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mtimesx_RealTimesReal.c
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/*************************************************************************************
*
* MATLAB (R) is a trademark of The Mathworks (R) Corporation
*
* Filename: mtimesx_RealTimesReal.c
* Programmer: James Tursa
* Version: 1.41
* Date: February 23, 2011
* Copyright: (c) 2009, 2010, 2011 by James Tursa, All Rights Reserved
*
* This code uses the BSD License:
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the distribution
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
* mtimesx_RealTimesReal.c is a support file for the mtimesx.c mex routine.
*
* Change Log:
* 2009/Sep/27 --> 1.00, Initial Release
* 2009/Dec/03 --> 1.01, Fixed scalar * sparse for scalar with inf or NaN
* 2009/Dec/05 --> 1.02, Fixed bug, added line scalarmultiply = 0;
* 2009/Dec/08 --> 1.10, Added singleton expansion capability
* 2009/Dec/10 --> 1.11, Slight code simplification for singleton expansion
* 2010/Feb/23 --> 1.20, Fixed bug for dgemv and sgemv calls
* 2010/Aug/02 --> 1.30, Added (nD scalar) * (nD array) capability
* Replaced buggy mxRealloc with custom code
* 2010/Oct/04 --> 1.40, Added OpenMP support for custom code
* Expanded sparse * single and sparse * nD support
* Fixed (nD complex scalar)C * (nD array) bug.
* 2011/Feb/23 --> 1.41, Fixed typos in _syrk and _syr2k BLAS prototypes.
*
****************************************************************************/
/*---------------------------------------------------------------------------------
* Complex type for function return
*--------------------------------------------------------------------------------- */
struct RealKindComplex {RealKind r; RealKind i;};
/*---------------------------------------------------------------------------------
* Function Prototypes
*--------------------------------------------------------------------------------- */
int AllRealZero(RealKind *x, mwSignedIndex n);
void RealKindEqP1P0TimesRealKindN(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqP1P0TimesRealKindG(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqP1P0TimesRealKindT(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqP1P0TimesRealKindC(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqP1P1TimesRealKindN(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqP1P1TimesRealKindG(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqP1P1TimesRealKindT(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqP1P1TimesRealKindC(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqP1M1TimesRealKindN(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqP1M1TimesRealKindG(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqP1M1TimesRealKindT(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqP1M1TimesRealKindC(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqP1PxTimesRealKindN(RealKind *Cpr, RealKind *Cpi, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqP1PxTimesRealKindG(RealKind *Cpr, RealKind *Cpi, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqP1PxTimesRealKindT(RealKind *Cpr, RealKind *Cpi, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqP1PxTimesRealKindC(RealKind *Cpr, RealKind *Cpi, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqM1P0TimesRealKindN(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqM1P0TimesRealKindG(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqM1P0TimesRealKindT(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqM1P0TimesRealKindC(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqM1P1TimesRealKindN(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqM1P1TimesRealKindG(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqM1P1TimesRealKindT(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqM1P1TimesRealKindC(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqM1M1TimesRealKindN(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqM1M1TimesRealKindG(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqM1M1TimesRealKindT(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqM1M1TimesRealKindC(RealKind *Cpr, RealKind *Cpi,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqM1PxTimesRealKindN(RealKind *Cpr, RealKind *Cpi, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqM1PxTimesRealKindG(RealKind *Cpr, RealKind *Cpi, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqM1PxTimesRealKindT(RealKind *Cpr, RealKind *Cpi, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqM1PxTimesRealKindC(RealKind *Cpr, RealKind *Cpi, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqPxP1TimesRealKindN(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqPxP1TimesRealKindG(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqPxP1TimesRealKindT(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqPxP1TimesRealKindC(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqPxM1TimesRealKindN(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqPxM1TimesRealKindG(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqPxM1TimesRealKindT(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqPxM1TimesRealKindC(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqPxP0TimesRealKindN(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqPxP0TimesRealKindG(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqPxP0TimesRealKindT(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqPxP0TimesRealKindC(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqPxPxTimesRealKindN(RealKind *Cpr, RealKind *Cpi, RealKind ar,
