/// @file
/// Test Simultaneous Diagonalization
/// \test Simultaneous Diagonalization
#include <ceed.h>
#include <math.h>

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

  CeedInit(argv[1], &ceed);

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

  CeedSimultaneousDiagonalization(ceed, K, M, X, lambda, P);

  // Check X^T M X = I
  CeedScalar work[P*P];
  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 += M[P*i+k]*X[P*k+j];
      work[P*i+j] = sum;
    }
  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 += X[P*k+i]*work[P*k+j];
      M[P*i+j] = sum;
    }
  for (int i=0; i<P; i++)
    for (int j=0; j<P; j++)
      if (fabs(M[P*i+j] - (i == j ? 1.0 : 0.0)) > 1E-14)
        // LCOV_EXCL_START
        printf("Error in diagonalization of M [%d, %d]: %f != %f\n",
               i, j, M[P*i+j], (i == j ? 1.0 : 0.0));
  // LCOV_EXCL_STOP

  // Check X^T K X = Lamda
  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 += K[P*i+k]*X[P*k+j];
      work[P*i+j] = sum;
    }
  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 += X[P*k+i]*work[P*k+j];
      K[P*i+j] = sum;
    }
  for (int i=0; i<P; i++)
    for (int j=0; j<P; j++)
      if (fabs(K[P*i+j] - (i == j ? lambda[i] : 0.0)) > 1E-14)
        // LCOV_EXCL_START
        printf("Error in diagonalization of K [%d, %d]: %f != %f\n",
               i, j, K[P*i+j], (i == j ? lambda[i] : 0.0));
  // LCOV_EXCL_STOP

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