/* blas/source_trsv_c.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 conj = (TransA == CblasConjTrans) ? -1 : 1;

  const int Trans = (TransA != CblasConjTrans) ? TransA : CblasTrans;

  const int nonunit = (Diag == CblasNonUnit);

  INDEX i, j;

  INDEX ix, jx;

  CHECK_ARGS9(TRSV,order,Uplo,TransA,Diag,N,A,lda,X,incX);

  if (N == 0)

    return;

  /* form  x := inv( A )*x */

  if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasUpper)

      || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasLower)) {

    ix = OFFSET(N, incX) + incX * (N - 1);

    if (nonunit) {

      const BASE a_real = CONST_REAL(A, lda * (N - 1) + (N - 1));

      const BASE a_imag = conj * CONST_IMAG(A, lda * (N - 1) + (N - 1));

      const BASE x_real = REAL(X, ix);

      const BASE x_imag = IMAG(X, ix);

      const BASE s = xhypot(a_real, a_imag);

      const BASE b_real = a_real / s;

      const BASE b_imag = a_imag / s;

      REAL(X, ix) = (x_real * b_real + x_imag * b_imag) / s;

      IMAG(X, ix) = (x_imag * b_real - b_imag * x_real) / s;

    }

    ix -= incX;

    for (i = N - 1; i > 0 && i--;) {

      BASE tmp_real = REAL(X, ix);

      BASE tmp_imag = IMAG(X, ix);

      jx = ix + incX;

      for (j = i + 1; j < N; j++) {

        const BASE Aij_real = CONST_REAL(A, lda * i + j);

        const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + j);

        const BASE x_real = REAL(X, jx);

        const BASE x_imag = IMAG(X, jx);

        tmp_real -= Aij_real * x_real - Aij_imag * x_imag;

        tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;

        jx += incX;

      }

      if (nonunit) {

        const BASE a_real = CONST_REAL(A, lda * i + i);

        const BASE a_imag = conj * CONST_IMAG(A, lda * i + i);

        const BASE s = xhypot(a_real, a_imag);

        const BASE b_real = a_real / s;

        const BASE b_imag = a_imag / s;

        REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;

        IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;

      } else {

        REAL(X, ix) = tmp_real;

        IMAG(X, ix) = tmp_imag;

      }

      ix -= incX;

    }

  } else if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasLower)

             || (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasUpper)) {

    /* forward substitution */

    ix = OFFSET(N, incX);

    if (nonunit) {

      const BASE a_real = CONST_REAL(A, lda * 0 + 0);

      const BASE a_imag = conj * CONST_IMAG(A, lda * 0 + 0);

      const BASE x_real = REAL(X, ix);

      const BASE x_imag = IMAG(X, ix);

      const BASE s = xhypot(a_real, a_imag);

      const BASE b_real = a_real / s;

      const BASE b_imag = a_imag / s;

      REAL(X, ix) = (x_real * b_real + x_imag * b_imag) / s;

      IMAG(X, ix) = (x_imag * b_real - b_imag * x_real) / s;

    }

    ix += incX;

    for (i = 1; i < N; i++) {

      BASE tmp_real = REAL(X, ix);

      BASE tmp_imag = IMAG(X, ix);

      jx = OFFSET(N, incX);

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

        const BASE Aij_real = CONST_REAL(A, lda * i + j);

        const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + j);

        const BASE x_real = REAL(X, jx);

        const BASE x_imag = IMAG(X, jx);

        tmp_real -= Aij_real * x_real - Aij_imag * x_imag;

        tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;

        jx += incX;

      }

      if (nonunit) {

        const BASE a_real = CONST_REAL(A, lda * i + i);

        const BASE a_imag = conj * CONST_IMAG(A, lda * i + i);

        const BASE s = xhypot(a_real, a_imag);

        const BASE b_real = a_real / s;

        const BASE b_imag = a_imag / s;

        REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;

        IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;

      } else {

        REAL(X, ix) = tmp_real;