RealKind ai, RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqPxPxTimesRealKindG(RealKind *Cpr, RealKind *Cpi, RealKind ar, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSignedIndex n);
void RealKindEqPxPxTimesRealKindT(RealKind *Cpr, RealKind *Cpi, RealKind ar, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealKindEqPxPxTimesRealKindC(RealKind *Cpr, RealKind *Cpi, RealKind ar, RealKind ai,
RealKind *Bpr, RealKind *Bpi, mwSize m2, mwSize n2, mwSignedIndex p);
void RealTimesScalar(RealKind *Cpr, RealKind *Cpi, RealKind *Bpr, RealKind *Bpi, char transb,
mwSize m2, mwSize n2, RealKind ar, RealKind ai, mwSize n, mwSize p,int);
void RealTimesScalarX(RealKind *Cpr, RealKind *Cpi, RealKind *Bpr, RealKind *Bpi, char transb,
mwSize m2, mwSize n2, RealKind ar, RealKind ai, mwSize n, mwSize p, int);
void xFILLPOS(RealKind *Cpr, mwSignedIndex n);
void xFILLNEG(RealKind *Cpr, mwSignedIndex n);
RealKind xDOT(mwSignedIndex *, RealKind *, mwSignedIndex *, RealKind *, mwSignedIndex *);
void xGER(mwSignedIndex *, mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *,
RealKind *, mwSignedIndex *, RealKind *, mwSignedIndex *);
void xSYR(char *, mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *,
RealKind *, mwSignedIndex *);
void xSYR2(char *, mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *,
RealKind *, mwSignedIndex *, RealKind *, mwSignedIndex *);
void xGEMV(char *, mwSignedIndex *, mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *,
RealKind *, mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *);
void xGEMM(char *, char *, mwSignedIndex *, mwSignedIndex *, mwSignedIndex *,
RealKind *, RealKind *, mwSignedIndex *, RealKind *, mwSignedIndex *,
RealKind *, RealKind *, mwSignedIndex *);
void xSYRK(char *, char *, mwSignedIndex *, mwSignedIndex *, RealKind *, RealKind *,
mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *);
void xSYR2K(char *, char *, mwSignedIndex *, mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *,
RealKind *, mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *);
void xAXPY(mwSignedIndex *, RealKind *, RealKind *, mwSignedIndex *, RealKind *, mwSignedIndex *);
struct RealKindComplex RealKindDotProduct(mwSignedIndex, RealKind *, RealKind *, RealKind,
RealKind *, RealKind *, RealKind, int);
struct RealKindComplex RealKindDotProductX(mwSignedIndex, RealKind *, RealKind *, RealKind,
RealKind *, RealKind *, RealKind, int);
void RealKindOuterProduct(mwSignedIndex, mwSignedIndex, RealKind *, RealKind *, char,
RealKind *, RealKind *, char, RealKind *, RealKind *, int);
void RealKindOuterProductX(mwSignedIndex, mwSignedIndex, RealKind *, RealKind *, char,
RealKind *, RealKind *, char, RealKind *, RealKind *, int);
mxArray *RealScalarTimesReal(mxArray *, char, mwSize, mwSize, mxArray *, char, mwSize, mwSize);
/*-------------------------------------------------------------------------------------
* Function for multiplying two MATLAB variables
*------------------------------------------------------------------------------------- */
mxArray *RealTimesReal(mxArray *A, char transa, mxArray *B, char transb)
{
mwSignedIndex inc = 1;
RealKind Zero = zero;
RealKind One = one;
RealKind Minusone = minusone;
char uplo = 'L'; /* Arbitrary choice. Pick the symmetric case as lower triangular */
mwSize m1, n1, m2, n2, Andim, Bndim, Cndim, Ap, Bp, Cp, ip, p, Asize, Bsize, Csize, ndim;
mwSize Ablock, Bblock;
mwSize *Adims, *Bdims, *Cdims, *Adimz, *Bdimz, *Cindx;
register mwSignedIndex i, j;
mwSignedIndex m, n, k, l, lda, ldb, ldc;
mxArray *C, *result, *rhs[4];
RealKind *Apr, *Api, *Bpr, *Bpi, *Cpr, *Cpi, *Apr0, *Api0, *Bpr0, *Bpi0;
RealKind *apr, *api, *bpr, *bpi, *cpr, *cpi;
RealKind ai, bi, sr, si, aibi;
RealKind Apr11, Apr12, Apr13, Apr14,
Apr21, Apr22, Apr23, Apr24,
Apr31, Apr32, Apr33, Apr34,
Apr41, Apr42, Apr43, Apr44;
RealKind Api11, Api12, Api13, Api14,
Api21, Api22, Api23, Api24,
Api31, Api32, Api33, Api34,
Api41, Api42, Api43, Api44;
RealKind Bpr11, Bpr12, Bpr13, Bpr14,
Bpr21, Bpr22, Bpr23, Bpr24,
Bpr31, Bpr32, Bpr33, Bpr34,
Bpr41, Bpr42, Bpr43, Bpr44;
RealKind Bpi11, Bpi12, Bpi13, Bpi14,
Bpi21, Bpi22, Bpi23, Bpi24,
Bpi31, Bpi32, Bpi33, Bpi34,
Bpi41, Bpi42, Bpi43, Bpi44;
char ptransa, ptransb;
char transstring[2] = "_";
struct RealKindComplex z;
int scalarmultiply;
int scalar_method, dot_method, outer_method;
int singleton_expansion;
int destroyA = 0, destroyB = 0;
/*--------------------------------------------------------------------------------
* Get sizes. Note that in the multi-dimensional case, mxGetN returns the product
* of all of the dimension sizes 2 through end.
