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+/* -*- 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
+ * @para 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 m 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.
+ * @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.
+ **/
+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 */ 
+