text: /* -*- c-basic-offset: 4; indent-tabs-mode: nil -*- */
  /* ====================================================================
   * Copyright (c) 1997-2000 Carnegie Mellon University.  All rights 
   * reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer. 
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * This work was supported in part by funding from the Defense Advanced 
   * Research Projects Agency and the National Science Foundation of the 
   * United States of America, and the CMU Sphinx Speech Consortium.
   *
   * THIS SOFTWARE IS PROVIDED BY CARNEGIE MELLON UNIVERSITY ``AS IS'' AND 
   * ANY EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, 
   * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
   * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL CARNEGIE MELLON UNIVERSITY
   * NOR ITS EMPLOYEES BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 
   * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 
   * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 
   * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 
   * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 
   * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   *
   * ====================================================================
   *
   */
  /*********************************************************************
   *
   * File: matrix.h
   * 
   * Description: Matrix and linear algebra functions
   * 
   * Author: 
   * 
   *********************************************************************/
  
  #ifndef MATRIX_H
  #define MATRIX_H
  
  /** \file matrix.h
   * \brief Matrix and linear algebra functions.
   *
   * This file contains some basic matrix and linear algebra operations.
   * In general these operate on positive definite matrices ONLY,
   * because all matrices we're likely to encounter are either
   * covariance matrices or are derived from them, and therefore a
   * non-positive-definite matrix indicates some kind of pathological
   * condition.
   */
  #ifdef __cplusplus
  extern "C" {
  #endif
  #if 0
  /* Fool Emacs. */
  }
  #endif
  
  /* Win32/WinCE DLL gunk */
  #include <sphinxbase/sphinxbase_export.h>
  #include <sphinxbase/prim_type.h>
  
  
  /**
   * Norm an array
   * @param arr array
   * @param d1 dimension
   * @param d2 dimension
   * @param d3 dimension
   **/
  SPHINXBASE_EXPORT void norm_3d(float32 ***arr, uint32 d1, uint32 d2, uint32 d3);
  
  /**
   * Floor 3-d array
   * @param out output array
   * @param in input array
   * @param d1 dimension
   * @param d2 dimension
   * @param d3 dimension
   **/
  SPHINXBASE_EXPORT void
  accum_3d(float32 ***out, float32 ***in, uint32 d1, uint32 d2, uint32 d3);
  
  /** Ensures that non-zero values x such that -band < x < band, band > 0 are set to -band if x < 0 and band if x > 0.
   * @param v array
   * @param d1 array size
   * @param band band value
   */
  SPHINXBASE_EXPORT void band_nz_1d(float32 *v, uint32 d1, float32 band);
  
  /**
   * Floor 3-d array
   * @param m array
   * @param d1 dimension
   * @param d2 dimension
   * @param d3 dimension
   * @param floor floor value
   **/
  SPHINXBASE_EXPORT void floor_nz_3d(float32 ***m, uint32 d1, uint32 d2, uint32 d3, float32 floor);
  
  /**
   * Floor 1-d array
   * @param v array
   * @param d1 dimension
   * @param floor floor value
   **/
  SPHINXBASE_EXPORT void floor_nz_1d(float32 *v, uint32 d1, float32 floor);
  
  /**
   * Calculate the determinant of a positive definite matrix.
   * @param a The input matrix, must be positive definite.
   * @param len The dimension of the input matrix.
   * @return The determinant of the input matrix, or -1.0 if the matrix is
   * not positive definite.
   *
   * \note These can be vanishingly small hence the float64 return type.
   * Also note that only the upper triangular portion of a is
   * considered, therefore the check for positive-definiteness is not
   * reliable.
   **/
  SPHINXBASE_EXPORT
  float64 determinant(float32 **a, int32 len);
  
  /**
   * Invert (if possible) a positive definite matrix with QR
   * algorithm.
   *
   * @param out_ainv The inverse of a will be stored here.
   * @param a The input matrix, must be positive definite.
   * @param len The dimension of the input matrix.
   * @return 0 for success or -1 for a non-positive-definite matrix.
   *
   * \note Only the upper triangular portion of a is considered,
   * therefore the check for positive-definiteness is not reliable.
   *
   * \note The inversion can be done in-place, so you can use the same matrix
   * if you do not need to keep a.
   **/
  SPHINXBASE_EXPORT
  int32 invert(float32 **out_ainv, float32 **a, int32 len);
  
  /**
   * Solve (if possible) a positive-definite system of linear equations AX=B for X.
   * @param a The A matrix on the left-hand side of the equation, must be positive-definite.
   * @param b The B vector on the right-hand side of the equation.
   * @param out_x The X vector will be stored here.
   * @param n The dimension of the A matrix (n by n) and the B and X vectors.
   * @return 0 for success or -1 for a non-positive-definite matrix.
   *
   * \note Only the upper triangular portion of a is considered,
   * therefore the check for positive-definiteness is not reliable.
   **/
  SPHINXBASE_EXPORT
  int32 solve(float32 **a, float32 *b,
              float32 *out_x, int32 n);
  
  /**
   * Calculate the outer product of two vectors.
   * @param out_a A (pre-allocated) len x len array. The outer product
   * will be stored here.
   * @param x A vector of length len.
   * @param y A vector of length len.
   * @param len The length of the input vectors.
   **/
  SPHINXBASE_EXPORT
  void outerproduct(float32 **out_a, float32 *x, float32 *y, int32 len);
  
  /**
   * Multiply C=AB where A and B are symmetric matrices.
   * @param out_c The output matrix C.
   * @param a The input matrix A.
   * @param b The input matrix B.
   * @param n Dimensionality of A and B.
   **/
  SPHINXBASE_EXPORT
  void matrixmultiply(float32 **out_c, /* = */
                      float32 **a, /* * */ float32 **b,
                      int32 n);
  
  /**
   * Multiply a symmetric matrix by a constant in-place.
   * @param inout_a The matrix to multiply.
   * @param x The constant to multiply it by.
   * @param n dimension of a.
   **/
  SPHINXBASE_EXPORT
  void scalarmultiply(float32 **inout_a, float32 x, int32 n);
  
  /**
   * Add A += B.
   * @param inout_a The A matrix to add.
   * @param b The B matrix to add to A.
   * @param n dimension of a and b.
   **/
  SPHINXBASE_EXPORT
  void matrixadd(float32 **inout_a, float32 **b, int32 n);
  
  #if 0
  { /* Fool indent. */
  #endif
  #ifdef __cplusplus
  }
  #endif
  
  #endif /* MATRIX_H */ 
  