*-------------------------------------------------------------------------------- */
debug_message = debug;
threads_used = 0;
m1 = mxGetM(A);
n1 = mxGetN(A);
m2 = mxGetM(B);
n2 = mxGetN(B);
/*--------------------------------------------------------------------------------
* Get pointers to the data areas of the operands.
*-------------------------------------------------------------------------------- */
Apr0 = Apr = mxGetData(A);
Api0 = Api = mxGetImagData(A);
Bpr0 = Bpr = mxGetData(B);
Bpi0 = Bpi = mxGetImagData(B);
/*--------------------------------------------------------------------------------
* Simplify transa & transb if appropriate.
*-------------------------------------------------------------------------------- */
if( !Api ) {
if( transa == 'C' ) transa = 'T';
if( transa == 'G' ) transa = 'N';
}
if( !Bpi ) {
if( transb == 'C' ) transb = 'T';
if( transb == 'G' ) transb = 'N';
}
/*--------------------------------------------------------------------------------
* Scalar expansion cases (custom sparse array code for these cases only).
* If there is a inf or NaN in the scalar and the other variable is sparse,
* then don't do the custom code because the sparse zeros will not remain
* zero. So in that case just fall through and call mtimesx_sparse.
* (1 x 1) * (K x N) or (M x K) * (1 x 1)
*-------------------------------------------------------------------------------- */
scalarmultiply = 0;
if( m1 == 1 && n1 == 1 ) {
if( debug ) {
mexPrintf("MTIMESX: (1 x 1) * (array)\n");
}
scalarmultiply = 1;
if( mxIsSparse(B) ) {
if( mxIsInf(*Apr) || mxIsNaN(*Apr) ) {
scalarmultiply = 0;
} else if( (Api != NULL) && (mxIsInf(*Api) || mxIsNaN(*Api)) ) {
scalarmultiply = 0;
}
}
} else if( m2 == 1 && n2 == 1 ) {
if( debug ) {
mexPrintf("MTIMESX: (array) * (1 x 1)\n");
}
scalarmultiply = 1;
if( mxIsSparse(A) ) {
if( mxIsInf(*Bpr) || mxIsNaN(*Bpr) ) {
scalarmultiply = 0;
} else if( (Bpi != NULL) && (mxIsInf(*Bpi) || mxIsNaN(*Bpi)) ) {
scalarmultiply = 0;
}
}
}
if( scalarmultiply ) {
return RealScalarTimesReal(A, transa, m1, n1, B, transb, m2, n2);
}
/*--------------------------------------------------------------------------------
* Multi-dimensional sparse matrix results are not supported in MATLAB, so we are
* forced to convert the sparse matrix to a full matrix for these cases. Just hope
* the memory isn't blown.
*-------------------------------------------------------------------------------- */
if( mxIsSparse(A) && mxGetNumberOfDimensions(B) > 2 ) {
k = mexCallMATLAB(1, rhs, 1, &A, "full");
A = rhs[0];
m1 = mxGetM(A);
n1 = mxGetN(A);
Apr0 = Apr = mxGetData(A);
Api0 = Api = mxGetImagData(A);
destroyA = 1;
}
if( mxIsSparse(B) && mxGetNumberOfDimensions(A) > 2 ) {
k = mexCallMATLAB(1, rhs, 1, &B, "full");
B = rhs[0];
m2 = mxGetM(B);
n2 = mxGetN(B);
Bpr0 = Bpr = mxGetData(B);
Bpi0 = Bpi = mxGetImagData(B);
destroyB = 1;
}
/*--------------------------------------------------------------------------------
* Generic sparse matrix or vector operations are not directly supported.
* So just call an m-file to do the work. Won't save any time, but at least
* the function will be supported.
*-------------------------------------------------------------------------------- */
if( mxIsSparse(A) || mxIsSparse(B) ) {
if( debug ) {
mexPrintf("MTIMESX: Unsupported sparse operation ... calling MATLAB intrinsic function mtimes\n");
}
rhs[0] = A;
transstring[0] = transa;
rhs[1] = mxCreateString(transstring);
rhs[2] = B;
transstring[0] = transb;
rhs[3] = mxCreateString(transstring);
mexCallMATLAB(1, &result, 4, rhs, "mtimesx_sparse");
mxDestroyArray(rhs[3]);
mxDestroyArray(rhs[1]);
return result;
}
/*-------------------------------------------------------------------------------
* Rename array sizes for convenience. Also makes sure that the integer arguments
* to the BLAS routines are of type mwSignedIndex.
