IProduct.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: IProduct.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
 
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: IProduct operators for multiple calls in different operators
//
///////////////////////////////////////////////////////////////////////////////
 
#include <Collections/Collection.h>
#include <Collections/IProduct.h>
 
using namespace std;
 
namespace Nektar::Collections
{
 
/**
 *
 */
void QuadIProduct(bool colldir0, bool colldir1, int numElmt, int nquad0,
                  int nquad1, int nmodes0, int nmodes1,
                  const Array<OneD, const NekDouble> &base0,
                  const Array<OneD, const NekDouble> &base1,
                  const Array<OneD, const NekDouble> &jac,
                  const Array<OneD, const NekDouble> &input,
                  Array<OneD, NekDouble> &output, Array<OneD, NekDouble> &wsp)
{
    int totpoints = nquad0 * nquad1;
    int totmodes  = nmodes0 * nmodes1;
 
    Vmath::Vmul(numElmt * totpoints, jac, 1, input, 1, wsp, 1);
 
    if (colldir0 && colldir1)
    {
        Vmath::Vcopy(numElmt * totmodes, wsp.data(), 1, output.data(), 1);
    }
    else
    {
        Array<OneD, NekDouble> wsp1 = wsp + max(totpoints, totmodes) * numElmt;
        if (colldir0)
        {
            for (int i = 0; i < nquad0; ++i)
            {
                Vmath::Vcopy(nquad1 * numElmt, &wsp[i], nquad0,
                             &wsp1[i * nquad1 * numElmt], 1);
            }
        }
        else
        {
            Blas::Dgemm('T', 'N', nquad1 * numElmt, nmodes0, nquad0, 1.0,
                        &wsp[0], nquad0, base0.data(), nquad0, 0.0, &wsp1[0],
                        nquad1 * numElmt);
        }
 
        if (numElmt > 1)
        {
            if (colldir1)
            {
                for (int i = 0; i < nquad1; ++i)
                {
                    Vmath::Vcopy(numElmt * nmodes0, &wsp1[i], nquad1,
                                 &wsp[i * numElmt * nmodes0], 1);
                }
            }
            else
            {
 
                Blas::Dgemm('T', 'N', numElmt * nmodes0, nmodes1, nquad1, 1.0,
                            &wsp1[0], nquad1, base1.data(), nquad1, 0.0,
                            &wsp[0], numElmt * nmodes0);
            }
 
            for (int i = 0; i < totmodes; ++i)
            {
                Vmath::Vcopy(numElmt, &wsp[i * numElmt], 1, &output[i],
                             totmodes);
            }
        }
        else
        {
            if (colldir1)
            {
                for (int i = 0; i < nquad1; ++i)
                {
                    Vmath::Vcopy(numElmt * nmodes0, &wsp1[i], nquad1,
                                 &output[i * numElmt * nmodes0], 1);
                }
            }
            else
            {
                Blas::Dgemm('T', 'N', nmodes0, nmodes1, nquad1, 1.0, &wsp1[0],
                            nquad1, base1.data(), nquad1, 0.0, &output[0],
                            nmodes0);
            }
        }
    }
}
 
/**
 *
 */
void TriIProduct(bool sortTopVertex, int numElmt, int nquad0, int nquad1,
                 int nmodes0, int nmodes1,
                 const Array<OneD, const NekDouble> &base0,
                 const Array<OneD, const NekDouble> &base1,
                 const Array<OneD, const NekDouble> &jac,
                 const Array<OneD, const NekDouble> &input,
                 Array<OneD, NekDouble> &output, Array<OneD, NekDouble> &wsp)
{
    int totmodes =
        LibUtilities::StdTriData::getNumberOfCoefficients(nmodes0, nmodes1);
    int totpoints = nquad0 * nquad1;
 
    Vmath::Vmul(numElmt * totpoints, jac, 1, input, 1, wsp, 1);
 
    Array<OneD, NekDouble> wsp1 = wsp + max(totpoints, totmodes) * numElmt;
 
    Blas::Dgemm('T', 'N', nquad1 * numElmt, nmodes0, nquad0, 1.0, &wsp[0],
                nquad0, base0.data(), nquad0, 0.0, &wsp1[0], nquad1 * numElmt);
 
    int i, mode;
    // Inner product with respect to 'b' direction
    for (mode = i = 0; i < nmodes0; ++i)
    {
        Blas::Dgemm('T', 'N', nmodes1 - i, numElmt, nquad1, 1.0,
                    base1.data() + mode * nquad1, nquad1,
                    wsp1.data() + i * nquad1 * numElmt, nquad1, 0.0,
                    &output[mode], totmodes);
 
        mode += nmodes1 - i;
    }
 
    // fix for modified basis by splitting top vertex mode
    if (sortTopVertex)
    {
        Blas::Dgemv('T', nquad1, numElmt, 1.0, wsp1.data() + nquad1 * numElmt,
                    nquad1, base1.data() + nquad1, 1, 1.0, &output[1],
                    totmodes);
    }
}
 
