spsolve.c

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/*
 *  MATRIX SOLVE MODULE
 *
 *  Author:                     Advising professor:
 *      Kenneth S. Kundert          Alberto Sangiovanni-Vincentelli
 *      UC Berkeley
 */
/*! \file
 *  This file contains the forward and backward substitution routines for
 *  the sparse matrix routines.
 *
 *  Objects that begin with the \a spc prefix are considered private
 *  and should not be used.
 *
 *  \author
 *  Kenneth S. Kundert <[e-mail]>
 */
/*  >>> User accessible functions contained in this file:
 *  spSolve
 *  spSolveTransposed
 *
 *  >>> Other functions contained in this file:
 *  SolveComplexMatrix
 *  SolveComplexTransposedMatrix
 */


/*
 *  Revision and copyright information.
 *
 *  Copyright (c) 1985-2003
 *  by Kenneth S. Kundert
 */
#if 0
static char copyright[] =
    "Sparse1.4: Copyright (c) 1985-2003 by Kenneth S. Kundert";
#endif


/*
 *  IMPORTS
 *
 *  >>> Import descriptions:
 *  spConfig.h
 *     Macros that customize the sparse matrix routines.
 *  spMatrix.h
 *     Macros and declarations to be imported by the user.
 *  spDefs.h
 *     Matrix type and macro definitions for the sparse matrix routines.
 */

#define spINSIDE_SPARSE
#include <stdio.h>
#include "spConfig.h"
#include "spMatrix.h"
#include "spDefs.h"




/*
 * Function declarations
 */

#if spSEPARATED_COMPLEX_VECTORS
static void SolveComplexMatrix( MatrixPtr,
                        RealVector, RealVector, RealVector, RealVector );
static void SolveComplexTransposedMatrix( MatrixPtr,
                        RealVector, RealVector, RealVector, RealVector );
#elseif spCOMPLEX
static void SolveComplexMatrix( MatrixPtr, RealVector, RealVector );
static void SolveComplexTransposedMatrix( MatrixPtr,
                        RealVector, RealVector );
#endif







/*!
 *  Performs forward elimination and back substitution to find the
 *  unknown vector from the \a RHS vector and factored matrix.  This
 *  routine assumes that the pivots are associated with the lower
 *  triangular matrix and that the diagonal of the upper triangular
 *  matrix consists of ones.  This routine arranges the computation
 *  in different way than is traditionally used in order to exploit the
 *  sparsity of the right-hand side.  See the reference in spRevision.
 *
 *  \param eMatrix
 *      Pointer to matrix.
 *  \param RHS
 *      \a RHS is the input data array, the right hand side. This data is
 *      undisturbed and may be reused for other solves.
 *  \param Solution
 *      \a Solution is the output data array. This routine is constructed
 *      such that \a RHS and \a Solution can be the same array.
 *  \param iRHS
 *      \a iRHS is the imaginary portion of the input data array, the right
 *      hand side. This data is undisturbed and may be reused for other solves.
 *      This argument is only necessary if matrix is complex and if
 *      \a spSEPARATED_COMPLEX_VECTOR is set true.
 *  \param iSolution
 *      \a iSolution is the imaginary portion of the output data array. This
 *      routine is constructed such that \a iRHS and \a iSolution can be
 *      the same array.  This argument is only necessary if matrix is complex
 *      and if \a spSEPARATED_COMPLEX_VECTOR is set true.
 */
/*  >>> Local variables:
 *  Intermediate  (RealVector)
 *      Temporary storage for use in forward elimination and backward
 *      substitution.  Commonly referred to as c, when the LU factorization
 *      equations are given as  Ax = b, Lc = b, Ux = c Local version of
 *      Matrix->Intermediate, which was created during the initial
 *      factorization in function spcCreateInternalVectors() in the matrix
 *      factorization module.
 *  pElement  (ElementPtr)
 *      Pointer used to address elements in both the lower and upper triangle
 *      matrices.
 *  pExtOrder  (int *)
 *      Pointer used to sequentially access each entry in IntToExtRowMap
 *      and IntToExtColMap arrays.  Used to quickly scramble and unscramble
 *      RHS and Solution to account for row and column interchanges.
 *  pPivot  (ElementPtr)
 *      Pointer that points to current pivot or diagonal element.
 *  Size  (int)
 *      Size of matrix. Made local to reduce indirection.
 *  Temp  (RealNumber)
 *      Temporary storage for entries in arrays.
 *
 *  >>> Obscure Macros
 *  IMAG_VECTORS
 *      Replaces itself with `, iRHS, iSolution' if the options spCOMPLEX and
 *      spSEPARATED_COMPLEX_VECTORS are set, otherwise it disappears
 *      without a trace.
 */

