TypeError: Dimensions of C Mismatch in NumPy / SciPy

Verified FixPython 3.10+NumPy 1.24+Silo: numpy

Quick Fix / Solution Rapide

Verify that matrix dimensions conform to linear algebra rules and use np.broadcast_to() or .reshape() to align array shapes.

Root Cause Analysis

This error occurs when Python tries to execute a mathematical matrix operation, contour visualization, or linear system solve where matrix C or parameter C has dimensions incompatible with operands A and B.

1. Matrix Incompatibility in Linear Algebra Operations

In linear algebra computations of the form C = A @ B or C + A @ B, the resulting matrix C must have exact dimensions matching (A.shape[0], B.shape[1]). When custom solvers or SciPy wrappers receive a pre-allocated matrix C with mismatched rows or columns, a dimension mismatch error is raised.

2. 1D vs 2D Array Confusion in Solvers

A common scenario occurs when passing a 1D column vector of shape (N, 1) or (N,) into an algorithm expecting a 2D matrix of shape (N, N) or vice-versa. NumPy and underlying BLAS routines strictly enforce dimension consistency.

3. Matplotlib and SciPy Contour Grid Parameters

In plotting libraries and contour evaluators where C represents a 2D scalar field evaluated over grid coordinates X and Y, passing a 1D or transposed array C results in a dimension mismatch with coordinate axes.

4. Transposition and Slicing Errors

Omitting matrix transposition (e.g., forgetting .T after matrix decomposition or filtering) causes column counts to swap with row counts, producing incompatible dimensions.

Reproduction Code (MCVE)

Example: Bug Reproduction

import numpy as np

def evaluate_linear_system(A, B, C):
    expected_shape = (A.shape[0], B.shape[1])
    if C.shape != expected_shape:
        raise TypeError(f'Dimensions of C {C.shape} do not match expected shape {expected_shape}')
    return np.dot(A, B) + C

A = np.ones((50, 10))
B = np.ones((10, 50))
C = np.ones((50, 1))  # Incompatible shape (50, 1) instead of (50, 50)
evaluate_linear_system(A, B, C)

Solution 1: Align Matrix C with Expected Shape Using np.broadcast_to

Ensure array C matches the shape of A @ B either by initializing the correct output matrix or using broadcasting.

Example: Recommended Solution

import numpy as np

def evaluate_linear_system(A, B, C):
    expected_shape = (A.shape[0], B.shape[1])
    if C.shape != expected_shape:
        C = np.broadcast_to(C, expected_shape)
    return np.dot(A, B) + C

A = np.ones((50, 10))
B = np.ones((10, 50))
C = np.ones((50, 1))
result = evaluate_linear_system(A, B, C)
print(f'Computed successfully with shape: {result.shape}')

Solution 2: Initialize C Explicitly with Output Dimensions

Directly instantiate C with the exact shape required for the matrix product.

Example: Alternative Solution

import numpy as np

A = np.ones((50, 10))
B = np.ones((10, 50))
C = np.zeros((A.shape[0], B.shape[1]))
result = np.matmul(A, B) + C
print(f'Matrix computed with exact matching dimensions: {result.shape}')

Developers frequently mistake 1D arrays of shape (N,) for 2D column vectors of shape (N, 1). In NumPy, 1D arrays broadcast differently across multidimensional matrix operations than true 2D matrices. Always inspect .shape and .ndim before passing matrices into linear algebra subroutines. When working with grid data (such as meshgrid outputs), passing mismatched coordinate arrays X, Y against values C will trigger dimension errors unless indexing='ij' or indexing='xy' is chosen consistently. Contrasting this error with ValueError: shapes (A, B) and (C, D) not aligned, the TypeError in custom wrappers typically indicates a type or shape contract validation check rather than an internal core BLAS computation failure.

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