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source_her2k.h

/* blas/source_her2k.h
 *
 * Copyright (C) 2001, 2007 Brian Gough
 *
 * 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, k;
  int uplo, trans;

  CHECK_ARGS13(HER2K,Order,Uplo,Trans,N,K,alpha,A,lda,B,ldb,beta,C,ldc);

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

    if (beta == 1.0 && ((alpha_real == 0.0 && alpha_imag == 0.0) || K == 0))
      return;

    if (Order == CblasRowMajor) {
      uplo = Uplo;
      trans = Trans;
    } else {
      uplo = (Uplo == CblasUpper) ? CblasLower : CblasUpper;
      trans = (Trans == CblasNoTrans) ? CblasConjTrans : CblasNoTrans;
      alpha_imag *= -1;           /* conjugate alpha */
    }

    /* form  C := beta*C */

    if (beta == 0.0) {
      if (uplo == CblasUpper) {
        for (i = 0; i < N; i++) {
          for (j = i; j < N; j++) {
            REAL(C, ldc * i + j) = 0.0;
            IMAG(C, ldc * i + j) = 0.0;
          }
        }
      } else {
        for (i = 0; i < N; i++) {
          for (j = 0; j <= i; j++) {
            REAL(C, ldc * i + j) = 0.0;
            IMAG(C, ldc * i + j) = 0.0;
          }
        }
      }
    } else if (beta != 1.0) {
      if (uplo == CblasUpper) {
        for (i = 0; i < N; i++) {
          REAL(C, ldc * i + i) *= beta;
          IMAG(C, ldc * i + i) = 0.0;
          for (j = i + 1; j < N; j++) {
            REAL(C, ldc * i + j) *= beta;
            IMAG(C, ldc * i + j) *= beta;
          }
        }
      } else {
        for (i = 0; i < N; i++) {
          for (j = 0; j < i; j++) {
            REAL(C, ldc * i + j) *= beta;
            IMAG(C, ldc * i + j) *= beta;
          }
          REAL(C, ldc * i + i) *= beta;
          IMAG(C, ldc * i + i) = 0.0;
        }
      }
    } else {
      for (i = 0; i < N; i++) {
        IMAG(C, ldc * i + i) = 0.0;
      }
    }

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

    if (uplo == CblasUpper && trans == CblasNoTrans) {

      for (i = 0; i < N; i++) {

        /* Cii += alpha Aik conj(Bik) + conj(alpha) Bik conj(Aik) */
        {
          BASE temp_real = 0.0;
          /* BASE temp_imag = 0.0; */
          for (k = 0; k < K; k++) {
            const BASE Aik_real = CONST_REAL(A, i * lda + k);
            const BASE Aik_imag = CONST_IMAG(A, i * lda + k);
            /* temp1 = alpha * Aik */
            const BASE temp1_real = alpha_real * Aik_real - alpha_imag * Aik_imag;
            const BASE temp1_imag = alpha_real * Aik_imag + alpha_imag * Aik_real;
            const BASE Bik_real = CONST_REAL(B, i * ldb + k);
            const BASE Bik_imag = CONST_IMAG(B, i * ldb + k);
            temp_real += temp1_real * Bik_real + temp1_imag * Bik_imag;
          }

          REAL(C, i * ldc + i) += 2 * temp_real;
          IMAG(C, i * ldc + i) = 0.0;
        }

        /* Cij += alpha Aik conj(Bjk) + conj(alpha) Bik conj(Ajk) */
        for (j = i + 1; j < N; j++) {
          BASE temp_real = 0.0;
          BASE temp_imag = 0.0;
          for (k = 0; k < K; k++) {
            const BASE Aik_real = CONST_REAL(A, i * lda + k);
            const BASE Aik_imag = CONST_IMAG(A, i * lda + k);
            /* temp1 = alpha * Aik */
            const BASE temp1_real = alpha_real * Aik_real - alpha_imag * Aik_imag;
            const BASE temp1_imag = alpha_real * Aik_imag + alpha_imag * Aik_real;
            const BASE Bik_real = CONST_REAL(B, i * ldb + k);
            const BASE Bik_imag = CONST_IMAG(B, i * ldb + k);

            const BASE Ajk_real = CONST_REAL(A, j * lda + k);
            const BASE Ajk_imag = CONST_IMAG(A, j * lda + k);
            /* temp2 = alpha * Ajk */
            const BASE temp2_real = alpha_real * Ajk_real - alpha_imag * Ajk_imag;
            const BASE temp2_imag = alpha_real * Ajk_imag + alpha_imag * Ajk_real;
            const BASE Bjk_real = CONST_REAL(B, j * ldb + k);
            const BASE Bjk_imag = CONST_IMAG(B, j * ldb + k);

