Makefile: Converting C-code to mex code

I have a C-code which works fine using makefile. Now, I am trying to convert it to mex file so that I can run it from Matlab. Here also, I am u sing makefile approach . But, makefile for mex gives me error.

Organization of C-project:

    tsnnls_test_DKU.c
    Include_4_TSNNLS.c
    Include_4_TSNNLS.h

Include_4_TSNNLS.h, .c files have function TestingLibraries() which call 3rd part libraries; while I tried to keep tsnnls_test_DKU.c very simple as:

*Original Code: tsnnls_test_DKU.c*

    int TestingLibraries() ;

    int main( int argc, char* argv[] ) 
    {

      int k = TestingLibraries() ;
      return(1);
    }

Now, the code was changed:

*Changed code: tsnnls_test_DKU.c:*

    #include "mex.h"
    #include <math.h>

    int TestingLibraries() ;

    void mexFunction (int nlhs, mxArray *plhs[],  int nrhs, const mxArray *prhs[]) {
            
      int k = TestingLibraries() ;
            
    }

*Original make file (that works*

    CXX       = gcc
    FLAGS     = 
    CFLAGS    = "-m64"   ## "-m32"
    INCLUDE_TSNNLS  = -I/home/dkumar/libtsnnls-2.3.3 -I/home/dkumar/libtsnnls-2.3.3/tsnnls  -I/home/dkumar/libtsnnls-2.3.3/tsnnls/taucs_basic

    #################### ALL TSNNLS lib related ##########################
    ## this is where all object file (*.o) generated by tsnnls library makefile are located.
    tsnnl_PATH = /home/dkumar/libtsnnls-2.3.3/tsnnls/

    # Here is a simple Make Macro.
    OBJS_tsnnls1     = tsnnls_test_DKU.o
    OBJS_ADD     = Include_4_TSNNLS.o

    # Here is a Make Macro that uses the backslash to extend to multiple lines.
    OBJS_tsnnls0 =   libtsnnls_la-taucs_malloc.o libtsnnls_la-taucs_ccs_order.o \
      libtsnnls_la-taucs_ccs_ops.o libtsnnls_la-taucs_vec_base.o \
      libtsnnls_la-taucs_complex.o libtsnnls_la-colamd.o \
      libtsnnls_la-amdbar.o libtsnnls_la-amdexa.o \
      libtsnnls_la-amdtru.o libtsnnls_la-genmmd.o \
      libtsnnls_la-taucs_timer.o libtsnnls_la-taucs_sn_llt.o \
      libtsnnls_la-taucs_ccs_base.o libtsnnls_la-tlsqr.o \
      libtsnnls_la-tsnnls.o libtsnnls_la-lsqr.o

     ## adding "$(OBJS_PATH)" to each word in "$(OBJS)"
    # which in our case is basically to add the same folder in front of all "*.o" object files.
    OBJS_TEMP = $(addprefix $(tsnnl_PATH), $(OBJS_tsnnls0)) 

    # OBJS_LOC is in current working directory,
    OBJS_tsnnlsALL = $(OBJS_TEMP)  $(OBJS_tsnnls1)

    # Libraries for tsnnls
    STLIB_tsnnls   = /usr/local/lib/taucs_full/lib/linux/libtaucs.a 
    LIBS_tsnnls   = -largtable2 -llapack -lblas -lquadmath -lm

    ########################################################################
    TARGET   = tsnnls_test_DKU
    REBUILDABLES = $(OBJS_tsnnls1) $(TARGET) 
    LIBS      =    $(LIBS_tsnnls)  $(STLIB_tsnnls)

    INCLUDE = $(INCLUDE_TSNNLS)

    all : $(TARGET)
      echo All done

    clean : 
      rm -f $(REBUILDABLES)  
      echo Clean done

    $(OBJS_ADD):  Include_4_TSNNLS.c
      gcc -c -o Include_4_TSNNLS.o Include_4_TSNNLS.c

    # Final linking
    $(TARGET) : $(OBJS_tsnnlsALL)  $(OBJS_ADD) $(LIBS)
      $(CXX) -g -o $@ $(INCLUDE) $(CFLAGS) $^

*Changed Makefile that does not run* I made changes at three places marked by string `##CHANGED PART STARTS ##`