*------------------------------------------------------------------------------- */
Andim = mxGetNumberOfDimensions(A);
Adims = (mwSize *) mxGetDimensions(A);
Bndim = mxGetNumberOfDimensions(B);
Bdims = (mwSize *) mxGetDimensions(B);
m1 = Adims[0];
n1 = Adims[1];
m2 = Bdims[0];
n2 = Bdims[1];
if( transa == 'N' || transa == 'G' ) {
m = m1;
k = n1;
} else {
m = n1;
k = m1;
}
if( transb == 'N' || transb == 'G' ) {
l = m2;
n = n2;
} else {
l = n2;
n = m2;
}
lda = m1;
ldb = m2;
ldc = m;
/*-------------------------------------------------------------------------------
* Check for conforming sizes. Allow nD scalar multiply.
*------------------------------------------------------------------------------- */
if( (k != l) && (m*k != 1) && (l*n != 1) ) {
if( destroyA ) mxDestroyArray(A);
if( destroyB ) mxDestroyArray(B);
mexErrMsgTxt("Inner matrix dimensions must agree.");
}
ndim = (Andim <= Bndim) ? Andim : Bndim;
for( Cp=2; Cp<ndim; Cp++ ) {
if( Adims[Cp] != Bdims[Cp] && Adims[Cp] != 1 && Bdims[Cp] != 1 ) {
if( destroyA ) mxDestroyArray(A);
if( destroyB ) mxDestroyArray(B);
mexErrMsgTxt("Dimensions 3:end must agree or be 1 in ND case.");
}
}
/*-------------------------------------------------------------------------------
* Check for nD scalar multiply.
*------------------------------------------------------------------------------- */
if( m*k == 1 ) {
scalarmultiply = 1;
} else if( l*n == 1 ) {
scalarmultiply = 2;
} else {
scalarmultiply = 0;
}
/*-------------------------------------------------------------------------------
* Construct the dimensions of the result. Also use the p variable to keep track
* of the total number of individual matrix multiples that are involved. The
* first two dimensions are simply the result of a single matrix multiply, with
* accouting for the transa and transb pre-operations. The remaining dimensions
* are copied from A or B, whichever happens to be non-singleton.
*------------------------------------------------------------------------------- */
Cndim = (Andim > Bndim) ? Andim : Bndim;
Cindx = mxMalloc( Cndim * sizeof(*Cindx) );
Cdims = mxMalloc( Cndim * sizeof(*Cdims) );
if( scalarmultiply == 1 ) {
Cdims[0] = l;
Cdims[1] = n;
} else if( scalarmultiply == 2 ) {
Cdims[0] = m;
Cdims[1] = k;
} else {
Cdims[0] = m;
Cdims[1] = n;
}
Adimz = mxMalloc( Cndim * sizeof(*Adimz) );
Adimz[0] = Adims[0];
Adimz[1] = Adims[1];
Bdimz = mxMalloc( Cndim * sizeof(*Bdimz) );
Bdimz[0] = Bdims[0];
Bdimz[1] = Bdims[1];
p = 1;
for( Cp=2; Cp<Cndim; Cp++ ) {
Adimz[Cp] = (Cp < Andim) ? Adims[Cp] : 1;
Bdimz[Cp] = (Cp < Bndim) ? Bdims[Cp] : 1;
Cdims[Cp] = (Adimz[Cp] > Bdimz[Cp]) ? Adimz[Cp] : Bdimz[Cp];
p *= Cdims[Cp];
}
for( Cp=0; Cp<Cndim; Cp++ ) {
Cindx[Cp] = 0;
}
/*------------------------------------------------------------------------------
* Create output array
*------------------------------------------------------------------------------ */
if( mxGetNumberOfElements(A) == 0 || mxGetNumberOfElements(B) == 0 ) {
result = mxCreateNumericArray(Cndim, Cdims, MatlabReturnType, mxREAL);
mxFree(Cindx);
mxFree(Cdims);
mxFree(Adimz);
mxFree(Bdimz);
if( destroyA ) mxDestroyArray(A);
if( destroyB ) mxDestroyArray(B);
return result;
}
if( mxIsComplex(A) || mxIsComplex(B) ) {
result = mxCreateNumericArray(Cndim, Cdims, MatlabReturnType, mxCOMPLEX);
} else {
result = mxCreateNumericArray(Cndim, Cdims, MatlabReturnType, mxREAL);
}
C = result;
Cpr = mxGetData(C);
Cpi = mxGetImagData(C);
/*----------------------------------------------------------------------------
* See if we can do a simple reshape to do the nD multiply all at once
