Hello Trideep Majumdar

Yes, I’m familiar with MCR-ALS (Multivariate Curve Resolution Alternating Least Squares)! It’s a great matrix decomposition method used especially in chemometrics to resolve overlapping signals in spectroscopic data — extracting both pure component spectra and their concentration profiles over variables like temperature or time.

How to do MCR-ALS in MATLAB, Python, or R:

• MATLAB: There’s a popular toolbox called MCR-ALS GUI available on MATLAB File Exchange. It provides an interactive interface and functions to perform MCR-ALS. You can also implement it from scratch using alternating least squares iterations with non-negativity constraints.
• Python: The pyMCR package is designed specifically for MCR-ALS. It’s open-source and easy to use. You can install it via pip (pip install pyMCR). It supports constraints like non-negativity and closure, and you can find examples in their GitHub repo: https://github.com/pyMCR/pyMCR
• R: While R doesn’t have as many dedicated MCR-ALS packages, you can use optimization packages (like nnls for non-negative least squares) to build your own MCR-ALS routines. Alternatively, some users export data to Python or MATLAB for more straightforward implementations.

Below are the basic step how to do in Matlab and Python.

🧰 MATLAB

✅ Option 1: Use the MCR-ALS GUI Toolbox

• Download from MathWorks File Exchange
• Easy GUI-based interface.
• Designed for chemometric datasets (UV-Vis, Raman, IR, etc.).

Steps:

✅ Option 2: Manual Implementation (Coding)

Here’s a basic manual outline:

matlabCopyEdit% Load your data matrix D (samples x variables) D = load('your_data.txt'); % Initial estimates (e.g., from PCA or known spectra) S_init = rand(size(D,2), 3); % 3 components % Alternating Least Squares (ALS) loop for i = 1:100 % Max iterations C = lsqnonneg(S_init, D'); % Solve for C S = lsqnonneg(C, D); % Solve for S S_init = S; end % Plot results plot(S') % Pure component spectra figure plot(C) % Concentration profiles

🐍 Python with pyMCR

✅ Step 1: Installation

bashCopyEditpip install pyMCR

✅ Step 2: Sample Python Code

pythonCopyEditimport numpy as np from pyMCR.mcr import McrAR from pyMCR.constraints import ConstraintNonneg # Load your data matrix D (e.g., absorbance matrix) D = np.loadtxt("your_data.txt") # Rows: samples, Columns: wavelengths # Initialize MCR-ALS with non-negativity constraint mcrar = McrAR(c_regr='NNLS', st_regr='NNLS', c_constraints=[ConstraintNonneg()], st_constraints=[ConstraintNonneg()]) # Choose number of components (e.g., 3) mcrar.fit(D, n_components=3) # Access results pure_spectra = mcrar.ST_ # (Variables x Components) concentrations = mcrar.C_ # (Samples x Components) # Plot or analyze results import matplotlib.pyplot as plt plt.plot(pure_spectra) plt.title("Pure Component Spectra") plt.show() plt.plot(concentrations) plt.title("Concentration Profiles") plt.show()

📘 Documentation & Tutorials:

• Official: https://pyMCR.readthedocs.io
• GitHub with real examples: https://github.com/pyMCR/pyMCR

MCR-ALS is a chemometric technique used to decompose complex multivariate data (like spectroscopic data from chemical mixtures) into a set of "pure" component profiles (e.g., spectra) and their corresponding concentration profiles over time or space. The "alternating least squares" part refers to an iterative optimization algorithm that alternates between estimating the pure component profiles and the concentration profiles until convergence.

Here's a breakdown of how to approach MCR-ALS in MATLAB, Python, and R, along with considerations:

Core Concept of MCR-ALS

Imagine you have a series of measurements (e.g., UV-Vis spectra) taken from a chemical reaction over time. Each spectrum is a mixture of the individual components (reactants, intermediates, products). MCR-ALS aims to:

• Resolve the pure spectrum of each component.
• Determine the concentration of each component at every measurement point.

It does this by decomposing the data matrix D (where rows are measurements, columns are variables like wavelength) into the product of a concentration matrix C and a pure component spectra matrix ST:

D=CST

During the iterative process, various constraints can be applied to C and S (e.g., non-negativity, unimodality, closure, known profiles) to ensure physically meaningful solutions and improve convergence.

How to do MCR-ALS in MATLAB, Python, or R

While the core algorithm is the same, the implementation and available libraries vary.

1. MATLAB

MATLAB has a strong history in chemometrics, and it's quite common to find MCR-ALS implementations here.

