.. _c-capi:

*****
C API
*****

The API can be used to extend CVXOPT with interfaces to external C routines
and libraries.  A C program that creates or manipulates the dense or sparse
matrix objects defined in CVXOPT must include the :const:`cvxopt.h` header 
file in the :const:`src` directory of the distribution.

Before the C API can be used in an extension module it must be initialized 
by calling the macro :c:macro:`import_cvxopt`.  As an example we show the 
module initialization from the :mod:`cvxopt.blas` module, which itself uses
the API:

.. highlight:: c

::

    #if PY_MAJOR_VERSION >= 3

    static PyModuleDef blas_module = {
        PyModuleDef_HEAD_INIT,
        "blas",
        blas__doc__,
        -1,
        blas_functions,
        NULL, NULL, NULL, NULL
    };
    
    PyMODINIT_FUNC PyInit_blas(void)
    {
      PyObject *m;
      if (!(m = PyModule_Create(&blas_module))) return NULL;
      if (import_cvxopt() < 0) return NULL;
      return m;
    }
    
    #else 
    
    PyMODINIT_FUNC initblas(void)
    {
      PyObject *m;
      m = Py_InitModule3("cvxopt.blas", blas_functions, blas__doc__);
      if (import_cvxopt() < 0) return ;
    }
    
    #endif


  
Dense Matrices
==============

As can be seen from the header file :const:`cvxopt.h`, a :class:`matrix` is
essentially a  structure with four fields.  The fields :c:member:`nrows` and 
:c:member:`ncols` are two integers that specify the dimensions.  The 
:c:member:`id` field controls the type of the matrix and can have values 
:const:`DOUBLE`, :const:`INT`, and :const:`COMPLEX`.  The :c:member:`buffer`
field is an array that contains the matrix elements stored contiguously in 
column-major order. 

The following C functions can be used to create matrices.

.. c:function:: matrix * Matrix_New(int nrows, int ncols, int id)

    Returns a :class:`matrix` object of type `id` with `nrows` rows and 
    `ncols` columns.  The elements of the matrix are uninitialized.


.. c:function:: matrix * Matrix_NewFromMatrix(matrix *src, int id)

    Returns a copy of the matrix `src` converted to type `id`.  The 
    following type conversions are allowed:  :const:`'i'` to :const:`'d'`,
    :const:`'i'` to :const:`'z'`, and :const:`'d'`  to :const:`'z'`.


.. c:function:: matrix * Matrix_NewFromSequence(PyListObject *x, int id)

    Creates a matrix of type `id` from the Python sequence type `x`. The
    returned matrix has size ``(len(x), 1)``.  The size can be changed 
    by modifying the :c:member:`nrows` and :c:member:`ncols` fields of the 
    returned matrix.


To illustrate the creation and manipulation of dense matrices (as well as 
the Python C API), we show the code for the :func:`cvxopt.uniform` function 
described in the section :ref:`s-random`.

::

    PyObject * uniform(PyObject *self, PyObject *args, PyObject *kwrds) 
    {
      matrix *obj;
      int i, nrows, ncols = 1;
      double a = 0, b = 1;
      char *kwlist[] = {"nrows", "ncols", "a", "b", NULL};

      if (!PyArg_ParseTupleAndKeywords(args, kwrds, "i|idd", kwlist, 
              &nrows, &ncols, &a, &b)) return NULL;
      
      if ((nrows<0) || (ncols<0)) {
        PyErr_SetString(PyExc_TypeError, "dimensions must be non-negative");
        return NULL;
      }
      
      if (!(obj = Matrix_New(nrows, ncols, DOUBLE)))
        return PyErr_NoMemory();
      
      for (i = 0; i < nrows*ncols; i++)
        MAT_BUFD(obj)[i] = Uniform(a,b);
      
      return (PyObject *)obj;
    }


Sparse Matrices
===============

Sparse matrices are stored in compressed column storage (CCS) format.  For 
a general `nrows` by `ncols` sparse matrix with `nnz` nonzero entries this 
means the following.  The sparsity pattern and the nonzero values are 
stored in three fields:

:c:member:`values` 
    A :const:`'d'` or :const:`'z'` matrix of size ``(nnz,1)``  with the 
    nonzero entries of the matrix stored columnwise.  