/**
 *
 */
void HexIProduct(bool colldir0, bool colldir1, bool colldir2, int numElmt,
                 int nquad0, int nquad1, int nquad2, int nmodes0, int nmodes1,
                 int nmodes2, const Array<OneD, const NekDouble> &base0,
                 const Array<OneD, const NekDouble> &base1,
                 const Array<OneD, const NekDouble> &base2,
                 const Array<OneD, const NekDouble> &jac,
                 const Array<OneD, const NekDouble> &input,
                 Array<OneD, NekDouble> &output, Array<OneD, NekDouble> &wsp)
{
    int totmodes  = nmodes0 * nmodes1 * nmodes2;
    int totpoints = nquad0 * nquad1 * nquad2;
 
    if (colldir0 && colldir1 && colldir2)
    {
 
        Vmath::Vmul(numElmt * totpoints, jac, 1, input, 1, output, 1);
    }
    else
    {
        Vmath::Vmul(numElmt * totpoints, jac, 1, input, 1, wsp, 1);
 
        // Assign second half of workspace for 2nd DGEMM operation.
        Array<OneD, NekDouble> wsp1 = wsp + totpoints * numElmt;
 
        // note sure what criterion we should use to swap around these
        // strategies
        if (numElmt < nmodes0 || 1)
        {
            Array<OneD, NekDouble> wsp2 = wsp1 + nmodes0 * nquad1 * nquad2;
 
            // loop over elements
            for (int n = 0; n < numElmt; ++n)
            {
                if (colldir0)
                {
                    for (int i = 0; i < nmodes0; ++i)
                    {
                        Vmath::Vcopy(nquad1 * nquad2, &wsp[n * totpoints] + i,
                                     nquad0, wsp1.data() + nquad1 * nquad2 * i,
                                     1);
                    }
                }
                else
                {
                    Blas::Dgemm('T', 'N', nquad1 * nquad2, nmodes0, nquad0, 1.0,
                                &wsp[n * totpoints], nquad0, base0.data(),
                                nquad0, 0.0, wsp1.data(), nquad1 * nquad2);
                }
 
                if (colldir1)
                {
                    // reshuffle data for next operation.
                    for (int i = 0; i < nmodes1; ++i)
                    {
                        Vmath::Vcopy(nquad2 * nmodes0, wsp1.data() + i, nquad1,
                                     wsp2.data() + nquad2 * nmodes0 * i, 1);
                    }
                }
                else
                {
                    Blas::Dgemm('T', 'N', nquad2 * nmodes0, nmodes1, nquad1,
                                1.0, wsp1.data(), nquad1, base1.data(), nquad1,
                                0.0, wsp2.data(), nquad2 * nmodes0);
                }
 
                if (colldir2)
                {
                    // reshuffle data for next operation.
                    for (int i = 0; i < nmodes2; ++i)
                    {
                        Vmath::Vcopy(
                            nmodes0 * nmodes1, wsp2.data() + i, nquad2,
                            &output[n * totmodes] + nmodes0 * nmodes1 * i, 1);
                    }
                }
                else
                {
                    Blas::Dgemm('T', 'N', nmodes0 * nmodes1, nmodes2, nquad2,
                                1.0, wsp2.data(), nquad2, base2.data(), nquad2,
                                0.0, &output[n * totmodes], nmodes0 * nmodes1);
                }
            }
        }
        else
        {
            Array<OneD, NekDouble> wsp2 =
                wsp1 + numElmt * (max(totpoints, totmodes));
 
            if (colldir0)
            {
                for (int i = 0; i < nquad0; ++i)
                {
                    Vmath::Vcopy(nquad1 * nquad2 * numElmt, &wsp[i], nquad0,
                                 &wsp1[i * nquad1 * nquad2 * numElmt], 1);
                }
            }
            else
            {
                // large degmm but copy at end.
                Blas::Dgemm('T', 'N', nquad1 * nquad2 * numElmt, nmodes0,
                            nquad0, 1.0, &wsp[0], nquad0, base0.data(), nquad0,
                            0.0, &wsp1[0], nquad1 * nquad2 * numElmt);
            }
 