*---------------------------------------------------------------------------- */
if( Andim == 2 && Bndim > 2 && !scalarmultiply && (k == 1 || n == 1 || transb == 'N' || transb == 'G') ) {
if( debug_message ) {
mexPrintf("MTIMESX: Reshaping nD multiply as a single multiply\n");
}
if( transb == 'T' ) transb = 'N';
if( transb == 'C' ) transb = 'G';
m2 = k;
n2 = n * p;
n = n2;
p = 1;
ldb = m2;
}
if( Bndim == 2 && Andim > 2 && !scalarmultiply && m == 1 ) {
if( debug_message ) {
mexPrintf("MTIMESX: Reshaping and reordering nD multiply as a single multiply\n");
}
apr = Apr; Apr = Bpr; Bpr = apr;
api = Api; Api = Bpi; Bpi = api;
ptransa = transa; transa = transb; transb = ptransa;
if( transa == 'N' ) {
transa = 'T';
} else if( transa == 'T' ) {
transa = 'N';
} else if( transa == 'G' ) {
transa = 'C';
} else {
transa = 'G';
}
if( transb == 'C' ) {
transb = 'G';
} else if( transb == 'T' ) {
transb = 'N';
}
m1 = m2;
n1 = n2;
m2 = k;
n2 = m * p;
if( transa == 'N' || transa == 'G' ) {
m = m1;
} else {
m = n1;
}
l = k;
n = n2;
p = 1;
lda = m1;
ldb = k;
ldc = m;
}
/*------------------------------------------------------------------------------
* Set up conjugate factors
*------------------------------------------------------------------------------ */
ai = ( transa == 'C' || transa == 'G' ) ? -one : one;
bi = ( transb == 'C' || transb == 'G' ) ? -one : one;
aibi = - ai * bi;
/*----------------------------------------------------------------------------
* Individual matrix block sizes
*---------------------------------------------------------------------------- */
Asize = m1 * n1;
Bsize = m2 * n2;
Csize = Cdims[0] * Cdims[1];
#ifdef _OPENMP
/*----------------------------------------------------------------------------
* Check to see if singleton expansion is present
*---------------------------------------------------------------------------- */
singleton_expansion = 0;
for( i=2; i<Andim; i++ ) {
if( Adims[i] == 1 ) {
singleton_expansion = 1;
break;
}
}
if( !singleton_expansion ) {
for( i=2; i<Bndim; i++ ) {
if( Bdims[i] == 1 ) {
singleton_expansion = 1;
break;
}
}
}
/*----------------------------------------------------------------------------
* Check to see if we can do a fast OpenMP inline (1x1)*(KxN) nD multiply
*---------------------------------------------------------------------------- */
if( (mtimesx_mode == MTIMESX_LOOPS_OMP || mtimesx_mode == MTIMESX_SPEED_OMP) && max_threads > 1 &&
scalarmultiply== 1 && p >= OMP_SPECIAL_SMALL && !singleton_expansion ) {
if( debug_message ) {
mexPrintf("MTIMESX: Performing %d individual multiplies\n",p);
mexPrintf("MTIMESX: OpenMP multi-threaded LOOPS\n");
mexPrintf("MTIMESX: (%d x %d) * (%d x %d)\n",m,k,l,n);
}
Ablock = Asize;
Bblock = Bsize;
Asize *= (Andim > 2);
Bsize *= (Bndim > 2);
omp_set_dynamic(1);
#pragma omp parallel num_threads(max_threads)
{
RealKind sr_, si_;
RealKind *Apr_, *Bpr_, *Cpr_, *Api_, *Bpi_, *Cpi_;
mwSize ip_, p_, blocksize, offset;
int thread_num = omp_get_thread_num();
int num_threads = omp_get_num_threads();
#pragma omp master
{
threads_used = num_threads;
}
blocksize = p / num_threads;
offset = thread_num * blocksize;
if( thread_num == num_threads-1 ) {
p_ = p - offset;
} else {
p_ = blocksize;
}
Apr_ = Apr + offset * Asize;
Bpr_ = Bpr + offset * Bsize;
Cpr_ = Cpr + offset * Csize;
Api_ = (Api?Api+offset*Asize:NULL);
Bpi_ = (Bpi?Bpi+offset*Bsize:NULL);
Cpi_ = (Cpi?Cpi+offset*Csize:NULL);
for( ip_=0; ip_<p_; ip_++ ) {
sr_ = *Apr_;
si_ = Api_ ? (transa=='N'||transa=='T'?*Api_:-*Api_) : zero;