/*VARARGS3*/

void
spSolve(
    spMatrix eMatrix,
    spREAL RHS[],
    spREAL Solution[]
#   if spCOMPLEX AND spSEPARATED_COMPLEX_VECTORS
        , spREAL iRHS[]
        , spREAL iSolution[]
#   endif
)
{
MatrixPtr  Matrix = (MatrixPtr)eMatrix;
register  ElementPtr  pElement;
register  RealVector  Intermediate;
register  RealNumber  Temp;
register  int  I, *pExtOrder, Size;
ElementPtr  pPivot;
void SolveComplexMatrix();

/* Begin `spSolve'. */
    ASSERT_IS_SPARSE( Matrix );
    ASSERT_NO_ERRORS( Matrix );
    ASSERT_IS_FACTORED( Matrix );

#if spCOMPLEX
    if (Matrix->Complex)
    {   SolveComplexMatrix( Matrix, RHS, Solution IMAG_VECTORS );
        return;
    }
#endif

#if REAL
    Intermediate = Matrix->Intermediate;
    Size = Matrix->Size;

/* Correct array pointers for ARRAY_OFFSET. */
#if NOT ARRAY_OFFSET
    --RHS;
    --Solution;
#endif

/* Initialize Intermediate vector. */
    pExtOrder = &Matrix->IntToExtRowMap[Size];
    for (I = Size; I > 0; I--)
        Intermediate[I] = RHS[*(pExtOrder--)];

/* Forward elimination. Solves Lc = b.*/
    for (I = 1; I <= Size; I++)
    {   
/* This step of the elimination is skipped if Temp equals zero. */
        if ((Temp = Intermediate[I]) != 0.0)
        {   pPivot = Matrix->Diag[I];
            Intermediate[I] = (Temp *= pPivot->Real);

            pElement = pPivot->NextInCol;
            while (pElement != NULL)
            {   Intermediate[pElement->Row] -= Temp * pElement->Real;
                pElement = pElement->NextInCol;
            }
        }
    }

/* Backward Substitution. Solves Ux = c.*/
    for (I = Size; I > 0; I--)
    {   Temp = Intermediate[I];
        pElement = Matrix->Diag[I]->NextInRow;
        while (pElement != NULL)
        {   Temp -= pElement->Real * Intermediate[pElement->Col];
            pElement = pElement->NextInRow;
        }
        Intermediate[I] = Temp;
    }

/* Unscramble Intermediate vector while placing data in to Solution vector. */
    pExtOrder = &Matrix->IntToExtColMap[Size];
    for (I = Size; I > 0; I--)
        Solution[*(pExtOrder--)] = Intermediate[I];