            if (colldir1)
            {
                for (int i = 0; i < nquad1; ++i)
                {
                    Vmath::Vcopy(nquad2 * numElmt * nmodes0, &wsp1[i], nquad1,
                                 &wsp2[i * nquad2 * numElmt * nmodes0], 1);
                }
            }
            else
            {
                Blas::Dgemm('T', 'N', nquad2 * numElmt * nmodes0, nmodes1,
                            nquad1, 1.0, &wsp1[0], nquad1, base1.data(), nquad1,
                            0.0, &wsp2[0], nquad2 * numElmt * nmodes0);
            }
 
            if (numElmt > 1)
            {
                if (colldir2)
                {
                    for (int i = 0; i < nquad2; ++i)
                    {
                        Vmath::Vcopy(nmodes0 * nmodes1, &wsp2[i], nquad2,
                                     &output[i * nmodes0 * nmodes1], 1);
                    }
                }
                else
                {
                    Blas::Dgemm('T', 'N', numElmt * nmodes0 * nmodes1, nmodes2,
                                nquad2, 1.0, &wsp2[0], nquad2, base2.data(),
                                nquad2, 0.0, &wsp1[0],
                                numElmt * nmodes0 * nmodes1);
                }
 
                for (int i = 0; i < totmodes; ++i)
                {
                    Vmath::Vcopy(numElmt, &wsp1[i * numElmt], 1, &output[i],
                                 totmodes);
                }
            }
            else
            {
                if (colldir2)
                {
                    for (int i = 0; i < nquad2; ++i)
                    {
                        Vmath::Vcopy(nmodes0 * nmodes1, &wsp2[i], nquad2,
                                     &output[i * nmodes0 * nmodes1], 1);
                    }
                }
                else
                {
                    Blas::Dgemm('T', 'N', numElmt * nmodes0 * nmodes1, nmodes2,
                                nquad2, 1.0, &wsp2[0], nquad2, base2.data(),
                                nquad2, 0.0, &output[0],
                                numElmt * nmodes0 * nmodes1);
                }
            }
        }
    }
}
 
/**
 *
 */
void PrismIProduct(bool sortTopVertex, int numElmt, int nquad0, int nquad1,
                   int nquad2, int nmodes0, int nmodes1, int nmodes2,
                   const Array<OneD, const NekDouble> &base0,
                   const Array<OneD, const NekDouble> &base1,
                   const Array<OneD, const NekDouble> &base2,
                   const Array<OneD, const NekDouble> &jac,
                   const Array<OneD, const NekDouble> &input,
                   Array<OneD, NekDouble> &output, Array<OneD, NekDouble> &wsp)
{
    int totmodes = LibUtilities::StdPrismData::getNumberOfCoefficients(
        nmodes0, nmodes1, nmodes2);
    int totpoints = nquad0 * nquad1 * nquad2;
    int cnt;
    int mode, mode1;
 
    Vmath::Vmul(numElmt * totpoints, jac, 1, input, 1, wsp, 1);
 
    Array<OneD, NekDouble> wsp1 =
        wsp + numElmt * nquad2 * (max(nquad0 * nquad1, nmodes0 * nmodes1));
 
    // Perform iproduct  with respect to the  '0' direction
    Blas::Dgemm('T', 'N', nquad1 * nquad2 * numElmt, nmodes0, nquad0, 1.0,
                wsp.data(), nquad0, base0.data(), nquad0, 0.0, wsp1.data(),
                nquad1 * nquad2 * numElmt);
 
    // Perform iproduct  with respect to the  '1' direction
    Blas::Dgemm('T', 'N', nquad2 * numElmt * nmodes0, nmodes1, nquad1, 1.0,
                wsp1.data(), nquad1, base1.data(), nquad1, 0.0, wsp.data(),
                nquad2 * numElmt * nmodes0);
 
    // Inner product with respect to the '2' direction (not sure if it would
    // be better to swap loops?)
    mode = mode1 = cnt = 0;
    for (int i = 0; i < nmodes0; ++i)
    {
        cnt = i * nquad2 * numElmt;
        for (int j = 0; j < nmodes1; ++j)
        {
            Blas::Dgemm('T', 'N', nmodes2 - i, numElmt, nquad2, 1.0,
                        base2.data() + mode * nquad2, nquad2,
                        wsp.data() + j * nquad2 * numElmt * nmodes0 + cnt,
                        nquad2, 0.0, output.data() + mode1, totmodes);
            mode1 += nmodes2 - i;
        }
        mode += nmodes2 - i;
    }
 