RealTimesScalar(Cpr_, Cpi_, Bpr_, Bpi_, transb, m2, n2, sr_, si_, Bblock, 1, METHOD_LOOPS);
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
if( Api_ ) {
Api_ += Asize;
}
if( Bpi_ ) {
Bpi_ += Bsize;
}
if( Cpi_ ) {
Cpi_ += Csize;
}
}
}
mxFree(Cindx);
mxFree(Cdims);
mxFree(Adimz);
mxFree(Bdimz);
if( AllRealZero(Cpi, m*n*p) ) {
mxFree(Cpi);
mxSetImagData(C, NULL);
}
if( destroyA ) mxDestroyArray(A);
if( destroyB ) mxDestroyArray(B);
return result;
}
/*----------------------------------------------------------------------------
* Check to see if we can do a fast OpenMP inline (MxK)*(1x1) nD multiply
*---------------------------------------------------------------------------- */
if( (mtimesx_mode == MTIMESX_LOOPS_OMP || mtimesx_mode == MTIMESX_SPEED_OMP) && max_threads > 1 &&
scalarmultiply== 2 && p >= OMP_SPECIAL_SMALL && !singleton_expansion ) {
if( debug_message ) {
mexPrintf("MTIMESX: Performing %d individual multiplies\n",p);
mexPrintf("MTIMESX: OpenMP multi-threaded LOOPS\n");
mexPrintf("MTIMESX: (%d x %d) * (%d x %d)\n",m,k,l,n);
}
Ablock = Asize;
Bblock = Bsize;
Asize *= (Andim > 2);
Bsize *= (Bndim > 2);
omp_set_dynamic(1);
#pragma omp parallel num_threads(max_threads)
{
RealKind sr_, si_;
RealKind *Apr_, *Bpr_, *Cpr_, *Api_, *Bpi_, *Cpi_;
mwSize ip_, p_, blocksize, offset;
int thread_num = omp_get_thread_num();
int num_threads = omp_get_num_threads();
#pragma omp master
{
threads_used = num_threads;
}
blocksize = p / num_threads;
offset = thread_num * blocksize;
if( thread_num == num_threads-1 ) {
p_ = p - offset;
} else {
p_ = blocksize;
}
Apr_ = Apr + offset * Asize;
Bpr_ = Bpr + offset * Bsize;
Cpr_ = Cpr + offset * Csize;
Api_ = (Api?Api+offset*Asize:NULL);
Bpi_ = (Bpi?Bpi+offset*Bsize:NULL);
Cpi_ = (Cpi?Cpi+offset*Csize:NULL);
for( ip_=0; ip_<p_; ip_++ ) {
sr_ = *Bpr_;
si_ = Bpi_ ? (transb=='N'||transb=='T'?*Bpi_:-*Bpi_) : zero;
RealTimesScalar(Cpr_, Cpi_, Apr_, Api_, transa, m1, n1, sr_, si_, Ablock, 1, METHOD_LOOPS);
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
if( Api_ ) {
Api_ += Asize;
}
if( Bpi_ ) {
Bpi_ += Bsize;
}
if( Cpi_ ) {
Cpi_ += Csize;
}
}
}
mxFree(Cindx);
mxFree(Cdims);
mxFree(Adimz);
mxFree(Bdimz);
if( AllRealZero(Cpi, m*n*p) ) {
mxFree(Cpi);
mxSetImagData(C, NULL);
}
if( destroyA ) mxDestroyArray(A);
if( destroyB ) mxDestroyArray(B);
return result;
}
/*----------------------------------------------------------------------------
* Check to see if we can do a fast OpenMP inline (2x2)*(2x2) nD multiply
*---------------------------------------------------------------------------- */
if( (mtimesx_mode == MTIMESX_LOOPS_OMP || mtimesx_mode == MTIMESX_SPEED_OMP) && max_threads > 1 &&
m == 2 && k == 2 && n == 2 && p >= OMP_SPECIAL_SMALL && !singleton_expansion && !Cpi ) {
if( debug_message ) {
mexPrintf("MTIMESX: Performing %d individual multiplies\n",p);
mexPrintf("MTIMESX: OpenMP multi-threaded LOOPS (unrolled into inline multiplies)\n");
mexPrintf("MTIMESX: (%d x %d) * (%d x %d)\n",m,k,l,n);
}
Asize *= (Andim > 2);
Bsize *= (Bndim > 2);
omp_set_dynamic(1);
#pragma omp parallel num_threads(max_threads)
{
RealKind *Apr_, *Bpr_, *Cpr_;
mwSize ip_, p_, blocksize, offset;
int thread_num = omp_get_thread_num();
int num_threads = omp_get_num_threads();
#pragma omp master
{
threads_used = num_threads;
}
blocksize = p / num_threads;
offset = thread_num * blocksize;
if( thread_num == num_threads-1 ) {
p_ = p - offset;
} else {
p_ = blocksize;
}
Apr_ = Apr + offset * Asize;
Bpr_ = Bpr + offset * Bsize;
Cpr_ = Cpr + offset * Csize;
if( transa == 'T' ) {
if( transb == 'T' ) {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[1] * Bpr_[2];