    ###########CHANGED PART STARTS #################################
      MEXSUFFIX  = mex64
      MATLABHOME = /usr/local/MATLAB/R2014b
      MEX        = mex
      CXX        = gcc
      CFLAGS     = -fPIC -ansi -pthread -DMX_COMPAT_32 \
                   -DMATLAB_MEX_FILE
      MEXFLAGS  = -cxx CC='$(CXX)' CXX='$(CXX)' LD='$(CXX)'
    ###########CHANGED PART ENDS #################################

    INCLUDE_TSNNLS  = -I/home/dkumar/libtsnnls-2.3.3 -I/home/dkumar/libtsnnls-2.3.3/tsnnls  -I/home/dkumar/libtsnnls-2.3.3/tsnnls/taucs_basic

    #################### ALL TSNNLS lib related ##########################
    ## this is where all object file (*.o) generated by tsnnls library makefile are located.
    tsnnl_PATH = /home/dkumar/libtsnnls-2.3.3/tsnnls/

    # Here is a simple Make Macro.
    OBJS_tsnnls1     = tsnnls_test_DKU.o
    OBJS_ADD     = Include_4_TSNNLS.o

    # Here is a Make Macro that uses the backslash to extend to multiple lines.
    OBJS_tsnnls0 =   libtsnnls_la-taucs_malloc.o libtsnnls_la-taucs_ccs_order.o \
      libtsnnls_la-taucs_ccs_ops.o libtsnnls_la-taucs_vec_base.o \
      libtsnnls_la-taucs_complex.o libtsnnls_la-colamd.o \
      libtsnnls_la-amdbar.o libtsnnls_la-amdexa.o \
      libtsnnls_la-amdtru.o libtsnnls_la-genmmd.o \
      libtsnnls_la-taucs_timer.o libtsnnls_la-taucs_sn_llt.o \
      libtsnnls_la-taucs_ccs_base.o libtsnnls_la-tlsqr.o \
      libtsnnls_la-tsnnls.o libtsnnls_la-lsqr.o

     ## adding "$(OBJS_PATH)" to each word in "$(OBJS)"
    # which in our case is basically to add the same folder in front of all "*.o" object files.
    OBJS_TEMP = $(addprefix $(tsnnl_PATH), $(OBJS_tsnnls0)) 

    # OBJS_LOC is in current working directory,
    OBJS_tsnnlsALL = $(OBJS_TEMP)  $(OBJS_tsnnls1)

    # Libraries for tsnnls
    STLIB_tsnnls   = /usr/local/lib/taucs_full/lib/linux/libtaucs.a 
    LIBS_tsnnls   = -largtable2 -llapack -lblas -lquadmath -lm

    ########################################################################

    ###########CHANGED PART STARTS #################################
    TARGET = tsnnls_test_DKU.$(MEXSUFFIX)
    INCLUDE = -I$(MATLABHOME)/extern/include $(INCLUDE_TSNNLS) 
    ###########CHANGED PART ENDS #################################

    REBUILDABLES = $(OBJS_tsnnls1) $(TARGET) 
    LIBS      =    $(LIBS_tsnnls)  $(STLIB_tsnnls)

    all : $(TARGET) 
      echo All done

    clean : 
      rm -f $(REBUILDABLES)  
      echo Clean done

    $(OBJS_ADD):  Include_4_TSNNLS.c
      gcc -c -o Include_4_TSNNLS.o Include_4_TSNNLS.c

    ###########CHANGED PART STARTS #################################
    # Final linking
    $(TARGET) : $(OBJS_tsnnlsALL)  $(OBJS_ADD) $(LIBS)
      $(MEX) -g -o $@ $(INCLUDE) $(CFLAGS) $^
    ###########CHANGED PART ENDS #################################

*Error:*

Now, I am gettingn error which indicates that I am not able to use "INCLUDE" properly:

         fatal error: mex.h: No such file or directory
          #include "mex.h"
                         ^
         compilation terminated.
         make: *** [tsnnls_test_DKU.o] Error 1

Could someone please help me with compiler options?

[Geoff Hayes]

Dushyant - have you verified that

 -I$(MATLABHOME)/extern/include

is the valid path to where the mex.h file is?