From 4047a43539be76ad838f937051da5f701fcac0c4 Mon Sep 17 00:00:00 2001
From: BhaktiVagadia <bhakti.vagadia@gmail.com>
Date: Thu, 7 May 2026 12:28:33 +0530
Subject: [PATCH 1/2] add QR Decomposition of matrix in linear algebra

---
 linear_algebra/qr_decomposition.py | 92 ++++++++++++++++++++++++++++++
 1 file changed, 92 insertions(+)
 create mode 100644 linear_algebra/qr_decomposition.py

diff --git a/linear_algebra/qr_decomposition.py b/linear_algebra/qr_decomposition.py
new file mode 100644
index 000000000000..a76408c0f4ae
--- /dev/null
+++ b/linear_algebra/qr_decomposition.py
@@ -0,0 +1,92 @@
+"""
+In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization,
+is a decomposition of a matrix A into a product A = QR
+of an orthonormal matrix Q and an upper triangular matrix R.
+QR decomposition is often used to solve the linear least squares (LLS) problem
+and is the basis for a particular eigenvalue algorithm, the QR algorithm.
+
+This algorithm will simply attempt to perform QR decomposition on any square matrix.
+
+Reference: https://en.wikipedia.org/wiki/QR_decomposition
+"""
+
+from __future__ import annotations
+import numpy as np
+from scipy.linalg import qr
+
+def qr_decomposition(A: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """
+    Perform QR decomposition on a given matrix and raises an error if in
+    m×n matrix A if m is smaller than n or m,n is less than 2
+
+    >>> A = np.array([[1, 2, 3], [4, 5, 9], [7, 8, 15]])
+    >>> Q,R = qr_decomposition(A)
+    >>> Q
+    array([[-0.17,  0.9 ,  0.41],
+           [-0.51,  0.28, -0.82],
+           [-0.85, -0.35,  0.41]])
+    >>> R
+    array([[-17.75,  -9.63,  -8.11],
+           [  0.  ,   0.41,  -0.41],
+           [  0.  ,   0.  ,   0.  ]])
+    >>> A = np.array([[1, 2], [4, 5], [7, 8]])
+    >>> Q,R = qr_decomposition(A)
+    >>> Q
+    array([[-0.21,  0.89,  0.41],
+           [-0.52,  0.25, -0.82],
+           [-0.83, -0.38,  0.41]])
+    >>> R
+    array([[-9.64, -8.09],
+           [ 0.  , -0.76],
+           [ 0.  ,  0.  ]])
+    >>> A = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> Q,R = qr_decomposition(A)
+    Traceback (most recent call last):
+        ...
+    ValueError: row size should be greater than column size
+    >>> A = np.array([[1], [4]])
+    >>> Q,R = qr_decomposition(A)
+    Traceback (most recent call last):
+        ...
+    ValueError: row size and column size should be greater than 2
+    >>> A = np.array([[1,4]])
+    >>> Q,R = qr_decomposition(A)
+    Traceback (most recent call last):
+        ...
+    ValueError: row size should be greater than column size
+    """
+
+
+    rows, columns = np.shape(A)
+    if rows < columns:
+        msg = (
+            "row size should be greater than column size"
+        )
+        raise ValueError(msg)
+    if rows < 2 or columns < 2:
+        msg = (
+            "row size and column size should be greater than 2"
+        )
+        raise ValueError(msg)
+    # Perform QR decomposition with pivoting
+    # Q: Orthogonal matrix
+    # R: Upper triangular matrix
+    # P: Pivot indices (permutation vector)
+
+    Q, R, P = qr(A, pivoting=True)
+
+    # Note: The bottom row of R is all zeros because the matrix is rank-deficient.
+    # Verification: A[:, P] should equal Q @ R
+    AP = A[:, P]
+    if(np.allclose(AP, Q @ R)):
+        return np.round(Q,2), np.round(R,2)
+    else:
+        msg = (
+            "No matrix found which decompose given matrix"
+        )
+        raise ValueError(msg)
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

From db844e65e8968a369c5b049c0f08348c0c1f2c77 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 7 May 2026 07:02:49 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 linear_algebra/qr_decomposition.py | 19 +++++++------------
 1 file changed, 7 insertions(+), 12 deletions(-)

diff --git a/linear_algebra/qr_decomposition.py b/linear_algebra/qr_decomposition.py
index a76408c0f4ae..88c248bd3bfd 100644
--- a/linear_algebra/qr_decomposition.py
+++ b/linear_algebra/qr_decomposition.py
@@ -14,6 +14,7 @@
 import numpy as np
 from scipy.linalg import qr
 
+
 def qr_decomposition(A: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
     """
     Perform QR decomposition on a given matrix and raises an error if in
@@ -56,17 +57,12 @@ def qr_decomposition(A: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
     ValueError: row size should be greater than column size
     """
 
-
     rows, columns = np.shape(A)
     if rows < columns:
-        msg = (
-            "row size should be greater than column size"
-        )
+        msg = "row size should be greater than column size"
         raise ValueError(msg)
     if rows < 2 or columns < 2:
-        msg = (
-            "row size and column size should be greater than 2"
-        )
+        msg = "row size and column size should be greater than 2"
         raise ValueError(msg)
     # Perform QR decomposition with pivoting
     # Q: Orthogonal matrix
@@ -78,14 +74,13 @@ def qr_decomposition(A: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
     # Note: The bottom row of R is all zeros because the matrix is rank-deficient.
     # Verification: A[:, P] should equal Q @ R
     AP = A[:, P]
-    if(np.allclose(AP, Q @ R)):
-        return np.round(Q,2), np.round(R,2)
+    if np.allclose(AP, Q @ R):
+        return np.round(Q, 2), np.round(R, 2)
     else:
-        msg = (
-            "No matrix found which decompose given matrix"
-        )
+        msg = "No matrix found which decompose given matrix"
         raise ValueError(msg)
 
+
 if __name__ == "__main__":
     import doctest