Cpr_[1] = Apr_[2] * Bpr_[0] + Apr_[3] * Bpr_[2];
Cpr_[2] = Apr_[0] * Bpr_[1] + Apr_[1] * Bpr_[3];
Cpr_[3] = Apr_[2] * Bpr_[1] + Apr_[3] * Bpr_[3];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
} else {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[1] * Bpr_[1];
Cpr_[1] = Apr_[2] * Bpr_[0] + Apr_[3] * Bpr_[1];
Cpr_[2] = Apr_[0] * Bpr_[2] + Apr_[1] * Bpr_[3];
Cpr_[3] = Apr_[2] * Bpr_[2] + Apr_[3] * Bpr_[3];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
}
} else {
if( transb == 'T' ) {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[2] * Bpr_[2];
Cpr_[1] = Apr_[1] * Bpr_[0] + Apr_[3] * Bpr_[2];
Cpr_[2] = Apr_[0] * Bpr_[1] + Apr_[2] * Bpr_[3];
Cpr_[3] = Apr_[1] * Bpr_[1] + Apr_[3] * Bpr_[3];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
} else {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[2] * Bpr_[1];
Cpr_[1] = Apr_[1] * Bpr_[0] + Apr_[3] * Bpr_[1];
Cpr_[2] = Apr_[0] * Bpr_[2] + Apr_[2] * Bpr_[3];
Cpr_[3] = Apr_[1] * Bpr_[2] + Apr_[3] * Bpr_[3];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
}
}
}
mxFree(Cindx);
mxFree(Cdims);
mxFree(Adimz);
mxFree(Bdimz);
/*
if( AllRealZero(Cpi, m*n*p) ) {
mxFree(Cpi);
mxSetImagData(C, NULL);
}
*/
if( destroyA ) mxDestroyArray(A);
if( destroyB ) mxDestroyArray(B);
return result;
}
/*----------------------------------------------------------------------------
* Check to see if we can do a fast OpenMP inline (2x2)*(2x1) nD multiply
*---------------------------------------------------------------------------- */
if( (mtimesx_mode == MTIMESX_LOOPS_OMP || mtimesx_mode == MTIMESX_SPEED_OMP) && max_threads > 1 &&
m == 2 && k == 2 && l == 2 && n == 1 && p >= OMP_SPECIAL_SMALL && !singleton_expansion && !Cpi ) {
if( debug_message ) {
mexPrintf("MTIMESX: Performing %d individual multiplies\n",p);
mexPrintf("MTIMESX: OpenMP multi-threaded LOOPS (unrolled into inline multiplies)\n");
mexPrintf("MTIMESX: (%d x %d) * (%d x %d)\n",m,k,l,n);
}
Asize *= (Andim > 2);
Bsize *= (Bndim > 2);
omp_set_dynamic(1);
#pragma omp parallel num_threads(max_threads)
{
RealKind *Apr_, *Bpr_, *Cpr_;
mwSize ip_, p_, blocksize, offset;
int thread_num = omp_get_thread_num();
int num_threads = omp_get_num_threads();
#pragma omp master
{
threads_used = num_threads;
}
blocksize = p / num_threads;
offset = thread_num * blocksize;
if( thread_num == num_threads-1 ) {
p_ = p - offset;
} else {
p_ = blocksize;
}
Apr_ = Apr + offset * Asize;
Bpr_ = Bpr + offset * Bsize;
Cpr_ = Cpr + offset * Csize;
if( transa == 'T' ) {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[1] * Bpr_[1];
Cpr_[1] = Apr_[2] * Bpr_[0] + Apr_[3] * Bpr_[1];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
} else {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[2] * Bpr_[1];
Cpr_[1] = Apr_[1] * Bpr_[0] + Apr_[3] * Bpr_[1];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
}
}
mxFree(Cindx);
mxFree(Cdims);
mxFree(Adimz);
mxFree(Bdimz);
/*
if( AllRealZero(Cpi, m*n*p) ) {
mxFree(Cpi);
mxSetImagData(C, NULL);
}
*/
if( destroyA ) mxDestroyArray(A);
if( destroyB ) mxDestroyArray(B);
return result;
}
/*----------------------------------------------------------------------------
* Check to see if we can do a fast OpenMp inline (1x2)*(2x2) nD multiply
*---------------------------------------------------------------------------- */
if( (mtimesx_mode == MTIMESX_LOOPS_OMP || mtimesx_mode == MTIMESX_SPEED_OMP) && max_threads > 1 &&
m == 1 && k == 2 && n == 2 && p >= OMP_SPECIAL_SMALL && !singleton_expansion && !Cpi ) {
if( debug_message ) {