    return;
#endif /* REAL */
}











#if spCOMPLEX
/*!
 *  Performs forward elimination and back substitution to find the
 *  unknown vector from the RHS vector and factored matrix.  This
 *  routine assumes that the pivots are associated with the lower
 *  triangular matrix and that the diagonal of the upper triangular
 *  matrix consists of ones.  This routine arranges the computation
 *  in different way than is traditionally used in order to exploit the
 *  sparsity of the right-hand side.  See the reference in spRevision.
 *
 *  \param Matrix
 *      Pointer to matrix.
 *  \param RHS
 *      RHS is the real portion of the input data array, the right hand
 *      side. This data is undisturbed and may be reused for other solves.
 *  \param Solution
 *      Solution is the real portion of the output data array. This routine
 *      is constructed such that RHS and Solution can be the same
 *      array.
 *  \param iRHS
 *      iRHS is the imaginary portion of the input data array, the right
 *      hand side. This data is undisturbed and may be reused for other solves.
 *      If spSEPARATED_COMPLEX_VECTOR is set false, there is no need to
 *      supply this array.
 *  \param iSolution
 *      iSolution is the imaginary portion of the output data array. This
 *      routine is constructed such that iRHS and iSolution can be
 *      the same array.  If spSEPARATED_COMPLEX_VECTOR is set false, there is no
 *      need to supply this array.
 */
/*  >>> Local variables:
 *  Intermediate  (ComplexVector)
 *      Temporary storage for use in forward elimination and backward
 *      substitution.  Commonly referred to as c, when the LU factorization
 *      equations are given as  Ax = b, Lc = b, Ux = c.
 *      Local version of Matrix->Intermediate, which was created during
 *      the initial factorization in function spcCreateInternalVectors() in the
 *      matrix factorization module.
 *  pElement  (ElementPtr)
 *      Pointer used to address elements in both the lower and upper triangle
 *      matrices.
 *  pExtOrder  (int *)
 *      Pointer used to sequentially access each entry in IntToExtRowMap
 *      and IntToExtColMap arrays.  Used to quickly scramble and unscramble
 *      RHS and Solution to account for row and column interchanges.
 *  pPivot  (ElementPtr)
 *      Pointer that points to current pivot or diagonal element.
 *  Size  (int)
 *      Size of matrix. Made local to reduce indirection.
 *  Temp  (ComplexNumber)
 *      Temporary storage for entries in arrays.
 */

static void
SolveComplexMatrix(
    MatrixPtr Matrix,
    RealVector RHS,
    RealVector Solution
#   if spSEPARATED_COMPLEX_VECTORS
        , RealVector iRHS
        , RealVector iSolution
#   endif
)
{
register  ElementPtr  pElement;
register  ComplexVector  Intermediate;
register  int  I, *pExtOrder, Size;
ElementPtr  pPivot;
register ComplexVector  ExtVector;
ComplexNumber  Temp;

/* Begin `SolveComplexMatrix'. */

    Size = Matrix->Size;
    Intermediate = (ComplexVector)Matrix->Intermediate;

/* Correct array pointers for ARRAY_OFFSET. */
#if NOT ARRAY_OFFSET
#if spSEPARATED_COMPLEX_VECTORS
    --RHS;      --iRHS;
    --Solution; --iSolution;
#else
    RHS -= 2; Solution -= 2;
#endif
#endif

/* Initialize Intermediate vector. */
    pExtOrder = &Matrix->IntToExtRowMap[Size];

#if spSEPARATED_COMPLEX_VECTORS
    for (I = Size; I > 0; I--)
    {   Intermediate[I].Real = RHS[*(pExtOrder)];
        Intermediate[I].Imag = iRHS[*(pExtOrder--)];
    }
#else
    ExtVector = (ComplexVector)RHS;
    for (I = Size; I > 0; I--)
        Intermediate[I] = ExtVector[*(pExtOrder--)];
#endif

/* Forward substitution. Solves Lc = b.*/
    for (I = 1; I <= Size; I++)
    {   Temp = Intermediate[I];

/* This step of the substitution is skipped if Temp equals zero. */
        if ((Temp.Real != 0.0) OR (Temp.Imag != 0.0))
        {   pPivot = Matrix->Diag[I];
/* Cmplx expr: Temp *= (1.0 / Pivot). */
            CMPLX_MULT_ASSIGN(Temp, *pPivot);
            Intermediate[I] = Temp;
            pElement = pPivot->NextInCol;
            while (pElement != NULL)
            {
/* Cmplx expr: Intermediate[Element->Row] -= Temp * *Element. */
                CMPLX_MULT_SUBT_ASSIGN(Intermediate[pElement->Row],
                                       Temp, *pElement);
                pElement = pElement->NextInCol;