`cholesky_corr_free` accepts matrices that are not correlation Cholesky factors

[sims1253]

cholesky_corr_free only checks squareness. A lower-triangular matrix with positive diagonal but non-unit row norms is accepted, and the round trip returns a different matrix:

Eigen::MatrixXd L(2, 2);
L << 1, 0, 0.5, 0.5;                    // row 2 norm is sqrt(0.5), not 1
Eigen::VectorXd z = stan::math::cholesky_corr_free(L);   // no throw
// z = [0.549306]  (= atanh(0.5))
Eigen::MatrixXd back = stan::math::cholesky_corr_constrain(z, 2);
// back(1,1) = 0.866025  — not the 0.5 in the input

There is a comment in the source noting the missing validation (// should validate lower-triangular, unit lengths), and check_cholesky_factor_corr already exists and is the natural seam.

Reachable from user code through the unconstraining path, same as #3379

Environment:

• Ubuntu 22.04.5 LTS (WSL2, kernel 6.18.33.2-microsoft-standard-WSL2), x86_64
• stan-dev/math develop @ d20b238
• g++ 11.4.0 (Ubuntu 22.04), -std=c++17

Related to #1700 (cholesky_corr_* housekeeping ask, closed without a fix). The in-source comment above is still unresolved.

[SteveBronder]

This would be a pretty expensive check each call. I'm not sure if we should have this check for the user facing code or assume the user is going to pass in the correct matrix type. Have to think about this

[WardBrian]

This would be a pretty expensive check each call. I'm not sure if we should have this check for the user facing code or assume the user is going to pass in the correct matrix type. Have to think about this

The only places this is called is when initializing or when the user calls it, both are reasonable places to have a check IMO. I don't think anyone will be calling this in a hot loop