/* nag_dbdsdc (f08mdc) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nagx02.h>
#include <nagx04.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagf16.h>

int main(void)
{
  /* Scalars */
  double        alpha, beta, eps, norm;
  Integer       abi, i, j, k1, k2, leniq, lenq, mlvl, n, pdab, pdb, pdu, pdvt;
  Integer       exit_status = 0, smlsiz = 25;

  /* Arrays */
  double        *ab = 0, *b = 0, *d = 0, *e = 0, *q = 0, *u = 0, *vt = 0;
  Integer       *iq = 0;
  char          nag_enum_arg[40];

  /* Nag Types */
  NagError      fail;
  Nag_OrderType order;
  Nag_UploType  uplo;
  Nag_ComputeSingularVecsType compq;

#ifdef NAG_COLUMN_MAJOR
#define B(I, J) b[(J - 1) * pdb + I - 1]
#define U(I, J) u[(J - 1) * pdu + I - 1]
  order = Nag_ColMajor;
#else
#define B(I, J) b[(I - 1) * pdb + J - 1]
#define U(I, J) u[(I - 1) * pdu + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_dbdsdc (f08mdc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%ld%*[^\n]", &n);
  if (n < 0)
    {
      printf("Invalid n\n");
      exit_status = 1;
      goto END;;
    }
  scanf(" %s%*[^\n]", nag_enum_arg);
  /* nag_enum_name_to_value(x04nac).
   * Converts NAG enum member name to value
   */
  uplo = (Nag_UploType) nag_enum_name_to_value(nag_enum_arg);
  scanf(" %s%*[^\n]", nag_enum_arg);
  /* Starting index for main diagonal in banded storage format = abi. */
  if ((order==Nag_ColMajor && uplo==Nag_Lower) || 
      (order==Nag_RowMajor && uplo==Nag_Upper)) {
    abi = 0;
  } else {
    abi = 1;
  }

  compq = (Nag_ComputeSingularVecsType) nag_enum_name_to_value(nag_enum_arg);
  /* size of u, vt, q and iq depends on value of compq input */ 
  if (compq==Nag_SingularVecs) {
    pdu = n;
    pdvt = n;
  } else {
    pdu = 1;
    pdvt = 1;
  }
 if (compq==Nag_PackedSingularVecs) {
    mlvl = (Integer) (log(n/(smlsiz+1.0))/log(2.0)) + 1;
    if (mlvl < 1) mlvl = 1;
    lenq = MAX(n*n+5*n,n*(3 + 2*smlsiz + 8*mlvl));
    leniq = n*3*mlvl;
  } else {
    lenq = 1;
    leniq = 1;
  }

  pdb = n;
  pdab = 2;
  /* Allocate memory */
  if (!(b  = NAG_ALLOC(n*n, double)) ||
      !(ab = NAG_ALLOC(pdab*n, double)) ||
      !(d  = NAG_ALLOC(n, double)) ||
      !(e  = NAG_ALLOC(n-1, double)) ||
      !(q  = NAG_ALLOC(lenq, double)) ||
      !(u  = NAG_ALLOC(pdu*pdu, double)) ||
      !(vt = NAG_ALLOC(pdvt*pdvt, double)) ||
      !(iq = NAG_ALLOC(leniq, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

  /* Read the bidiagonal matrix B from data file, 
   * first the diagonal elements, and then the off-diagonal elements.
   */
  for (i = 0; i < n; ++i) scanf("%lf", &d[i]);
  scanf("%*[^\n]");
  for (i = 0; i < n - 1; ++i) scanf("%lf", &e[i]);
  scanf("%*[^\n]");

  /* Store diagonal arrays in banded format in ab for printing */
  for(i=0; i<n; i++) ab[2*i+abi] = d[i];
  for(i=0; i<n-1; i++) ab[2*i+abi+1] = e[i];

  /* k1 = lower bandwidth, k2 = upper bandwidth */
  k1 = (uplo==Nag_Upper ? 0 : 1);
  k2 = 1 - k1;

  /* Print Bidiagonal Matrix B stored in ab.
   * nag_band_real_mat_print (x04cec).
   * Print real packed banded matrix (easy-to-use)
   */
  fflush(stdout);
  nag_band_real_mat_print(order, n, n, k1, k2, ab, 2, "Matrix B", 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_band_real_mat_print (x04cec).\n%s\n",
	     fail.message);
      exit_status = 1;
      goto END;
    }

  /* Calculate the singular values and left and right singular vectors of B
   * using nag_dbdsdc (f08mdc).
   */
  nag_dbdsdc(order, uplo, compq, n, d, e, u, pdu, vt, pdvt, q, iq, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dbdsdc (f08mdc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
 
  printf("\nSingular values\n");
  for (i = 0; i < n; ++i) printf(" %8.4f%s", d[i], i%8 == 7?"\n":"");
  printf("\n\n");

  if (compq==Nag_SingularVecs) {
    /* Reconstruct bidiagonal matrix from decomposition:
     * first, U <- U*S, then Compute B = U*S*V^T.
     * nag_dgemm (f16yac).
     */
    for(i = 1; i <= n; i++)
      for(j = 1; j <= n; j++) U(i, j) = U(i, j) * d[j-1];
    alpha = 1.0;
    beta = 0.0;
    nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, u, pdu, 
	      vt, pdvt, beta, b, pdb, &fail);
    if (fail.code != NE_NOERROR)
      {
	printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message);
	exit_status = 1;
	goto END;
      }

    /* Subtract original bidiagonal matrix:
     * this should give a matrix close to zero.
     */
    for(i=1; i<=n; i++) B(i,i) -= ab[2*i-2+abi];
    if (uplo==Nag_Upper)
      for(i=1; i<=n-1; i++) B(i,i+1) -= ab[2*i-1+abi];
    else
      for(i=1; i<=n-1; i++) B(i+1,i) -= ab[2*i-1+abi];

    /* nag_dge_norm (f16rac): Find norm of matrix B and print warning if
     * it is too large.
     */
    nag_dge_norm(order, Nag_OneNorm, n, n, b, pdb, &norm, &fail);
    if (fail.code != NE_NOERROR)
      {
	printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
	exit_status = 1;
	goto END;
      }
    /* Get the machine precision, using nag_machine_precision (x02ajc) */
    eps = nag_machine_precision;
    if (norm > pow(eps,0.8))
      {
	printf("Norm of B-(U*S*V^T) is much greater than 0.\nSchur "
	       "factorization has failed.\n norm = %11.4e\n", norm);
      }
  }
 END:
  if (ab) NAG_FREE(ab);
  if (b)  NAG_FREE(b);
  if (d)  NAG_FREE(d);
  if (e)  NAG_FREE(e);
  if (q)  NAG_FREE(q);
  if (u)  NAG_FREE(u);
  if (vt) NAG_FREE(vt);
  if (iq) NAG_FREE(iq);

  return exit_status;
}