    // fix for modified basis by splitting top vertex mode
    if (sortTopVertex)
    {
        // top singular vertex
        // ((1+a)/2 components entry into (1+c)/2)
        // Could be made into an mxv if we have specialised base1[1]
        for (int j = 0; j < nmodes1; ++j)
        {
            Blas::Dgemv('T', nquad2, numElmt, 1.0,
                        wsp.data() + j * nquad2 * numElmt * nmodes0 +
                            nquad2 * numElmt,
                        nquad2, base2.data() + nquad2, 1, 1.0,
                        &output[j * nmodes2 + 1], totmodes);
        }
    }
}
 
/**
 *
 */
void PyrIProduct(bool sortTopVertex, int numElmt, int nquad0, int nquad1,
                 int nquad2, int nmodes0, int nmodes1, int nmodes2,
                 const Array<OneD, const NekDouble> &base0,
                 const Array<OneD, const NekDouble> &base1,
                 const Array<OneD, const NekDouble> &base2,
                 const Array<OneD, const NekDouble> &jac,
                 const Array<OneD, const NekDouble> &input,
                 Array<OneD, NekDouble> &output, Array<OneD, NekDouble> &wsp)
{
    int totmodes = LibUtilities::StdPyrData::getNumberOfCoefficients(
        nmodes0, nmodes1, nmodes2);
    int totpoints = nquad0 * nquad1 * nquad2;
    int cnt;
    int mode, mode1;
 
    ASSERTL1(wsp.size() >=
                 numElmt * (nquad1 * nquad2 * nmodes0 +
                            nquad2 * max(nquad0 * nquad1, nmodes0 * nmodes1)),
             "Insufficient workspace size");
 
    Vmath::Vmul(numElmt * totpoints, jac, 1, input, 1, wsp, 1);
 
    Array<OneD, NekDouble> wsp1 =
        wsp + numElmt * nquad2 * (max(nquad0 * nquad1, nmodes0 * nmodes1));
 
    // Perform iproduct  with respect to the  '0' direction
    Blas::Dgemm('T', 'N', nquad1 * nquad2 * numElmt, nmodes0, nquad0, 1.0,
                wsp.data(), nquad0, base0.data(), nquad0, 0.0, wsp1.data(),
                nquad1 * nquad2 * numElmt);
 
    // Inner product with respect to the '1' direction
    mode = 0;
    for (int i = 0; i < nmodes0; ++i)
    {
        Blas::Dgemm('T', 'N', nquad2 * numElmt, nmodes1, nquad1, 1.0,
                    wsp1.data() + i * nquad1 * nquad2 * numElmt, nquad1,
                    base1.data(), nquad1, 0.0,
                    wsp.data() + mode * nquad2 * numElmt, nquad2 * numElmt);
        mode += nmodes1;
    }
 
    // Inner product with respect to the '2' direction
    mode = mode1 = cnt = 0;
    for (int i = 0; i < nmodes0; ++i)
    {
        for (int j = 0; j < nmodes1; ++j, ++cnt)
        {
            int ijmax = max(i, j);
            Blas::Dgemm('T', 'N', nmodes2 - ijmax, numElmt, nquad2, 1.0,
                        base2.data() + mode * nquad2, nquad2,
                        wsp.data() + cnt * nquad2 * numElmt, nquad2, 0.0,
                        output.data() + mode1, totmodes);
            mode += nmodes2 - ijmax;
            mode1 += nmodes2 - ijmax;
        }
 
        // increment mode in case order1!=order2
        for (int j = nmodes1; j < nmodes2; ++j)
        {
            mode += nmodes2 - j;
        }
    }
 
    // fix for modified basis for top singular vertex component
    // Already have evaluated (1+c)/2 (1-b)/2 (1-a)/2
    if (sortTopVertex)
    {
        for (int n = 0; n < numElmt; ++n)
        {
            // add in (1+c)/2 (1+b)/2 component
            output[1 + n * totmodes] +=
                Vmath::Dot(nquad2, base2.data() + nquad2, 1,
                           &wsp[nquad2 * numElmt + n * nquad2], 1);
 
            // add in (1+c)/2 (1-b)/2 (1+a)/2 component
            output[1 + n * totmodes] +=
                Vmath::Dot(nquad2, base2.data() + nquad2, 1,
                           &wsp[nquad2 * nmodes1 * numElmt + n * nquad2], 1);
 