            /* Cij += alpha * Aik * conj(Bjk) + conj(alpha) * Bik * conj(Ajk) */
            temp_real += ((temp1_real * Bjk_real + temp1_imag * Bjk_imag)
                          + (Bik_real * temp2_real + Bik_imag * temp2_imag));
            temp_imag += ((temp1_real * (-Bjk_imag) + temp1_imag * Bjk_real)
                          + (Bik_real * (-temp2_imag) + Bik_imag * temp2_real));
          }
          REAL(C, i * ldc + j) += temp_real;
          IMAG(C, i * ldc + j) += temp_imag;
        }
      }

    } else if (uplo == CblasUpper && trans == CblasConjTrans) {

      for (k = 0; k < K; k++) {
        for (i = 0; i < N; i++) {
          BASE Aki_real = CONST_REAL(A, k * lda + i);
          BASE Aki_imag = CONST_IMAG(A, k * lda + i);
          BASE Bki_real = CONST_REAL(B, k * ldb + i);
          BASE Bki_imag = CONST_IMAG(B, k * ldb + i);
          /* temp1 = alpha * conj(Aki) */
          BASE temp1_real = alpha_real * Aki_real - alpha_imag * (-Aki_imag);
          BASE temp1_imag = alpha_real * (-Aki_imag) + alpha_imag * Aki_real;
          /* temp2 = conj(alpha) * conj(Bki) */
          BASE temp2_real = alpha_real * Bki_real - alpha_imag * Bki_imag;
          BASE temp2_imag = -(alpha_real * Bki_imag + alpha_imag * Bki_real);

          /* Cii += alpha * conj(Aki) * Bki + conj(alpha) * conj(Bki) * Aki */
          {
            REAL(C, i * lda + i) += 2 * (temp1_real * Bki_real - temp1_imag * Bki_imag);
            IMAG(C, i * lda + i) = 0.0;
          }

          for (j = i + 1; j < N; j++) {
            BASE Akj_real = CONST_REAL(A, k * lda + j);
            BASE Akj_imag = CONST_IMAG(A, k * lda + j);
            BASE Bkj_real = CONST_REAL(B, k * ldb + j);
            BASE Bkj_imag = CONST_IMAG(B, k * ldb + j);
            /* Cij += alpha * conj(Aki) * Bkj + conj(alpha) * conj(Bki) * Akj */
            REAL(C, i * lda + j) += (temp1_real * Bkj_real - temp1_imag * Bkj_imag)
              + (temp2_real * Akj_real - temp2_imag * Akj_imag);
            IMAG(C, i * lda + j) += (temp1_real * Bkj_imag + temp1_imag * Bkj_real)
              + (temp2_real * Akj_imag + temp2_imag * Akj_real);
          }
        }
      }

    } else if (uplo == CblasLower && trans == CblasNoTrans) {

      for (i = 0; i < N; i++) {

        /* Cij += alpha Aik conj(Bjk) + conj(alpha) Bik conj(Ajk) */

        for (j = 0; j < i; j++) {
          BASE temp_real = 0.0;
          BASE temp_imag = 0.0;
          for (k = 0; k < K; k++) {
            const BASE Aik_real = CONST_REAL(A, i * lda + k);
            const BASE Aik_imag = CONST_IMAG(A, i * lda + k);
            /* temp1 = alpha * Aik */
            const BASE temp1_real = alpha_real * Aik_real - alpha_imag * Aik_imag;
            const BASE temp1_imag = alpha_real * Aik_imag + alpha_imag * Aik_real;
            const BASE Bik_real = CONST_REAL(B, i * ldb + k);
            const BASE Bik_imag = CONST_IMAG(B, i * ldb + k);

            const BASE Ajk_real = CONST_REAL(A, j * lda + k);
            const BASE Ajk_imag = CONST_IMAG(A, j * lda + k);
            /* temp2 = alpha * Ajk */
            const BASE temp2_real = alpha_real * Ajk_real - alpha_imag * Ajk_imag;
            const BASE temp2_imag = alpha_real * Ajk_imag + alpha_imag * Ajk_real;
            const BASE Bjk_real = CONST_REAL(B, j * ldb + k);
            const BASE Bjk_imag = CONST_IMAG(B, j * ldb + k);

