/// @file
/// Test Symmetric Schur Decomposition
/// \test Test Symmetric Schur Decomposition
#include <ceed.h>
#include <ceed/backend.h>
#include <math.h>

int main(int argc, char **argv) {
  Ceed ceed;
  CeedInt P = 4;
  CeedScalar M[16], Q[16], lambda[4], Q_lambda_Qt[16];
  CeedBasis basis;

  CeedInit(argv[1], &ceed);

  // Create mass matrix
  CeedBasisCreateTensorH1Lagrange(ceed, 1, 1, P, P, CEED_GAUSS, &basis);
  const CeedScalar *interp, *quad_weights;
  CeedBasisGetInterp(basis, &interp);
  CeedBasisGetQWeights(basis, &quad_weights);
  for (int i=0; i<P; i++)
    for (int j=0; j<P; j++) {
      CeedScalar sum = 0;
      for (int k=0; k<P; k++)
        sum += interp[P*k+i]*quad_weights[k]*interp[P*k+j];
      M[P*i+j] = sum;
      Q[P*i+j] = sum;
    }

  CeedSymmetricSchurDecomposition(ceed, Q, lambda, P);

  // Check diagonalization of M
  for (int i=0; i<P; i++)
    for (int j=0; j<P; j++) {
      CeedScalar sum = 0;
      for (int k=0; k<P; k++)
        sum += Q[P*i+k]*lambda[k]*Q[P*j+k];
      Q_lambda_Qt[P*i+j] = sum;
    }
  for (int i=0; i<P; i++)
    for (int j=0; j<P; j++)
      if (fabs(M[P*i+j] - Q_lambda_Qt[P*i+j]) > 1E-14)
        // LCOV_EXCL_START
        printf("Error in diagonalization [%d, %d]: %f != %f\n",
               i, j, M[P*i+j], Q_lambda_Qt[P*i+j]);
  // LCOV_EXCL_STOP

  CeedBasisDestroy(&basis);
  CeedDestroy(&ceed);
  return 0;
}