• Dedicated Toolboxes:PLS_Toolbox (Eigenvector Research, Inc.): This is the gold standard for chemometrics in MATLAB. It includes a highly robust and feature-rich MCR-ALS function (mcr_als) with extensive options for constraints, cross-validation, and visualization. It's a commercial toolbox, but widely used in industry and academia. Raman Toolbox (e.g., RAMAN_Toolbox): Some specialized toolboxes for spectroscopic data analysis might include MCR-ALS.
• Custom Implementation:You can certainly implement the MCR-ALS algorithm yourself in MATLAB. This is often done for research or educational purposes to understand the mechanics.Basic Algorithm Steps (Conceptual):Initialize: Estimate initial concentration profiles (C) or pure component spectra (S). This is often done using techniques like PCA, SIMPLISMA, or EFA. Iterate (Alternating Least Squares):Step 1 (Estimate S): Given D and current C, estimate S by solving D = C * S_transpose (e.g., S_transpose = pinv(C) * D). Apply constraints to S. Step 2 (Estimate C): Given D and new S, estimate C by solving D = C * S_transpose (e.g., C = D * pinv(S_transpose)). Apply constraints to C. Repeat until C and S converge (e.g., change in explained variance or profiles falls below a threshold). Evaluate: Check the residuals, explained variance, and plausibility of the resolved profiles. Example (Conceptual MATLAB Code Snippet without actual implementation):Matlab% D: your experimental data matrix (e.g., spectra, time points x wavelengths) % n_components: number of pure components to resolve % 1. Initialization (e.g., using PCA for initial C) % [U, S_val, V] = svd(D); % C_initial = U(:, 1:n_components); % Or use SIMPLISMA etc. % 2. MCR-ALS Iteration % C = C_initial; % for iter = 1:max_iterations % % Solve for S_transpose: D = C * S_transpose => S_transpose = pinv(C) * D % S_transpose = C \ D; % More robust than pinv for least squares % % Apply constraints to S (e.g., non-negativity) % S_transpose(S_transpose < 0) = 0; % Example: non-negativity % % Solve for C: D = C * S_transpose => C = D * pinv(S_transpose) % C = D / S_transpose; % More robust % % Apply constraints to C (e.g., non-negativity, closure, unimodality) % C(C < 0) = 0; % Example: non-negativity % % Check for convergence (e.g., change in C or S, or explained variance) % % if converged, break % end % result_C = C; % result_S = S_transpose'; % Transpose back to get S

2. Python

Python has rapidly become a powerful environment for scientific computing and chemometrics, with several libraries supporting MCR-ALS.

• PyImSp (Python Imaging Spectroscopy): This library (formerly PyMCR) is specifically designed for MCR-ALS and related techniques, particularly in the context of imaging spectroscopy. It's well-maintained and provides robust implementations of various constraints.Installation: pip install pyimsp Usage:Pythonfrom pyimsp.mcr import MCR import numpy as np import matplotlib.pyplot as plt # Example data (replace with your actual data) # D: your experimental data matrix (rows: observations/time, cols: variables/wavelengths) # For demonstration: create some synthetic data np.random.seed(0) n_observations = 100 n_variables = 50 n_components = 2 # Synthetic pure spectra s1 = np.sin(np.linspace(0, 10, n_variables)) + 1 s2 = np.exp(-np.linspace(0, 5, n_variables)) S_true = np.array([s1, s2]) # Synthetic concentrations c1 = np.linspace(0, 1, n_observations) c2 = 1 - c1 C_true = np.array([c1, c2]).T D = np.dot(C_true, S_true) + np.random.normal(0, 0.1, (n_observations, n_variables)) # Initialize MCR object mcr_obj = MCR(n_components=n_components) # Fit the model mcr_obj.fit(D, st_constraints=[['non_neg']], c_constraints=[['non_neg']]) # Access results C_resolved = mcr_obj.C_opt S_resolved = mcr_obj.ST_opt.T # Transpose back for spectra in rows print("Resolved Concentrations (first 5 rows):\n", C_resolved[:5]) print("\nResolved Spectra (first component):\n", S_resolved[0, :5]) # Plotting (optional) plt.figure(figsize=(12, 5)) plt.subplot(121) plt.plot(C_resolved) plt.title('Resolved Concentrations') plt.xlabel('Observation') plt.ylabel('Concentration') plt.subplot(122) plt.plot(S_resolved.T) # Transpose for plotting spectra plt.title('Resolved Pure Spectra') plt.xlabel('Variable (Wavelength)') plt.ylabel('Intensity') plt.tight_layout() plt.show()
• sklearn_chemo: This library aims to provide scikit-learn compatible chemometric tools, including MCR-ALS. It's built on top of scikit-learn's conventions.Installation: pip install sklearn-chemo Usage: Similar to pyimsp but follows scikit-learn's fit/transform API.
• Custom Implementation (using NumPy/SciPy): You can also implement MCR-ALS from scratch using NumPy for array operations and SciPy for linear algebra functions (scipy.linalg.lstsq for least squares, scipy.linalg.pinv for pseudoinverse). This gives you maximum control.

3. R

R is widely used in statistics and increasingly in chemometrics.

• mdatools package: This is a comprehensive package for multivariate data analysis, including MCR-ALS.Installation: install.packages("mdatools") Usage:Rlibrary(mdatools) library(ggplot2) # For plotting # Example data (replace with your actual data) # D: your experimental data matrix (rows: observations/time, cols: variables/wavelengths) set.seed(0) n_observations
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