mexPrintf("MTIMESX: Performing %d individual multiplies\n",p);
mexPrintf("MTIMESX: OpenMP multi-threaded LOOPS (unrolled into inline multiplies)\n");
mexPrintf("MTIMESX: (%d x %d) * (%d x %d)\n",m,k,l,n);
}
Asize *= (Andim > 2);
Bsize *= (Bndim > 2);
omp_set_dynamic(1);
#pragma omp parallel num_threads(max_threads)
{
RealKind *Apr_, *Bpr_, *Cpr_;
mwSize ip_, p_, blocksize, offset;
int thread_num = omp_get_thread_num();
int num_threads = omp_get_num_threads();
#pragma omp master
{
threads_used = num_threads;
}
blocksize = p / num_threads;
offset = thread_num * blocksize;
if( thread_num == num_threads-1 ) {
p_ = p - offset;
} else {
p_ = blocksize;
}
Apr_ = Apr + offset * Asize;
Bpr_ = Bpr + offset * Bsize;
Cpr_ = Cpr + offset * Csize;
if( transb == 'T' ) {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[1] * Bpr_[2];
Cpr_[1] = Apr_[0] * Bpr_[1] + Apr_[1] * Bpr_[3];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
} else {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[1] * Bpr_[1];
Cpr_[1] = Apr_[0] * Bpr_[2] + Apr_[1] * Bpr_[3];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
}
}
mxFree(Cindx);
mxFree(Cdims);
mxFree(Adimz);
mxFree(Bdimz);
/*
if( AllRealZero(Cpi, m*n*p) ) {
mxFree(Cpi);
mxSetImagData(C, NULL);
}
*/
if( destroyA ) mxDestroyArray(A);
if( destroyB ) mxDestroyArray(B);
return result;
}
/*----------------------------------------------------------------------------
* Check to see if we can do a fast OpenMP inline (3x3)*(3x3) nD multiply
*---------------------------------------------------------------------------- */
if( (mtimesx_mode == MTIMESX_LOOPS_OMP || mtimesx_mode == MTIMESX_SPEED_OMP) && max_threads > 1 &&
m == 3 && k == 3 && n == 3 && p >= OMP_SPECIAL_SMALL && !singleton_expansion && !Cpi ) {
if( debug_message ) {
mexPrintf("MTIMESX: Performing %d individual multiplies\n",p);
mexPrintf("MTIMESX: OpenMP multi-threaded LOOPS (unrolled into inline multiplies)\n");
mexPrintf("MTIMESX: (%d x %d) * (%d x %d)\n",m,k,l,n);
}
Asize *= (Andim > 2);
Bsize *= (Bndim > 2);
omp_set_dynamic(1);
#pragma omp parallel num_threads(max_threads)
{
RealKind *Apr_, *Bpr_, *Cpr_;
mwSize ip_, p_, blocksize, offset;
int thread_num = omp_get_thread_num();
int num_threads = omp_get_num_threads();
#pragma omp master
{
threads_used = num_threads;
}
blocksize = p / num_threads;
offset = thread_num * blocksize;
if( thread_num == num_threads-1 ) {
p_ = p - offset;
} else {
p_ = blocksize;
}
Apr_ = Apr + offset * Asize;
Bpr_ = Bpr + offset * Bsize;
Cpr_ = Cpr + offset * Csize;
if( transa == 'T' ) {
if( transb == 'T' ) {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[1] * Bpr_[3] + Apr_[2] * Bpr_[6];
Cpr_[1] = Apr_[3] * Bpr_[0] + Apr_[4] * Bpr_[3] + Apr_[5] * Bpr_[6];
Cpr_[2] = Apr_[6] * Bpr_[0] + Apr_[7] * Bpr_[3] + Apr_[8] * Bpr_[6];
Cpr_[3] = Apr_[0] * Bpr_[1] + Apr_[1] * Bpr_[4] + Apr_[2] * Bpr_[7];
Cpr_[4] = Apr_[3] * Bpr_[1] + Apr_[4] * Bpr_[4] + Apr_[5] * Bpr_[7];
Cpr_[5] = Apr_[6] * Bpr_[1] + Apr_[7] * Bpr_[4] + Apr_[8] * Bpr_[7];
Cpr_[6] = Apr_[0] * Bpr_[2] + Apr_[1] * Bpr_[5] + Apr_[2] * Bpr_[8];
Cpr_[7] = Apr_[3] * Bpr_[2] + Apr_[4] * Bpr_[5] + Apr_[5] * Bpr_[8];
Cpr_[8] = Apr_[6] * Bpr_[2] + Apr_[7] * Bpr_[5] + Apr_[8] * Bpr_[8];
Apr_ += Asize;
Bpr_ += Bsize;
Cpr_ += Csize;
}
} else {
for( ip_=0; ip_<p_; ip_++ ) {
Cpr_[0] = Apr_[0] * Bpr_[0] + Apr_[1] * Bpr_[1] + Apr_[2] * Bpr_[2];
Cpr_[1] = Apr_[3] * Bpr_[0] + Apr_[4] * Bpr_[1] + Apr_[5] * Bpr_[2];
Cpr_[2] = Apr_[6] * Bpr_[0] + Apr_[7] * Bpr_[1] + Apr_[8] * Bpr_[2];
Cpr_[3] = Apr_[0] * Bpr_[3] + Apr_[1] * Bpr_[4] + Apr_[2] * Bpr_[5];