text: /* blas/source_tpsv_r.h
   * 
   * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
   * 
   * This program is free software; you can redistribute it and/or modify
   * it under the terms of the GNU General Public License as published by
   * the Free Software Foundation; either version 3 of the License, or (at
   * your option) any later version.
   * 
   * This program is distributed in the hope that it will be useful, but
   * WITHOUT ANY WARRANTY; without even the implied warranty of
   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   * General Public License for more details.
   * 
   * You should have received a copy of the GNU General Public License
   * along with this program; if not, write to the Free Software
   * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
   */
  
  {
    INDEX i, j;
    const int nonunit = (Diag == CblasNonUnit);
    const int Trans = (TransA != CblasConjTrans) ? TransA : CblasTrans;
  
    if (N == 0)
      return;
  
    /* form  x := inv( A )*x */
  
    if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasUpper)
        || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasLower)) {
      /* backsubstitution */
      INDEX ix = OFFSET(N, incX) + incX * (N - 1);
      if (nonunit) {
        X[ix] = X[ix] / Ap[TPUP(N, (N - 1), (N - 1))];
      }
      ix -= incX;
      for (i = N - 1; i > 0 && i--;) {
        BASE tmp = X[ix];
        INDEX jx = ix + incX;
        for (j = i + 1; j < N; j++) {
          const BASE Aij = Ap[TPUP(N, i, j)];
          tmp -= Aij * X[jx];
          jx += incX;
        }
        if (nonunit) {
          X[ix] = tmp / Ap[TPUP(N, i, i)];
        } else {
          X[ix] = tmp;
        }
        ix -= incX;
      }
    } else if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasLower)
               || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasUpper)) {
  
      /* forward substitution */
      INDEX ix = OFFSET(N, incX);
      if (nonunit) {
        X[ix] = X[ix] / Ap[TPLO(N, 0, 0)];
      }
      ix += incX;
      for (i = 1; i < N; i++) {
        BASE tmp = X[ix];
        INDEX jx = OFFSET(N, incX);
        for (j = 0; j < i; j++) {
          const BASE Aij = Ap[TPLO(N, i, j)];
          tmp -= Aij * X[jx];
          jx += incX;
        }
        if (nonunit) {
          X[ix] = tmp / Ap[TPLO(N, i, j)];
        } else {
          X[ix] = tmp;
        }
        ix += incX;
      }
    } else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasUpper)
               || (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasLower)) {
  
      /* form  x := inv( A' )*x */
  
      /* forward substitution */
      INDEX ix = OFFSET(N, incX);
      if (nonunit) {
        X[ix] = X[ix] / Ap[TPUP(N, 0, 0)];
      }
      ix += incX;
      for (i = 1; i < N; i++) {
        BASE tmp = X[ix];
        INDEX jx = OFFSET(N, incX);
        for (j = 0; j < i; j++) {
          const BASE Aji = Ap[TPUP(N, j, i)];
          tmp -= Aji * X[jx];
          jx += incX;
        }
        if (nonunit) {
          X[ix] = tmp / Ap[TPUP(N, i, i)];
        } else {
          X[ix] = tmp;
        }
        ix += incX;
      }
    } else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasLower)
               || (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasUpper)) {
  
      /* backsubstitution */
      INDEX ix = OFFSET(N, incX) + (N - 1) * incX;
      if (nonunit) {
        X[ix] = X[ix] / Ap[TPLO(N, (N - 1), (N - 1))];
      }
      ix -= incX;
      for (i = N - 1; i > 0 && i--;) {
        BASE tmp = X[ix];
        INDEX jx = ix + incX;
        for (j = i + 1; j < N; j++) {
          const BASE Aji = Ap[TPLO(N, j, i)];
          tmp -= Aji * X[jx];
          jx += incX;
        }
        if (nonunit) {
          X[ix] = tmp / Ap[TPLO(N, i, i)];
        } else {
          X[ix] = tmp;
        }
        ix -= incX;
      }
    } else {
      BLAS_ERROR("unrecognized operation");
    }
  
  }
  