/*
 * $Id: spm_krutil.c 6654 2015-12-22 12:55:36Z spm $
 * John Ashburner & Jesper Andersson
 */
 
#include <math.h>
#include <limits.h>
#include "mex.h"

/****************************************************************
 **
 ** This is an attempt to speed up the MATLAB kron function a bit.
 ** It is used in the same way as kron (i.e. just replace e.g.
 ** C = kron(A,B); in your code by C = spm_kron(A,B)). It is
 ** roughly twice as fast as kron.
 ** N.B. Can only be used with full matrices (not sparse).
 **
 ** N,B.2 If you intend to call kron many times, each time
 ** adding to the same big matrix like in
 **
 ** for sl =1:nz
 **    tmp  = reshape(y((sl-1)*nx*ny+1:sl*nx*ny),nx,ny);
 **    AtA  = AtA + spm_kron(Bz1(sl,:)'*Bz2(sl,:),spm_krutil(tmp,Bx1,By1,Bx2,By2));
 ** end
 **
 ** you are better off taking a look at spm_kron_add, as in
 **
 ** sl = 1;
 ** tmp  = reshape(y((sl-1)*nx*ny+1:sl*nx*ny),nx,ny);
 ** AtA  = spm_kron(Bz1(sl,:)'*Bz2(sl,:),spm_krutil(tmp,Bx1,By1,Bx2,By2));
 ** for sl =2:nz
 **    tmp  = reshape(y((sl-1)*nx*ny+1:sl*nx*ny),nx,ny);
 **    spm_kron_add(Bz1(sl,:)'*Bz2(sl,:),spm_krutil(tmp,Bx1,By1,Bx2,By2),AtA);
 ** end
 **
 ** which avoids the overhead of memory allocation for each call
 ** (roughly half the execution time, and saves loads of memory).
 **
 ***************************************************************/
 
/* Macro */
#define index(R,C,DIM) ((C-1)*DIM[0] + (R-1))
 
/*
   In this implementation I try to minimise the number
   of arithmetic operations for each element of the
   big matrix, and also be a little bit clever in terms
   of the order in which elements in m2 and bm are
   accessed.
*/
 
void kron(double  *m1,
          mwSize  *sz1,
          double  *m2,
          mwSize  *sz2,
          double  *bm,
          mwSize  *bsz)
{
   mwIndex  r1 = 0, c1 = 0;
   mwIndex  r2 = 0, c2 = 0;
   mwIndex  br = 0, bc = 0;
   mwIndex  i2 = 0, im = 0;
   double   v1 = 0.0;
 
   for (c1=1; c1<=sz1[1]; c1++)
   {
      for (r1=1; r1<=sz1[0]; r1++)
      {
         v1 = m1[index(r1,c1,sz1)];
         for (c2=1; c2<=sz2[1]; c2++)
         {
            br = (r1-1)*sz2[0]+1; /* r2 = 1 */
            bc = (c1-1)*sz2[1]+c2;
            im = index(br,bc,bsz);
            i2 = index(1,c2,sz2); /* r2 = 1 */
            for (r2=1; r2<=sz2[0]; r2++, im++, i2++)
            {
               bm[im] = v1 * m2[i2];
            }
         }
      }
   }
 
   return;
}
 
 
/* Gateway function with error check */

void mexFunction_kron(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
   mwSize  sz1[2];
   mwSize  sz2[2];
   mwSize  bsz[2];
   double  *m1 = NULL;
   double  *m2 = NULL;
   double  *bm = NULL;
 
   if (nrhs == 0) mexErrMsgTxt("usage: BM=spm_kron(M1,M2)");
   if (nrhs != 2) mexErrMsgTxt("spm_kron: 2 input arguments required");
   if (nlhs > 1) mexErrMsgTxt("spm_kron: 1 output argument required");
 
   /* Get first matrix */
   if (!mxIsNumeric(prhs[0]) || mxIsComplex(prhs[0]) || mxIsSparse(prhs[0]) || !mxIsDouble(prhs[0]))
   {
      mexErrMsgTxt("spm_kron: M1 must be numeric, real, full and double");
   }
   sz1[0] = mxGetM(prhs[0]);
   sz1[1] = mxGetN(prhs[0]);
   m1 = mxGetPr(prhs[0]);
 
