source_trsm_c.h

开放gsl矩阵运算

/* blas/source_trsm_c.h
 * 
 * Copyright (C) 2001 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 2 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., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

{
  INDEX i, j, k;
  INDEX n1, n2;
  const int nonunit = (Diag == CblasNonUnit);
  const int conj = (TransA == CblasConjTrans) ? -1 : 1;
  int side, uplo, trans;

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

  if (Order == CblasRowMajor) {
    n1 = M;
    n2 = N;
    side = Side;
    uplo = Uplo;
    trans = TransA;
    trans = (TransA == CblasNoTrans) ? CblasNoTrans : CblasTrans;
  } else {
    n1 = N;
    n2 = M;
    side = (Side == CblasLeft) ? CblasRight : CblasLeft;	/* exchanged */
    uplo = (Uplo == CblasUpper) ? CblasLower : CblasUpper;	/* exchanged */
    trans = (TransA == CblasNoTrans) ? CblasNoTrans : CblasTrans;	/* same */
  }

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

    /* form  B := alpha * inv(TriU(A)) *B */

    if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
      for (i = 0; i < n1; i++) {
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
	  IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
	}
      }
    }

    for (i = n1; i > 0 && i--;) {
      if (nonunit) {
	const BASE Aii_real = CONST_REAL(A, lda * i + i);
	const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
	const BASE s = xhypot(Aii_real, Aii_imag);
	const BASE a_real = Aii_real / s;
	const BASE a_imag = Aii_imag / s;

	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
	  IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
	}
      }

      for (k = 0; k < i; k++) {
	const BASE Aki_real = CONST_REAL(A, k * lda + i);
	const BASE Aki_imag = conj * CONST_IMAG(A, k * lda + i);
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * k + j) -= Aki_real * Bij_real - Aki_imag * Bij_imag;
	  IMAG(B, ldb * k + j) -= Aki_real * Bij_imag + Aki_imag * Bij_real;
	}
      }
    }

  } else if (side == CblasLeft && uplo == CblasUpper && trans == CblasTrans) {

    /* form  B := alpha * inv(TriU(A))' *B */

    if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
      for (i = 0; i < n1; i++) {
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
	  IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
	}
      }
    }

    for (i = 0; i < n1; i++) {

      if (nonunit) {
	const BASE Aii_real = CONST_REAL(A, lda * i + i);
	const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
	const BASE s = xhypot(Aii_real, Aii_imag);
	const BASE a_real = Aii_real / s;
	const BASE a_imag = Aii_imag / s;

	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
	  IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
	}
      }

      for (k = i + 1; k < n1; k++) {
	const BASE Aik_real = CONST_REAL(A, i * lda + k);
	const BASE Aik_imag = conj * CONST_IMAG(A, i * lda + k);
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * k + j) -= Aik_real * Bij_real - Aik_imag * Bij_imag;
	  IMAG(B, ldb * k + j) -= Aik_real * Bij_imag + Aik_imag * Bij_real;
	}
      }
    }

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

    /* form  B := alpha * inv(TriL(A))*B */

    if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
      for (i = 0; i < n1; i++) {
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
	  IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
	}
      }
    }

    for (i = 0; i < n1; i++) {

      if (nonunit) {
	const BASE Aii_real = CONST_REAL(A, lda * i + i);
	const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
	const BASE s = xhypot(Aii_real, Aii_imag);
	const BASE a_real = Aii_real / s;
	const BASE a_imag = Aii_imag / s;

	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
	  IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
	}
      }

      for (k = i + 1; k < n1; k++) {
	const BASE Aki_real = CONST_REAL(A, k * lda + i);
	const BASE Aki_imag = conj * CONST_IMAG(A, k * lda + i);
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * k + j) -= Aki_real * Bij_real - Aki_imag * Bij_imag;
	  IMAG(B, ldb * k + j) -= Aki_real * Bij_imag + Aki_imag * Bij_real;
	}
      }
    }


  } else if (side == CblasLeft && uplo == CblasLower && trans == CblasTrans) {

    /* form  B := alpha * TriL(A)' *B */

    if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
      for (i = 0; i < n1; i++) {
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
	  IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
	}
      }
    }

    for (i = n1; i > 0 && i--;) {
      if (nonunit) {
	const BASE Aii_real = CONST_REAL(A, lda * i + i);
	const BASE Aii_imag = conj * CONST_IMAG(A, lda * i + i);
	const BASE s = xhypot(Aii_real, Aii_imag);
	const BASE a_real = Aii_real / s;
	const BASE a_imag = Aii_imag / s;

	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
	  IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
	}
      }

      for (k = 0; k < i; k++) {
	const BASE Aik_real = CONST_REAL(A, i * lda + k);
	const BASE Aik_imag = conj * CONST_IMAG(A, i * lda + k);
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * k + j) -= Aik_real * Bij_real - Aik_imag * Bij_imag;
	  IMAG(B, ldb * k + j) -= Aik_real * Bij_imag + Aik_imag * Bij_real;
	}
      }
    }

