.\" Copyright (c) 1994 The Board of Trustees of The Leland Stanford
.\" Junior University.  All rights reserved.
.\" 
.\" Permission to use, copy, modify and distribute this software and its
.\" documentation for any purpose is hereby granted without fee, provided
.\" that the above copyright notice and this permission notice appear in
.\" all copies of this software and that you do not sell the software.
.\" Commercial licensing is available by contacting the author.
.\" 
.\" THE SOFTWARE IS PROVIDED "AS IS" AND WITHOUT WARRANTY OF ANY KIND,
.\" EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
.\" WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
.\" 
.\" Author:
.\"    Phil Lacroute
.\"    Computer Systems Laboratory
.\"    Electrical Engineering Dept.
.\"    Stanford University
.\" 
.\" $Date: 1994/12/31 19:49:53 $
.\" $Revision: 1.1 $
.\"
.\" Macros
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.TH LinearAlgebra 3 "" VolPack
.SH NAME
vpIdentity3, vpIdentity4, vpNormalize3, vpMatrixVectorMult4,
vpMatrixMult4, vpCrossProduct, vpSolveSystem4, vpSetVector3,
vpSetVector4 \- linear algebra routines
.SH SYNOPSIS
#include <volpack.h>
.sp
.FS void
\fBvpIdentity3(\fIm_dst\fB)\fR
.FA
vpMatrix3 \fIm_dst;\fR
.FE
.sp
.FS void
\fBvpIdentity4(\fIm_dst\fB)\fR
.FA
vpMatrix4 \fIm_dst;\fR
.FE
.sp
.FS vpResult
\fBvpNormalize3(\fIv_src1\fB)\fR
.FA
vpVector3 \fIv_src1;\fR
.FE
.sp
.FS void
\fBvpMatrixVectorMult4(\fIv_dst, m_src1, v_src1\fB)\fR
.FA
vpVector4 \fIv_dst;\fR
.FA
vpMatrix4 \fIm_src1;\fR
.FA
vpVector4 \fIv_src1;\fR
.FE
.sp
.FS void
\fBvpMatrixMult4(\fIm_dst, m_src1, m_src2\fB)\fR
.FA
vpVector4 \fIm_dst, m_src1, m_src2;\fR
.FE
.sp
.FS void
\fBvpCrossProduct(\fIv_dst, v_src1, v_src2\fB)\fR
.FA
vpVector3 \fIv_dst, v_src1, v_src2;\fR
.FE
.sp
.FS vpResult
\fBvpSolveSystem4(\fIm_src1, b, count\fB)\fR
.FA
vpMatrix4 \fIm_src1;\fR
.FA
vpVector4 \fIb[];\fR
.FA
int \fIcount;\fR
.FE
.sp
.FS void
\fBvpSetVector3(\fIv_dst, x, y, z\fB)\fR
.FA
vpVector3 \fIv_dst;\fR
.FA
double \fIx, y, z;\fR
.FE
.sp
.FS void
\fBvpSetVector4(\fIv_dst, x, y, z, w\fB)\fR
.FA
vpVector4 \fIv_dst;\fR
.FA
double \fIx, y, z, w;\fR
.FE
.SH ARGUMENTS
.IP "\fIm_src1, m_src2, m_dst\fR"
Source and destination matrices.
.IP "\fIv_src1, v_src2, v_dst\fR"
Source and destination vectors.
.IP \fIb\fR
Array of right-hand-side vectors.
.IP \fIcount\fR
Number of right-hand-side vectors.
.IP "\fIx, y, z, w\fR"
Vector components.
.SH DESCRIPTION
These routines form a simple linear algebra package used internally by
VolPack.  The routines are also available as utility routines for use
by the application.
.PP
\fBvpIdentity3\fR assigns the identity matrix to a 3-by-3 matrix.
.PP
\fBvpIdentity4\fR assigns the identity matrix to a 4-by-4 matrix.
.PP
\fBvpNormalize3\fR normalizes a 3-element vector (so the magnitude is
1.0).  The result overwrites the source vector.
.PP
\fBvpMatrixVectorMult4\fR multiplies a 4-by-4 matrix by a 4-element
column vector and stores the result in the destination vector
\fI(v_dst = m . v_src)\fR.
.PP
\fBvpMatrixMult4\fR multiplies two 4-by-4 matrices and stores the
result in the destination matrix \fI(m_dst = m_src1 . m_src2)\fR.
.PP
\fBvpCrossProduct\fR computes the cross product of two 3-element
vectors and stores the result in the destination vector \fI(v_dst =
v_src1 x v_src2)\fR.
.PP
\fBvpSolveSystem4\fR solves the linear system \fIm . x = b\fR for each
right-hand-side vector in the \fIb\fR array.  The solution vectors
overwrite the vectors in the \fIb\fR array.  The solution is computed
using Gauss-Jordan elimination with partial pivoting and implicit
scaling.
.PP
\fBvpSetVector3\fR initializes the components of a 3-element vector
\fI(v_dst = [x, y, z]).\fR  It is a macro.
.PP
\fBvpSetVector4\fR initializes the components of a 4-element vector
\fI(v_dst = [x, y, z, w]).\fR  It is a macro.
.SH ERRORS
\fBvpNormalize3\fR and \fBvpSolveSystem4\fR normally return VP_OK.
The following error return value is possible:
.IP VPERROR_SINGULAR
The vector is a 0 vector (\fBvpNormalize3\fR only), or the matrix is
singular (\fBvpSolveSystem4\fR only).
.SH SEE ALSO
VolPack(3)