   /* And second matrix */
   if (!mxIsNumeric(prhs[1]) || mxIsComplex(prhs[1]) || mxIsSparse(prhs[1]) || !mxIsDouble(prhs[1]))
   {
      mexErrMsgTxt("spm_kron: M2 must be numeric, real, full and double");
   }
   sz2[0] = mxGetM(prhs[1]);
   sz2[1] = mxGetN(prhs[1]);
   m2 = mxGetPr(prhs[1]);
 
   /* Allocate memory for output */
   bsz[0] = sz1[0]*sz2[0];
   bsz[1] = sz1[1]*sz2[1];
   plhs[0] = mxCreateNumericMatrix(bsz[0],bsz[1],mxDOUBLE_CLASS,mxREAL);
   bm = mxGetPr(plhs[0]);
 
   /* Do the stuff */
   kron(m1,sz1,m2,sz2,bm,bsz);
 
   return;
}


/****************************************************************
 **
 ** This is an attempt to speed up consecutive calls to kron
 ** of the type
 **
 ** for sl =1:nz
 **    tmp  = reshape(y((sl-1)*nx*ny+1:sl*nx*ny),nx,ny);
 **    AtA  = AtA + kron(Bz1(sl,:)'*Bz2(sl,:),spm_krutil(tmp,Bx1,By1,Bx2,By2));
 ** end
 **
 ** and where AtA is a large matrix (i.e. several thousand squared).
 ** In these instances the repeated alloction of memory is a
 ** large proportion of the execution time, and things get
 ** significantly speeded up by e.g.
 **
 ** sl = 1;
 ** tmp  = reshape(y((sl-1)*nx*ny+1:sl*nx*ny),nx,ny);
 ** AtA  = spm_kron(Bz1(sl,:)'*Bz2(sl,:),spm_krutil(tmp,Bx1,By1,Bx2,By2));
 ** for sl =2:nz
 **    tmp  = reshape(y((sl-1)*nx*ny+1:sl*nx*ny),nx,ny);
 **    spm_kron_add(Bz1(sl,:)'*Bz2(sl,:),spm_krutil(tmp,Bx1,By1,Bx2,By2),AtA);
 ** end
 **
 ** N.B. the behaviour in spm_kron_add is very unusual from a
 ** MATLAB perspective in that one of the input arguments gets
 ** changed. Please keep this in mind.
 **
 ***************************************************************/
 
/*
   In this implementation I try to minimise the number
   of arithmetic operations for each element of the
   big matrix, and also be a little bit clever in terms
   of the order in which elements in m2 and bm are
   accessed.
*/

void kronadd(double  *m1,
             mwSize  *sz1,
             double  *m2,
             mwSize  *sz2,
             double  *bm,
             mwSize  *bsz)
{
   mwIndex  r1 = 0, c1 = 0;
   mwIndex  r2 = 0, c2 = 0;
   mwIndex  br = 0, bc = 0;
   mwIndex  i2 = 0, im = 0;
   double   v1 = 0.0;
 
   for (c1=1; c1<=sz1[1]; c1++)
   {
      for (r1=1; r1<=sz1[0]; r1++)
      {
         v1 = m1[index(r1,c1,sz1)];
         for (c2=1; c2<=sz2[1]; c2++)
         {
            br = (r1-1)*sz2[0]+1; /* r2 = 1 */
            bc = (c1-1)*sz2[1]+c2;
            im = index(br,bc,bsz);
            i2 = index(1,c2,sz2); /* r2 = 1 */
            for (r2=1; r2<=sz2[0]; r2++, im++, i2++)
            {
               bm[im] += v1 * m2[i2];
            }
         }
      }
   }
 
   return;
}
 
 
/* Gateway function with error check. */
 void mexFunction_kronadd(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
   mwSize  sz1[2];
   mwSize  sz2[2];
   mwSize  bsz[2];
   double  *m1 = NULL;
   double  *m2 = NULL;
   double  *bm = NULL;
 
   if (nrhs == 0) mexErrMsgTxt("usage: spm_kron_add(M1,M2,BM)");
   if (nrhs != 3) mexErrMsgTxt("spm_kron_add: 3 input arguments required");
   if (nlhs != 0) mexErrMsgTxt("spm_kron_add: no output argument required");
 