        IMAG(X, ix) = tmp_imag;

      }

      ix += incX;

    }

  } else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasUpper)

             || (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasLower)) {

    /* form  x := inv( A' )*x */

    /* forward substitution */

    ix = OFFSET(N, incX);

    if (nonunit) {

      const BASE a_real = CONST_REAL(A, lda * 0 + 0);

      const BASE a_imag = conj * CONST_IMAG(A, lda * 0 + 0);

      const BASE x_real = REAL(X, ix);

      const BASE x_imag = IMAG(X, ix);

      const BASE s = xhypot(a_real, a_imag);

      const BASE b_real = a_real / s;

      const BASE b_imag = a_imag / s;

      REAL(X, ix) = (x_real * b_real + x_imag * b_imag) / s;

      IMAG(X, ix) = (x_imag * b_real - b_imag * x_real) / s;

    }

    ix += incX;

    for (i = 1; i < N; i++) {

      BASE tmp_real = REAL(X, ix);

      BASE tmp_imag = IMAG(X, ix);

      jx = OFFSET(N, incX);

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

        const BASE Aij_real = CONST_REAL(A, lda * j + i);

        const BASE Aij_imag = conj * CONST_IMAG(A, lda * j + i);

        const BASE x_real = REAL(X, jx);

        const BASE x_imag = IMAG(X, jx);

        tmp_real -= Aij_real * x_real - Aij_imag * x_imag;

        tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;

        jx += incX;

      }

      if (nonunit) {

        const BASE a_real = CONST_REAL(A, lda * i + i);

        const BASE a_imag = conj * CONST_IMAG(A, lda * i + i);

        const BASE s = xhypot(a_real, a_imag);

        const BASE b_real = a_real / s;

        const BASE b_imag = a_imag / s;

        REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;

        IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;

      } else {

        REAL(X, ix) = tmp_real;

        IMAG(X, ix) = tmp_imag;

      }

      ix += incX;

    }

  } else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasLower)

             || (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasUpper)) {

    /* backsubstitution */

    ix = OFFSET(N, incX) + incX * (N - 1);

    if (nonunit) {

      const BASE a_real = CONST_REAL(A, lda * (N - 1) + (N - 1));

      const BASE a_imag = conj * CONST_IMAG(A, lda * (N - 1) + (N - 1));

      const BASE x_real = REAL(X, ix);

      const BASE x_imag = IMAG(X, ix);

      const BASE s = xhypot(a_real, a_imag);

      const BASE b_real = a_real / s;

      const BASE b_imag = a_imag / s;

      REAL(X, ix) = (x_real * b_real + x_imag * b_imag) / s;

      IMAG(X, ix) = (x_imag * b_real - b_imag * x_real) / s;

    }

    ix -= incX;

    for (i = N - 1; i > 0 && i--;) {

      BASE tmp_real = REAL(X, ix);

      BASE tmp_imag = IMAG(X, ix);

      jx = ix + incX;

      for (j = i + 1; j < N; j++) {

        const BASE Aij_real = CONST_REAL(A, lda * j + i);

        const BASE Aij_imag = conj * CONST_IMAG(A, lda * j + i);

        const BASE x_real = REAL(X, jx);

        const BASE x_imag = IMAG(X, jx);

        tmp_real -= Aij_real * x_real - Aij_imag * x_imag;

        tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;

        jx += incX;

      }

      if (nonunit) {

        const BASE a_real = CONST_REAL(A, lda * i + i);

        const BASE a_imag = conj * CONST_IMAG(A, lda * i + i);

        const BASE s = xhypot(a_real, a_imag);

        const BASE b_real = a_real / s;

        const BASE b_imag = a_imag / s;

        REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;

        IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;

      } else {

        REAL(X, ix) = tmp_real;

        IMAG(X, ix) = tmp_imag;

      }

      ix -= incX;

    }

  } else {

    BLAS_ERROR("unrecognized operation");

  }

}