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source_tbsv_r.h

/* blas/source_tbsv_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.
 */

{
  const int nonunit = (Diag == CblasNonUnit);
  INDEX i, j;
  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);
    for (i = N; i > 0 && i--;) {
      BASE tmp = X[ix];
      const INDEX j_min = i + 1;
      const INDEX j_max = GSL_MIN(N, i + K + 1);
      INDEX jx = OFFSET(N, incX) + j_min * incX;
      for (j = j_min; j < j_max; j++) {
        const BASE Aij = A[lda * i + (j - i)];
        tmp -= Aij * X[jx];
        jx += incX;
      }
      if (nonunit) {
        X[ix] = tmp / A[lda * i + 0];
      } 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);

    for (i = 0; i < N; i++) {
      BASE tmp = X[ix];
      const INDEX j_min = (i > K ? i - K : 0);
      const INDEX j_max = i;
      INDEX jx = OFFSET(N, incX) + j_min * incX;
      for (j = j_min; j < j_max; j++) {
        const BASE Aij = A[lda * i + (K + j - i)];
        tmp -= Aij * X[jx];
        jx += incX;
      }
      if (nonunit) {
        X[ix] = tmp / A[lda * i + K];
      } 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);
    for (i = 0; i < N; i++) {
      BASE tmp = X[ix];
      const INDEX j_min = (K > i ? 0 : i - K);
      const INDEX j_max = i;
      INDEX jx = OFFSET(N, incX) + j_min * incX;
      for (j = j_min; j < j_max; j++) {
        const BASE Aji = A[(i - j) + lda * j];
        tmp -= Aji * X[jx];
        jx += incX;
      }
      if (nonunit) {
        X[ix] = tmp / A[0 + lda * 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;
    for (i = N; i > 0 && i--;) {
      BASE tmp = X[ix];
      const INDEX j_min = i + 1;
      const INDEX j_max = GSL_MIN(N, i + K + 1);
      INDEX jx = OFFSET(N, incX) + j_min * incX;
      for (j = j_min; j < j_max; j++) {
        const BASE Aji = A[(K + i - j) + lda * j];
        tmp -= Aji * X[jx];
        jx += incX;
      }
      if (nonunit) {
        X[ix] = tmp / A[K + lda * i];
      } else {
        X[ix] = tmp;
      }
      ix -= incX;
    }
  } else {
    BLAS_ERROR("unrecognized operation");
  }
}

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