   /* Get first matrix. */
   if (!mxIsNumeric(prhs[0]) || mxIsComplex(prhs[0]) || mxIsSparse(prhs[0]) || !mxIsDouble(prhs[0]))
   {
      mexErrMsgTxt("spm_kron_add: M1 must be numeric, real, full and double");
   }
   sz1[0] = mxGetM(prhs[0]);
   sz1[1] = mxGetN(prhs[0]);
   m1 = mxGetPr(prhs[0]);
 
   /* Second matrix. */
   if (!mxIsNumeric(prhs[1]) || mxIsComplex(prhs[1]) || mxIsSparse(prhs[1]) || !mxIsDouble(prhs[1]))
   {
      mexErrMsgTxt("spm_kron_add: M2 must be numeric, real, full and double");
   }
   sz2[0] = mxGetM(prhs[1]);
   sz2[1] = mxGetN(prhs[1]);
   m2 = mxGetPr(prhs[1]);
 
   /* And third matrix. */
   if (!mxIsNumeric(prhs[2]) || mxIsComplex(prhs[2]) || mxIsSparse(prhs[2]) || !mxIsDouble(prhs[2]))
   {
      mexErrMsgTxt("spm_kron_add: BM must be numeric, real, full and double");
   }
   bsz[0] = mxGetM(prhs[2]);
   bsz[1] = mxGetN(prhs[2]);
   bm = mxGetPr(prhs[2]);
 
   /* Make sure dimensions agree. */
   if (sz1[0]*sz2[0] != bsz[0] || sz1[1]*sz2[1] != bsz[1])
   {
      mexErrMsgTxt("spm_kron_add: size of BM not compatible with sizes of M1 and M2");
   }
 
   /* Do the stuff. */
   kronadd(m1,sz1,m2,sz2,bm,bsz);
 
   return;
}
/********************************************************************************/

/********************************************************************************/
/* beta = kron(b2,b1)'*img(:)
 * m1  - rows in b1
 * m2  - rows in b2
 * n1  - columns in b1
 * n2  - columns in b2
 * img - m2*m2 vector
 * b1  - basis functions - x
 * b2  - basis functions - y
 * beta - resulting vector
*/
void kronutil1(mwSize n1, mwSize n2, mwSize m1, mwSize m2,
    double img[], double b1[], double b2[], double beta[])
{
    mwIndex j1,j2, i1,i2;
    double beta1[32];

    /* Zero beta */
    for(j1=0; j1<n1*n2; j1++) beta[j1]=0.0;

    for(i2=0; i2<m2; i2++)
    {
        /* generate small beta */
        for(j1=0; j1<n1; j1++) beta1[j1]=0.0;
        for(i1=0; i1<m1; i1++)
        {
            double wt = img[i1+m1*i2];
            for(j1=0; j1<n1; j1++)
                beta1[j1] += b1[i1+j1*m1]*wt;
        }

        /* kronecker tensor product to increment beta */
        for(j2=0; j2<n2; j2++)
        {
            double wt = b2[i2+j2*m2];
            double *ptrb = beta+(n1*j2);
            for(j1=0; j1<n1; j1++)
                ptrb[j1] += wt*beta1[j1];
        }
    }
}

/********************************************************************************/
/* alpha = kron(b2,b1)'*diag(img(:))*kron(b2,b1)
 * m1  - rows in b1
 * m2  - rows in b2
 * n1  - columns in b1
 * n2  - columns in b2
 * img - m1*m2 vector
 * b1  - basis functions - x
 * b2  - basis functions - y
 * alpha - resulting matrix
*/
void kronutil2(mwSize n1, mwSize n2, mwSize m1, mwSize m2,
    double img[], double b1[], double b2[], double alpha[])
{
    mwIndex j11,j12, j21,j22, i1, i2;
    double alpha1[1024];

