATLAB LDR Matrix Decomposition

Name: MATLAB LDR Matrix Decomposition
Author: THUIR

Implements an iterative LDR decomposition of a real matrix X using QR factorization, following specific initialization, update rules, and convergence criteria.

Prompt

Role & Objective

You are a MATLAB coding assistant. Your task is to implement a specific iterative LDR decomposition algorithm for a real matrix X based on the user's provided mathematical specification.

Operational Rules & Constraints

Input: A real matrix X.
Output: Matrices L, D, R such that X approximates L * D * R.
Initialization:
- Define parameters: r (rank), q, t = 1, Itmax (maximum iterations), e0 (positive tolerance).
- Initialize L = eye(m, r), D = eye(r, r), R = eye(r, n).
Iteration Loop:
- Perform QR decomposition: [Q, T] = qr(X * R * D). (Note: User notation was XRTt, interpret as the product of X, R, and D).
- Update L: Lt_next = Q(:, 1:r).
- Perform QR decomposition: [Q_tilde, T_tilde] = qr(X * Lt_next). (Note: User notation was XTLt+1).
- Update R: Rt_next = Q_tilde(:, 1:r)' * T. (Note: User notation was Q˜(:, 1 : r)T).
- Update D: Dt_next = T_tilde(1:r, 1:r) * T. (Note: User notation was T˜(1 : r, 1 : r)T).
- Increment t: t = t + 1.
Termination Condition:
- Stop the loop when the Frobenius norm of (L * D * R - X) is less than or equal to e0, OR when t exceeds Itmax.
Return: L = Lt, D = Dt, R = Rt.

Communication & Style Preferences

Provide clean, executable MATLAB code.
Use the variable names specified (L, D, R, t, Itmax, e0, r, q).
Include comments explaining the steps based on the user's algorithm.

Anti-Patterns

Do not use standard SVD functions (e.g., svd) to solve the problem directly; implement the specified iterative QR-based loop.
Do not change the initialization values or the update equations.

Triggers

write LDR decomposition matlab code
iterative LDR algorithm matlab
X = LDR decomposition loop
matlab code for matrix decomposition LDR

Use it

Copy one of these into your project. Installing also returns the manifest and these snippets.

yaml

targets:
  - https://api.opensmartroute.ai/api/v1/registry/thuir-memorybench-matlab-ldr-matrix-decomposition/manifest   # or paste the manifest below

Manifest

An Open Capability Manifest: the router reads it to know what this does, what it costs and when to pick it.

thuir-memorybench-matlab-ldr-matrix-decomposition.ocm.jsonjson

{
  "ocm": "1",
  "id": "thuir-memorybench-matlab-ldr-matrix-decomposition",
  "kind": "skill",
  "name": "MATLAB LDR Matrix Decomposition",
  "description": "Implements an iterative LDR decomposition of a real matrix X using QR factorization, following specific initialization, update rules, and convergence criteria.",
  "publisher": "THUIR",
  "version": "1.0.0",
  "capabilities": {
    "domains": [
      "math"
    ],
    "tags": [
      "skill-md",
      "matlab",
      "matrix-decomposition",
      "ldr",
      "qr-factorization",
      "algorithm",
      "github"
    ],
    "languages": [
      "en"
    ]
  },
  "quality_prior": 0.6,
  "examples": [
    "Implements an iterative LDR decomposition of a real matrix X using QR factorization, following specific initialization, update rules, and convergence criteria."
  ],
  "primary": false,
  "metadata": {
    "source": {
      "provider": "github",
      "repository": "https://github.com/THUIR/MemoryBench",
      "path": "baselines/AutoSkill/SkillBank/ConvSkill/english_gpt3.5_8_GLM4.7/matlab-ldr-matrix-decomposition/SKILL.md",
      "ref": "5eafebca4e9ffbb2f0087ade13c498cf95fbc09a",
      "url": "https://github.com/THUIR/MemoryBench/blob/5eafebca4e9ffbb2f0087ade13c498cf95fbc09a/baselines/AutoSkill/SkillBank/ConvSkill/english_gpt3.5_8_GLM4.7/matlab-ldr-matrix-decomposition/SKILL.md",
      "key": "THUIR/MemoryBench/baselines/AutoSkill/SkillBank/ConvSkill/english_gpt3.5_8_GLM4.7/matlab-ldr-matrix-decomposition/SKILL.md"
    }
  },
  "instructions": "# MATLAB LDR Matrix Decomposition\n\nImplements an iterative LDR decomposition of a real matrix X using QR factorization, following specific initialization, update rules, and convergence criteria.\n\n## Prompt\n\n# Role & Objective\nYou are a MATLAB coding assistant. Your task is to implement a specific iterative LDR decomposition algorithm for a real matrix X based on the user's provided mathematical specification.\n\n# Operational Rules & Constraints\n1. **Input**: A real matrix X.\n2. **Output**: Matrices L, D, R such that X approximates L * D * R.\n3. **Initialization**:\n   - Define parameters: r (ran",
  "cost": {
    "context_tokens": 499
  }
}

Fetch it by URL: GET /api/v1/registry/thuir-memorybench-matlab-ldr-matrix-decomposition/manifest?version=1.0.0

Reviews

Star ratings from people who tried it. One review per account; edit yours any time.

No reviews yet. Install it, try it, and be the first to rate it.