mata ''=' found where '(' expected'

[sophie jane]

hi, i am trying to run sign restriction using mata:

mata:
void print_matrix(string name, real matrix M) {
printf("%s: %f x %f\n", name, rows(M), cols(M))
for (i = 1; i <= rows(M); i++) {
for (j = 1; j <= cols(M); j++) {
printf("%8.4f ", M[i, j])
}
printf("\n")
}
printf("\n")
}

// Function to perform Gram-Schmidt orthogonalization
real matrix orthogonalize(real matrix X) {
real scalar n
real matrix O
n = rows(X)
O = X

for (i = 1; i <= n; i++) {
// Normalize column i
norm_i = sqrt(sum(O[,i] :* O[,i]))
if (norm_i == 0) {
printf("Error: Column %f has zero norm. Cannot normalize.\n", i)
exit()
}
O[,i] = O[,i] / norm_i

// Remove projection of column i from subsequent columns
for (j = i + 1; j <= n; j++) {
projection = O[,j]' * O[,i]
O[,j] = O[,j] - projection * O[,i]
}
}

return(O)
}

// Function to apply random rotation
real matrix random_rotation(real matrix A, real matrix Q) {
printf("Entering random_rotation function\n")

if (rows(A) == 0 | cols(A) == 0) {
printf("Error: Matrix A is empty or undefined.\n")
exit()
}

print_matrix("Matrix A", A)

// Generate random matrix R
R = runiform(rows(A), rows(A)) + I(rows(A))
R = (R + R') / 2 // Make R symmetric
R = R + 0.1 * I(rows(R)) // Stabilize further
print_matrix("Matrix R (before orthogonalization)", R)

// Rescale R
R = R / max(R)
print_matrix("Rescaled Matrix R", R)

// Ensure R is valid
if (rows(R) != cols(R)) {
printf("Error: Matrix R is not square. Cannot perform orthogonalization.\n")
exit()
}

cond_R = cond(R)
printf("Condition number of R: %f\n", cond_R)

// Perform Gram-Schmidt orthogonalization
Q = orthogonalize(R)
print_matrix("Orthogonal Matrix Q", Q)

// Validate Q for invalid values
if (any(Q :!= Q) | any(abs(Q) :> 1e10)) {
printf("Error: Matrix Q contains invalid values (NaN, Inf, or excessively large values).\n")
exit()
}
P = Q * Q'
print_matrix("Orthogonality Check (P = Q * Q')", P)

// Calculate rotated matrix
R_rot = A * Q'
print_matrix("Rotated Matrix R_rot", R_rot)

return(R_rot)
}

// Import covariance matrix
S = st_matrix("V") // Import covariance matrix
if (rows(S) != cols(S)) { // Ensure S is square
printf("Error: Covariance matrix S is not square!\n")
exit() // Exit Mata session
}
printf("Dimensions of S: %f x %f\n", rows(S), cols(S))

A = cholesky(S) // Perform Cholesky decomposition
printf("Dimensions of A: %f x %f\n", rows(A), cols(A))

// Test random rotation
/*R_rot = random_rotation(A) // Apply random rotation
printf("Dimensions of R_rot: %f x %f\n", rows(R_rot), cols(R_rot))
*/


// Apply sign restrictions
restrictions = (1, -1, 1, 1) // Example restrictions
real matrix Q = .
for (i = 1; i <= 1000; i++) {

R_rot = random_rotation(A,Q) // Generate rotated matrix

// Debugging: Verify A and Q remain unchanged
printf("Iteration %d:\n", i)
print_matrix("Matrix A (Inside Loop)", A)
print_matrix("Matrix Q (Inside Loop)", Q)
print_matrix("Matrix Q' (Transpose of Q)", Q')

// Check dimensions
printf("Dimensions of A: %f x %f\n", rows(A), cols(A))
printf("Dimensions of Q': %f x %f\n", rows(Q'), cols(Q'))
printf("Dimensions of R_rot: %f x %f\n", rows(R_rot), cols(R_rot))

// Debug sign restrictions
print_matrix("R_rot[:,1]", R_rot[,1])
print_matrix("Restrictions", restrictions)

// Check sign restrictions
if (all((R_rot[,1]:*restrictions) >= 0)) { // Check restrictions
st_matrix("Identified", R_rot) // Save identified matrix
break
}
}
end

and the error says that
'=' found where '(' expected
(25 lines skipped)
---------------------------
after real matrix Q = .
and if I clear out mata and do the basic calculation, it doesn't seem to work.

for example,
mata:
real matrix Q = J(4, 4, 0)
end

gives me an error message as ''=' found where '(' expected'.
but the fact that "=" doesn't work is akward since I used = correctly before.
example: A = cholesky(S) <- nothing wrong happened.

if I replace real matrix Q = . with real matrix Q,
it also does not work. but it worked well with making Gram-Schmidt orthogonalization function.

what is the thing that I am misunderstanding? I am confused.
Thank you for your help in advance.

[John Mullahy]

When you specify "real matrix" what follows is expecting a function definition or declaration, not an assignment. See

help [M-2] declarations

For example:

mata:

Q = J(4, 4, 8)

Q

real matrix Q(n) return(J(n,n,2*n))

Q(4)


end

which gives

:
: Q = J(4, 4, 8)

:
: Q
[symmetric]
       1   2   3   4
    +-----------------+
  1 |  8              |
  2 |  8   8          |
  3 |  8   8   8      |
  4 |  8   8   8   8  |
    +-----------------+

:
: real matrix Q(n) return(J(n,n,2*n))

:
: Q(4)
[symmetric]
       1   2   3   4
    +-----------------+
  1 |  8              |
  2 |  8   8          |
  3 |  8   8   8      |
  4 |  8   8   8   8  |
    +-----------------+