NAME

       vpIdentity3,     vpIdentity4,     vpNormalize3,     vpMatrixVectorMult4,    vpMatrixMult4,
       vpCrossProduct, vpSolveSystem4, vpSetVector3, vpSetVector4 - linear algebra routines

SYNOPSIS

       #include <volpack.h>

       void
       vpIdentity3(m_dst)
           vpMatrix3 m_dst;

       void
       vpIdentity4(m_dst)
           vpMatrix4 m_dst;

       vpResult
       vpNormalize3(v_src1)
           vpVector3 v_src1;

       void
       vpMatrixVectorMult4(v_dst, m_src1, v_src1)
           vpVector4 v_dst;
           vpMatrix4 m_src1;
           vpVector4 v_src1;

       void
       vpMatrixMult4(m_dst, m_src1, m_src2)
           vpVector4 m_dst, m_src1, m_src2;

       void
       vpCrossProduct(v_dst, v_src1, v_src2)
           vpVector3 v_dst, v_src1, v_src2;

       vpResult
       vpSolveSystem4(m_src1, b, count)
           vpMatrix4 m_src1;
           vpVector4 b[];
           int count;

       void
       vpSetVector3(v_dst, x, y, z)
           vpVector3 v_dst;
           double x, y, z;

       void
       vpSetVector4(v_dst, x, y, z, w)
           vpVector4 v_dst;
           double x, y, z, w;

ARGUMENTS

       m_src1, m_src2, m_dst
              Source and destination matrices.

       v_src1, v_src2, v_dst
              Source and destination vectors.

       b      Array of right-hand-side vectors.

       count  Number of right-hand-side vectors.

       x, y, z, w
              Vector components.

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.

       vpIdentity3 assigns the identity matrix to a 3-by-3 matrix.

       vpIdentity4 assigns the identity matrix to a 4-by-4 matrix.

       vpNormalize3  normalizes  a  3-element  vector  (so  the  magnitude  is  1.0).  The result
       overwrites the source vector.

       vpMatrixVectorMult4 multiplies a 4-by-4 matrix by a 4-element column vector and stores the
       result in the destination vector (v_dst = m . v_src).

       vpMatrixMult4  multiplies  two  4-by-4  matrices  and stores the result in the destination
       matrix (m_dst = m_src1 . m_src2).

       vpCrossProduct computes the cross product of two 3-element vectors and stores  the  result
       in the destination vector (v_dst = v_src1 x v_src2).

       vpSolveSystem4 solves the linear system m . x = b for each right-hand-side vector in the b
       array.  The solution vectors overwrite the vectors  in  the  b  array.   The  solution  is
       computed using Gauss-Jordan elimination with partial pivoting and implicit scaling.

       vpSetVector3  initializes the components of a 3-element vector (v_dst = [x, y, z]).  It is
       a macro.

       vpSetVector4 initializes the components of a 4-element vector (v_dst = [x, y, z, w]).   It
       is a macro.

ERRORS

       vpNormalize3  and  vpSolveSystem4 normally return VP_OK.  The following error return value
       is possible:

       VPERROR_SINGULAR
              The  vector  is  a  0  vector  (vpNormalize3  only),  or  the  matrix  is  singular
              (vpSolveSystem4 only).

SEE ALSO

       VolPack(3)