            // add in (1+c)/2 (1+b)/2 (1+a)/2 component
            output[1 + n * totmodes] += Vmath::Dot(
                nquad2, base2.data() + nquad2, 1,
                &wsp[nquad2 * (nmodes1 + 1) * numElmt + n * nquad2], 1);
        }
    }
}
 
/**
 *
 */
void TetIProduct(bool sortTopEdge, int numElmt, int nquad0, int nquad1,
                 int nquad2, int nmodes0, int nmodes1, int nmodes2,
                 const Array<OneD, const NekDouble> &base0,
                 const Array<OneD, const NekDouble> &base1,
                 const Array<OneD, const NekDouble> &base2,
                 const Array<OneD, const NekDouble> &jac,
                 const Array<OneD, const NekDouble> &input,
                 Array<OneD, NekDouble> &output, Array<OneD, NekDouble> &wsp)
{
    int totmodes = LibUtilities::StdTetData::getNumberOfCoefficients(
        nmodes0, nmodes1, nmodes2);
    int totpoints = nquad0 * nquad1 * nquad2;
    int cnt;
    int mode, mode1;
 
    Vmath::Vmul(numElmt * totpoints, jac, 1, input, 1, wsp, 1);
 
    Array<OneD, NekDouble> wsp1 =
        wsp +
        nquad2 * numElmt *
            (max(nquad0 * nquad1, nmodes0 * (2 * nmodes1 - nmodes0 + 1) / 2));
 
    // Perform iproduct  with respect to the  '0' direction
    Blas::Dgemm('T', 'N', nquad1 * nquad2 * numElmt, nmodes0, nquad0, 1.0,
                wsp.data(), nquad0, base0.data(), nquad0, 0.0, wsp1.data(),
                nquad1 * nquad2 * numElmt);
 
    // Inner product with respect to the '1' direction
    mode = 0;
    for (int i = 0; i < nmodes0; ++i)
    {
        Blas::Dgemm('T', 'N', nquad2 * numElmt, nmodes1 - i, nquad1, 1.0,
                    wsp1.data() + i * nquad1 * nquad2 * numElmt, nquad1,
                    base1.data() + mode * nquad1, nquad1, 0.0,
                    wsp.data() + mode * nquad2 * numElmt, nquad2 * numElmt);
        mode += nmodes1 - i;
    }
 
    // fix for modified basis by splitting top vertex mode
    if (sortTopEdge)
    {
        // base singular vertex and singular edge (1+b)/2
        // ((1+a)/2 components entry into (1+b)/2)
        // Could be made into an mxm if we have specialised base1[1]
        for (int n = 0; n < numElmt; ++n)
        {
            Blas::Dgemv('T', nquad1, nquad2, 1.0,
                        wsp1.data() + numElmt * nquad1 * nquad2 +
                            n * nquad1 * nquad2,
                        nquad1, base1.data() + nquad1, 1, 1.0,
                        wsp.data() + nquad2 * numElmt + n * nquad2, 1);
        }
    }
 
    // Inner product with respect to the '2' direction
    mode = mode1 = cnt = 0;
    for (int i = 0; i < nmodes0; ++i)
    {
        for (int j = 0; j < nmodes1 - i; ++j, ++cnt)
        {
            Blas::Dgemm('T', 'N', nmodes2 - i - j, numElmt, nquad2, 1.0,
                        base2.data() + mode * nquad2, nquad2,
                        wsp.data() + cnt * nquad2 * numElmt, nquad2, 0.0,
                        output.data() + mode1, totmodes);
            mode += nmodes2 - i - j;
            mode1 += nmodes2 - i - j;
        }
 
        // increment mode in case order1!=order2
        mode += (nmodes2 - nmodes1) * (nmodes2 - nmodes1 + 1) / 2;
    }
 
    // fix for modified basis for top singular vertex component
    // Already have evaluated (1+c)/2 (1-b)/2 (1-a)/2
    if (sortTopEdge)
    {
        for (int n = 0; n < numElmt; ++n)
        {
            // add in (1+c)/2 (1+b)/2 component
            output[1 + n * totmodes] +=
                Vmath::Dot(nquad2, base2.data() + nquad2, 1,
                           &wsp[nquad2 * numElmt + n * nquad2], 1);
 
            // add in (1+c)/2 (1-b)/2 (1+a)/2 component
            output[1 + n * totmodes] +=
                Vmath::Dot(nquad2, base2.data() + nquad2, 1,
                           &wsp[nquad2 * nmodes1 * numElmt + n * nquad2], 1);
        }
    }
}
 
} // namespace Nektar::Collections