            /* Cij += alpha * Aik * conj(Bjk) + conj(alpha) * Bik * conj(Ajk) */
            temp_real += ((temp1_real * Bjk_real + temp1_imag * Bjk_imag)
                          + (Bik_real * temp2_real + Bik_imag * temp2_imag));
            temp_imag += ((temp1_real * (-Bjk_imag) + temp1_imag * Bjk_real)
                          + (Bik_real * (-temp2_imag) + Bik_imag * temp2_real));
          }
          REAL(C, i * ldc + j) += temp_real;
          IMAG(C, i * ldc + j) += temp_imag;
        }

        /* Cii += alpha Aik conj(Bik) + conj(alpha) Bik conj(Aik) */
        {
          BASE temp_real = 0.0;
          /* BASE temp_imag = 0.0; */
          for (k = 0; k < K; k++) {
            const BASE Aik_real = CONST_REAL(A, i * lda + k);
            const BASE Aik_imag = CONST_IMAG(A, i * lda + k);
            /* temp1 = alpha * Aik */
            const BASE temp1_real = alpha_real * Aik_real - alpha_imag * Aik_imag;
            const BASE temp1_imag = alpha_real * Aik_imag + alpha_imag * Aik_real;
            const BASE Bik_real = CONST_REAL(B, i * ldb + k);
            const BASE Bik_imag = CONST_IMAG(B, i * ldb + k);
            temp_real += temp1_real * Bik_real + temp1_imag * Bik_imag;
          }

          REAL(C, i * ldc + i) += 2 * temp_real;
          IMAG(C, i * ldc + i) = 0.0;
        }
      }

    } else if (uplo == CblasLower && trans == CblasConjTrans) {

      for (k = 0; k < K; k++) {
        for (i = 0; i < N; i++) {
          BASE Aki_real = CONST_REAL(A, k * lda + i);
          BASE Aki_imag = CONST_IMAG(A, k * lda + i);
          BASE Bki_real = CONST_REAL(B, k * ldb + i);
          BASE Bki_imag = CONST_IMAG(B, k * ldb + i);
          /* temp1 = alpha * conj(Aki) */
          BASE temp1_real = alpha_real * Aki_real - alpha_imag * (-Aki_imag);
          BASE temp1_imag = alpha_real * (-Aki_imag) + alpha_imag * Aki_real;
          /* temp2 = conj(alpha) * conj(Bki) */
          BASE temp2_real = alpha_real * Bki_real - alpha_imag * Bki_imag;
          BASE temp2_imag = -(alpha_real * Bki_imag + alpha_imag * Bki_real);

          for (j = 0; j < i; j++) {
            BASE Akj_real = CONST_REAL(A, k * lda + j);
            BASE Akj_imag = CONST_IMAG(A, k * lda + j);
            BASE Bkj_real = CONST_REAL(B, k * ldb + j);
            BASE Bkj_imag = CONST_IMAG(B, k * ldb + j);
            /* Cij += alpha * conj(Aki) * Bkj + conj(alpha) * conj(Bki) * Akj */
            REAL(C, i * lda + j) += (temp1_real * Bkj_real - temp1_imag * Bkj_imag)
              + (temp2_real * Akj_real - temp2_imag * Akj_imag);
            IMAG(C, i * lda + j) += (temp1_real * Bkj_imag + temp1_imag * Bkj_real)
              + (temp2_real * Akj_imag + temp2_imag * Akj_real);
          }

          /* Cii += alpha * conj(Aki) * Bki + conj(alpha) * conj(Bki) * Aki */
          {
            REAL(C, i * lda + i) += 2 * (temp1_real * Bki_real - temp1_imag * Bki_imag);
            IMAG(C, i * lda + i) = 0.0;
          }
        }
      }
    } else {
      BLAS_ERROR("unrecognized operation");
    }
  }
}

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