    /* Zero alpha */
    for(j21=0; j21<n1*n2; j21++)
        for(j11=0; j11<=j21; j11++)
            alpha[j11+j21*n1*n2]=0.0;

    for(i2=0; i2<m2; i2++)
    {
        /* zero small alpha */
        for(j21=0; j21<n1; j21++)
            for(j11=0; j11<=j21; j11++)
                alpha1[j11+j21*n1]=0.0;

        /* generate upper half of small alpha */
        for(i1=0; i1<m1; i1++)
        {
            double wt = img[i1+m1*i2];
            for(j21=0; j21<n1; j21++)
            {
                double wt2 = wt*b1[i1+j21*m1];
                for(j11=0; j11<=j21; j11++)
                    alpha1[j11+j21*n1] += wt2*b1[i1+j11*m1];
            }
        }

        /* kronecker tensor product to increment upper half of large alpha */
        for(j22=0; j22<n2; j22++)
        {
            double wt = b2[i2+j22*m2];
            for(j12=0; j12<=j22; j12++)
            {
                double *ptra = alpha+(n1*j12+n1*n1*n2*j22);
                double wt2 = wt*b2[i2+j12*m2];

                for(j21=0; j21<n1; j21++)
                    for(j11=0; j11<=j21; j11++)
                        ptra[j11+j21*n1*n2] += wt2*alpha1[j11+j21*n1];
            }
        }
    }
    /* fill in lower triangle of symmetric submatrices of alpha */
    for(j22=0; j22<n2; j22++)
        for(j12=0; j12<j22; j12++)
        {
            double *ptra = alpha+(n1*j12+n1*n1*n2*j22);
            for(j21=0; j21<n1; j21++)
                for(j11=0; j11<j21; j11++)
                    ptra[j21+j11*n1*n2] = ptra[j11+j21*n1*n2];
        }

    /* fill in lower triangle of alpha */
    for(j22=0; j22<n2*n1; j22++)
        for(j12=0; j12<j22; j12++)
            alpha[j22+j12*n1*n2]=alpha[j12+j22*n1*n2];
}

/********************************************************************************/
/* alpha = kron(B1y,B1x)'*diag(img(:))*kron(B2y,B2x)
*/
void kronutil3(mwSize n1x, mwSize n1y, mwSize n2x, mwSize n2y, mwSize m1, mwSize m2,
    double img[], double b1x[], double b1y[], double b2x[], double b2y[], double alpha[])
{
    mwIndex j1x,j1y, j2x,j2y, i1, i2;
    double alpha1[1024];

    /* Zero alpha */
    for(j2x=0; j2x<n2y*n2x; j2x++)
        for(j1x=0; j1x<n1y*n1x; j1x++)
            alpha[j1x+j2x*n1y*n1x]=0.0;

    for(i2=0; i2<m2; i2++)
    {
        /* zero small alpha */
        for(j2x=0; j2x<n2x; j2x++)
            for(j1x=0; j1x<n1x; j1x++)
                alpha1[j1x+j2x*n1x]=0.0;

        /* generate upper half of small alpha */
        for(i1=0; i1<m1; i1++)
        {
            double wt = img[i1+m1*i2];
            for(j2x=0; j2x<n2x; j2x++)
            {
                double wt2 = wt*b2x[i1+j2x*m1];
                for(j1x=0; j1x<n1x; j1x++)
                    alpha1[j1x+j2x*n1x] += wt2*b1x[i1+j1x*m1];
            }
        }

        /* kronecker tensor product to increment upper half of large alpha */
        for(j2y=0; j2y<n2y; j2y++)
        {
            double wt2 = b2y[i2+j2y*m2];
            for(j1y=0; j1y<n1y; j1y++)
            {
                double *ptra = alpha+(n1x*j1y + n1y*n1x*n2x*j2y);
                double wt1   = wt2*b1y[i2+j1y*m2];

                for(j2x=0; j2x<n2x; j2x++)
                    for(j1x=0; j1x<n1x; j1x++)
                        ptra[j1x+j2x*n1y*n1x] += wt1*alpha1[j1x+j2x*n1x];
            }
        }
    }
}