  } else if (side == CblasRight && uplo == CblasUpper && trans == CblasNoTrans) {

    /* form  B := alpha * B * inv(TriU(A)) */

    if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
      for (i = 0; i < n1; i++) {
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
	  IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
	}
      }
    }

    for (i = 0; i < n1; i++) {
      for (j = 0; j < n2; j++) {
	if (nonunit) {
	  const BASE Ajj_real = CONST_REAL(A, lda * j + j);
	  const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
	  const BASE s = xhypot(Ajj_real, Ajj_imag);
	  const BASE a_real = Ajj_real / s;
	  const BASE a_imag = Ajj_imag / s;
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
	  IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
	}

	{
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  for (k = j + 1; k < n2; k++) {
	    const BASE Ajk_real = CONST_REAL(A, j * lda + k);
	    const BASE Ajk_imag = conj * CONST_IMAG(A, j * lda + k);
	    REAL(B, ldb * i + k) -= Ajk_real * Bij_real - Ajk_imag * Bij_imag;
	    IMAG(B, ldb * i + k) -= Ajk_real * Bij_imag + Ajk_imag * Bij_real;
	  }
	}
      }
    }

  } else if (side == CblasRight && uplo == CblasUpper && trans == CblasTrans) {

    /* form  B := alpha * B * inv(TriU(A))' */

    if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
      for (i = 0; i < n1; i++) {
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
	  IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
	}
      }
    }

    for (i = 0; i < n1; i++) {
      for (j = n2; j > 0 && j--;) {

	if (nonunit) {
	  const BASE Ajj_real = CONST_REAL(A, lda * j + j);
	  const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
	  const BASE s = xhypot(Ajj_real, Ajj_imag);
	  const BASE a_real = Ajj_real / s;
	  const BASE a_imag = Ajj_imag / s;
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
	  IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
	}

	{
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  for (k = 0; k < j; k++) {
	    const BASE Akj_real = CONST_REAL(A, k * lda + j);
	    const BASE Akj_imag = conj * CONST_IMAG(A, k * lda + j);
	    REAL(B, ldb * i + k) -= Akj_real * Bij_real - Akj_imag * Bij_imag;
	    IMAG(B, ldb * i + k) -= Akj_real * Bij_imag + Akj_imag * Bij_real;
	  }
	}
      }
    }


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

    /* form  B := alpha * B * inv(TriL(A)) */

    if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
      for (i = 0; i < n1; i++) {
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
	  IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
	}
      }
    }

    for (i = 0; i < n1; i++) {
      for (j = n2; j > 0 && j--;) {

	if (nonunit) {
	  const BASE Ajj_real = CONST_REAL(A, lda * j + j);
	  const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
	  const BASE s = xhypot(Ajj_real, Ajj_imag);
	  const BASE a_real = Ajj_real / s;
	  const BASE a_imag = Ajj_imag / s;
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
	  IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
	}

	{
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  for (k = 0; k < j; k++) {
	    const BASE Ajk_real = CONST_REAL(A, j * lda + k);
	    const BASE Ajk_imag = conj * CONST_IMAG(A, j * lda + k);
	    REAL(B, ldb * i + k) -= Ajk_real * Bij_real - Ajk_imag * Bij_imag;
	    IMAG(B, ldb * i + k) -= Ajk_real * Bij_imag + Ajk_imag * Bij_real;
	  }
	}
      }
    }

  } else if (side == CblasRight && uplo == CblasLower && trans == CblasTrans) {

    /* form  B := alpha * B * inv(TriL(A))' */


    if (!(alpha_real == 1.0 && alpha_imag == 0.0)) {
      for (i = 0; i < n1; i++) {
	for (j = 0; j < n2; j++) {
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = alpha_real * Bij_real - alpha_imag * Bij_imag;
	  IMAG(B, ldb * i + j) = alpha_real * Bij_imag + alpha_imag * Bij_real;
	}
      }
    }

    for (i = 0; i < n1; i++) {
      for (j = 0; j < n2; j++) {
	if (nonunit) {
	  const BASE Ajj_real = CONST_REAL(A, lda * j + j);
	  const BASE Ajj_imag = conj * CONST_IMAG(A, lda * j + j);
	  const BASE s = xhypot(Ajj_real, Ajj_imag);
	  const BASE a_real = Ajj_real / s;
	  const BASE a_imag = Ajj_imag / s;
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);
	  REAL(B, ldb * i + j) = (Bij_real * a_real + Bij_imag * a_imag) / s;
	  IMAG(B, ldb * i + j) = (Bij_imag * a_real - Bij_real * a_imag) / s;
	}

	{
	  const BASE Bij_real = REAL(B, ldb * i + j);
	  const BASE Bij_imag = IMAG(B, ldb * i + j);

	  for (k = j + 1; k < n2; k++) {
	    const BASE Akj_real = CONST_REAL(A, k * lda + j);
	    const BASE Akj_imag = conj * CONST_IMAG(A, k * lda + j);
	    REAL(B, ldb * i + k) -= Akj_real * Bij_real - Akj_imag * Bij_imag;
	    IMAG(B, ldb * i + k) -= Akj_real * Bij_imag + Akj_imag * Bij_real;
	  }
	}
      }
    }


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