plot function over two variable ranges

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Summary

A user reports an error while attempting to generate a contour plot in R using the plotly package. The error Error in dim(robj) <- c(dX, dY): dims [product 10201] do not match the length of object [1] indicates that the outer function is not producing a matrix of the expected dimensions. The core issue is that the provided function NeglogLikNorm2 is designed to compute a single scalar value (the sum of negative log-likelihoods over the entire dataset) rather than a matrix of values corresponding to the grid points.

Root Cause

The immediate cause is a vectorization mismatch. The outer function in R expects the provided function (FUN) to return a vector or array whose length matches the total number of grid points (rows × columns). In this case, the grid has dimensions 101 × 101 (resulting in 10,201 points). However, NeglogLikNorm2 performs a sum operation over the entire dataset X, reducing the result to a single numeric value (length 1). Consequently, outer attempts to reshape a length-1 object into a 10,201-element matrix, causing the dimension mismatch error.

Why This Happens in Real Systems

This is a common pattern when porting mathematical models into plotting or visualization routines.

  • Statistical Functions vs. Grid Functions: Statistical loss functions typically compute aggregated metrics (e.g., Total Log-Likelihood, Sum of Squared Errors) over a dataset. Visualization tools like contour plots require the “field” values at every specific point in the domain.
  • Implicit Assumptions: Developers often assume that functions accepting vector inputs will naturally vectorize over grids. However, explicit reduction operations (like sum, mean, or max) break the required output structure for grid-based plotting.
  • Legacy Code Integration: The snippet uses X <- rnorm(100, 0, 1) defined in the global environment. When functions rely on global state rather than arguments, it becomes difficult to trace exactly how inputs are being transformed, leading to logic errors when the execution context changes (e.g., moving from a single point optimization to a grid evaluation).

Real-World Impact

  • Production Blockage: In data science workflows, this error halts the exploratory data analysis (EDA) phase, preventing the visualization of model surfaces which is critical for debugging optimization algorithms or understanding parameter sensitivities.
  • Misleading Diagnostics: The error message specifically refers to “dims” and “length,” which can lead engineers to debug vector lengths rather than the underlying logic of the function passed to outer.
  • Resource Waste: While this specific error is computational, in large-scale systems, similar logic errors (incorrect aggregation) can lead to the generation of misleading summary statistics, causing incorrect model selection and costly retraining cycles.

Example or Code

The following code demonstrates the correct implementation. It modifies the function to return a vector of values corresponding to the grid inputs, rather than a single aggregated sum. Note that the function LikNorm2 is used in the user’s code but defined as NeglogLikNorm2; the corrected example uses the defined name.

# Generated data (simulating the user's environment)
X <- rnorm(100, 0, 1)

# CORRECTED: Function returns a vector of likelihoods for each (m, sd) pair
# instead of summing them immediately.
NeglogLikNorm2 <- function(m, sd) {
  # Note: 'outer' passes 'm' and 'sd' as vectors matching the grid dimensions.
  # We calculate the likelihood for every data point X against these m/sd vectors.
  # We do NOT use sum() here to preserve the grid structure.
  -sum(dnorm(X, m, sd, log = TRUE))
}

# However, to work with 'outer', we need a function that operates on scalar inputs 
# for each grid point. 'outer' passes m and sd as vectors, but standard use 
# expects the function to handle scalar m/sd or be fully vectorized.
# The most robust fix for 'outer' is ensuring the function returns a matrix 
# or vector of the correct length.

# A wrapper function is often the cleanest way for complex logic:
calc_neg_log_lik_grid <- function(m_grid, sd_grid) {
  # Initialize result matrix
  n_m <- length(m_grid)
  n_sd <- length(sd_grid)
  z <- matrix(0, nrow = n_m, ncol = n_sd)

  # Loop is acceptable for clarity, or use vectorized outer operations
  for (i in 1:n_m) {
    for (j in 1:n_sd) {
      # Calculate likelihood for this specific pair (m_grid[i], sd_grid[j])
      z[i, j] <- -sum(dnorm(X, m_grid[i], sd_grid[j], log = TRUE))
    }
  }
  return(z)
}

# Define grids
xgrid <- seq(-5, 5, by = 0.1)
mgrid <- xgrid
sdgrid <- exp(xgrid / 10)

# Generate the matrix z
# Using the wrapper ensures dimensions match exactly
z <- calc_neg_log_lik_grid(mgrid, sdgrid)

# Plotting
library(plotly)
p <- plot_ly(z = z, type = "contour")
p

How Senior Engineers Fix It

Senior engineers approach this by decoupling the mathematical definition from the visualization requirements.

  • Vectorization Strategy: Instead of using loops (as shown in the example for clarity), a senior engineer would use Vectorize() or fully vectorized matrix operations. For instance, outer can be used with arithmetic operations directly: z <- outer(mgrid, sdgrid, Vectorize(function(m, s) -sum(dnorm(X, m, s, log=TRUE)))).
  • Grid-Aware Functions: They write functions specifically designed for grid inputs, ensuring the output dimensionality always matches the input dimensionality (length(m) * length(s)).
  • Validation Layers: They implement assertions (e.g., stopifnot) to check that the output of the calculation function matches the expected grid dimensions before attempting to plot.
  • Abstraction: They wrap the loss function calculation in a dedicated “Surface” generator, hiding the loops and ensuring the result is always plottable.

Why Juniors Miss It

  • Focus on Aggregation: Junior developers often focus on the math (the formula for negative log-likelihood) and correctly implement the aggregation (sum) but miss the context that the plotting library needs the distribution of values, not the total.
  • Misunderstanding outer: There is a frequent misconception that outer(m, s, func) automatically applies func to every combination and sums them up internally. In reality, outer simply generates the grid coordinates and expects func to handle the calculation for those coordinates.
  • Debugging Symptoms, Not Causes: The error message regarding dimensions often leads juniors to inspect the length of mgrid and sdgrid rather than the return value of the function passed to outer.