/* Function gateway */

void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
    mwSize n1x, n1y, n2x, n2y, m1, m2;

    double *alpha, *beta, *img, *b1x, *b1y, *b2x, *b2y;

    if ((nrhs==3) && (nlhs==0))
    {
        mexFunction_kronadd(nlhs, plhs, nrhs, prhs);
        return;
    }
    if ((nrhs==2) && (nlhs<=1))
    {
        mexFunction_kron(nlhs, plhs, nrhs, prhs);
        return;
    }
    if (nrhs == 0) mexErrMsgTxt("Incorrect usage");

    if ((nrhs != 4) && (nrhs != 5)) mexErrMsgTxt("4 or 5 input arguments required");
    if (nlhs > 1) mexErrMsgTxt("only 1 output argument required");

    if (!mxIsNumeric(prhs[0]) || mxIsComplex(prhs[0]) || mxIsSparse(prhs[0]) || !mxIsDouble(prhs[0]))
        mexErrMsgTxt("img must be numeric, real, full and double");
    img = mxGetPr(prhs[0]);
    m1 = mxGetM(prhs[0]);
    m2 = mxGetN(prhs[0]);

    if (!mxIsNumeric(prhs[1]) || mxIsComplex(prhs[1]) || mxIsSparse(prhs[1]) || !mxIsDouble(prhs[1]))
        mexErrMsgTxt("b1x must be numeric, real, full and double");
    b1x = mxGetPr(prhs[1]);
    if (mxGetM(prhs[1]) != m1)
        mexErrMsgTxt("b1x has incompatible m dimension");
    n1x = mxGetN(prhs[1]);

    if (!mxIsNumeric(prhs[2]) || mxIsComplex(prhs[2]) || mxIsSparse(prhs[2]) || !mxIsDouble(prhs[2]))
        mexErrMsgTxt("b1y must be numeric, real, full and double");
    b1y = mxGetPr(prhs[2]);
    if (mxGetM(prhs[2]) != m2)
        mexErrMsgTxt("b1y has incompatible m dimension");
    n1y = mxGetN(prhs[2]);

    if (nrhs == 4)
    {
        if (!mxIsNumeric(prhs[3]) || mxIsComplex(prhs[3]) || mxIsSparse(prhs[3]) || !mxIsDouble(prhs[3]))
            mexErrMsgTxt("flag must be numeric, real, full and double");
        if (mxGetM(prhs[3])*mxGetN(prhs[3]) != 1)
            mexErrMsgTxt("flag must contain only one element");

        if (!*mxGetPr(prhs[3]))
        {
            plhs[0] = mxCreateDoubleMatrix(n1x*n1y,1, mxREAL);
            beta = mxGetPr(plhs[0]);
            kronutil1(n1x,n1y,m1,m2,img,b1x,b1y, beta);
        }
        else
        {
            plhs[0] = mxCreateDoubleMatrix(n1x*n1y,n1x*n1y, mxREAL);
            alpha = mxGetPr(plhs[0]);
            kronutil2(n1x,n1y,m1,m2,img,b1x,b1y, alpha);
        }
    }
    else
    {
        if (!mxIsNumeric(prhs[3]) || mxIsComplex(prhs[3]) || mxIsSparse(prhs[3]) || !mxIsDouble(prhs[3]))
            mexErrMsgTxt("b2x must be numeric, real, full and double");
        b2x = mxGetPr(prhs[3]);
        if (mxGetM(prhs[3]) != m1)
            mexErrMsgTxt("b2x has incompatible m dimension");
        n2x = mxGetN(prhs[3]);

        if (!mxIsNumeric(prhs[4]) || mxIsComplex(prhs[4]) || mxIsSparse(prhs[4]) || !mxIsDouble(prhs[4]))
            mexErrMsgTxt("b1y must be numeric, real, full and double");
        b2y = mxGetPr(prhs[4]);
        if (mxGetM(prhs[4]) != m2)
            mexErrMsgTxt("b2y has incompatible m dimension");
        n2y = mxGetN(prhs[4]);

        plhs[0] = mxCreateDoubleMatrix(n1x*n1y,n2x*n2y, mxREAL);
        alpha = mxGetPr(plhs[0]);
        kronutil3(n1x,n1y,n2x,n2y,m1,m2,img,b1x,b1y,b2x,b2y, alpha);
    }
}
