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source_hbmv.h

/* blas/source_hbmv.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 conj = (order == CblasColMajor) ? -1 : 1;

  CHECK_ARGS12(CZ_HBMV,order,Uplo,N,K,alpha,A,lda,X,incX,beta,Y,incY);

  {
    const BASE alpha_real = CONST_REAL0(alpha);
    const BASE alpha_imag = CONST_IMAG0(alpha);

    const BASE beta_real = CONST_REAL0(beta);
    const BASE beta_imag = CONST_IMAG0(beta);

    if (N == 0)
      return;

    if ((alpha_real == 0.0 && alpha_imag == 0.0)
        && (beta_real == 1.0 && beta_imag == 0.0))
      return;

    /* form  y := beta*y */
    if (beta_real == 0.0 && beta_imag == 0.0) {
      INDEX iy = OFFSET(N, incY);
      for (i = 0; i < N; i++) {
        REAL(Y, iy) = 0.0;
        IMAG(Y, iy) = 0.0;
        iy += incY;
      }
    } else if (!(beta_real == 1.0 && beta_imag == 0.0)) {
      INDEX iy = OFFSET(N, incY);
      for (i = 0; i < N; i++) {
        const BASE y_real = REAL(Y, iy);
        const BASE y_imag = IMAG(Y, iy);
        const BASE tmpR = y_real * beta_real - y_imag * beta_imag;
        const BASE tmpI = y_real * beta_imag + y_imag * beta_real;
        REAL(Y, iy) = tmpR;
        IMAG(Y, iy) = tmpI;
        iy += incY;
      }
    }

    if (alpha_real == 0.0 && alpha_imag == 0.0)
      return;

    /* form  y := alpha*A*x + y */

    if ((order == CblasRowMajor && Uplo == CblasUpper)
        || (order == CblasColMajor && Uplo == CblasLower)) {
      INDEX ix = OFFSET(N, incX);
      INDEX iy = OFFSET(N, incY);
      for (i = 0; i < N; i++) {
        BASE x_real = CONST_REAL(X, ix);
        BASE x_imag = CONST_IMAG(X, ix);
        BASE temp1_real = alpha_real * x_real - alpha_imag * x_imag;
        BASE temp1_imag = alpha_real * x_imag + alpha_imag * x_real;
        BASE temp2_real = 0.0;
        BASE temp2_imag = 0.0;
        const INDEX j_min = i + 1;
        const INDEX j_max = GSL_MIN(N, i + K + 1);
        INDEX jx = OFFSET(N, incX) + j_min * incX;
        INDEX jy = OFFSET(N, incY) + j_min * incY;
        BASE Aii_real = CONST_REAL(A, lda * i + 0);
        /* Aii_imag is zero */
        REAL(Y, iy) += temp1_real * Aii_real;
        IMAG(Y, iy) += temp1_imag * Aii_real;
        for (j = j_min; j < j_max; j++) {
          BASE Aij_real = CONST_REAL(A, lda * i + (j - i));
          BASE Aij_imag = conj * CONST_IMAG(A, lda * i + (j - i));
          REAL(Y, jy) += temp1_real * Aij_real - temp1_imag * (-Aij_imag);
          IMAG(Y, jy) += temp1_real * (-Aij_imag) + temp1_imag * Aij_real;
          x_real = CONST_REAL(X, jx);
          x_imag = CONST_IMAG(X, jx);
          temp2_real += x_real * Aij_real - x_imag * Aij_imag;
          temp2_imag += x_real * Aij_imag + x_imag * Aij_real;
          jx += incX;
          jy += incY;
        }
        REAL(Y, iy) += alpha_real * temp2_real - alpha_imag * temp2_imag;
        IMAG(Y, iy) += alpha_real * temp2_imag + alpha_imag * temp2_real;
        ix += incX;
        iy += incY;
      }
    } else if ((order == CblasRowMajor && Uplo == CblasLower)
               || (order == CblasColMajor && Uplo == CblasUpper)) {
      INDEX ix = OFFSET(N, incX);
      INDEX iy = OFFSET(N, incY);
      for (i = 0; i < N; i++) {
        BASE x_real = CONST_REAL(X, ix);
        BASE x_imag = CONST_IMAG(X, ix);
        BASE temp1_real = alpha_real * x_real - alpha_imag * x_imag;
        BASE temp1_imag = alpha_real * x_imag + alpha_imag * x_real;
        BASE temp2_real = 0.0;
        BASE temp2_imag = 0.0;
        const INDEX j_min = (K > i ? 0 : i - K);
        const INDEX j_max = i;
        INDEX jx = OFFSET(N, incX) + j_min * incX;
        INDEX jy = OFFSET(N, incY) + j_min * incY;

        for (j = j_min; j < j_max; j++) {
          BASE Aij_real = CONST_REAL(A, i * lda + (K - i + j));
          BASE Aij_imag = conj * CONST_IMAG(A, i * lda + (K - i + j));
          REAL(Y, jy) += temp1_real * Aij_real - temp1_imag * (-Aij_imag);
          IMAG(Y, jy) += temp1_real * (-Aij_imag) + temp1_imag * Aij_real;
          x_real = CONST_REAL(X, jx);
          x_imag = CONST_IMAG(X, jx);
          temp2_real += x_real * Aij_real - x_imag * Aij_imag;
          temp2_imag += x_real * Aij_imag + x_imag * Aij_real;
          jx += incX;
          jy += incY;
        }

        {
          BASE Aii_real = CONST_REAL(A, lda * i + K);
          /* Aii_imag is zero */
          REAL(Y, iy) += temp1_real * Aii_real;
          IMAG(Y, iy) += temp1_imag * Aii_real;
        }

        REAL(Y, iy) += alpha_real * temp2_real - alpha_imag * temp2_imag;
        IMAG(Y, iy) += alpha_real * temp2_imag + alpha_imag * temp2_real;
        ix += incX;
        iy += incY;
      }

    } else {
      BLAS_ERROR("unrecognized operation");
    }
  }
}

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