:c:member:`rowind` 
    An array of integers of length `nnz` containing the row indices of 
    the nonzero entries, stored in the same order as :c:member:`values`.

:c:member:`colptr` 
    An array of integers of length `ncols` + 1 with for each column of the 
    matrix the index of the first element in :c:member:`values` from that 
    column.  More precisely, ``colptr[0]`` is :const:`0`, and for 
    k = 0, 1, ..., `ncols` - 1, ``colptr[k+1]`` is equal to 
    ``colptr[k]`` plus the number of nonzeros in column `k` of the
    matrix.  Thus, ``colptr[ncols]`` is equal to `nnz`, the number of 
    nonzero entries.


For example, for the matrix

.. math::

    A=\left [\begin{array}{cccc}
        1 & 0 & 0 & 5\\
        2 & 0 & 4 & 0\\
        0 & 0 & 0 & 6\\
        3 & 0 & 0 & 0
    \end{array}\right]

the elements of :c:member:`values`, :c:member:`rowind`, and :c:member:`colptr` 
are:

:c:member:`values`:
    1.0, 2.0, 3.0, 4.0, 5.0, 6.0

:c:member:`rowind`:
    0, 1,3, 1, 0, 2

:c:member:`colptr`: 
    0, 3, 3, 4, 6.

It is crucial that for each column the row indices in :c:member:`rowind` are
sorted; the equivalent representation 

:c:member:`values`:
    3.0, 2.0, 1.0, 4.0, 5.0, 6.0

:c:member:`rowind`:
    3, 1, 0, 1, 0, 2

:c:member:`colptr`: 
    0, 3, 3, 4, 6

is not allowed (and will likely cause the program to crash).

The :c:member:`nzmax` field specifies the number of non-zero elements the
matrix can store.  It is equal to the length of :c:member:`rowind` and 
:c:member:`values`; this number can be larger that ``colptr[nrows]``, 
but never less.  This field makes it possible to preallocate a certain 
amount of memory to avoid reallocations if the matrix is constructed
sequentially by filling in elements.  In general the :c:member:`nzmax` field
can safely be ignored, however, since it will always be adjusted 
automatically as the number of non-zero elements grows.

The :c:member:`id` field controls the type of the matrix and can have 
values :const:`DOUBLE` and :const:`COMPLEX`. 

Sparse matrices are created using the following functions from the API. 

.. c:function:: spmatrix * SpMatrix_New(int nrows, int ncols, int nzmax, int id) 

  Returns a sparse zero matrix with `nrows` rows and `ncols` columns. 
  `nzmax` is the number of elements that will be allocated (the length of 
  the :c:member:`values` and :c:member:`rowind` fields).  


.. c:function:: spmatrix * SpMatrix_NewFromMatrix(spmatrix *src, int id)

      Returns a copy the sparse matrix \var{src}. 


.. c:function:: spmatrix * SpMatrix_NewFromIJV(matrix *I, matrix *J, matrix *V, int nrows, int ncols, int nzmax, int id)

    Creates a sparse matrix with `nrows` rows and `ncols` columns from a 
    triplet description.  `I` and `J` must be integer matrices and `V` 
    either a double or complex matrix, or :const:`NULL`. If `V` is 
    :const:`NULL` the values of the entries in the matrix are undefined, 
    otherwise they are specified by `V`.  Repeated entries in `V` are 
    summed.  The number of allocated elements is given by `nzmax`, which is 
    adjusted if it is smaller than the required amount. 

We illustrate use of the sparse matrix class by listing the source
code for the :attr:`real` method, which returns the real part of
a sparse matrix: 

::

    static PyObject * spmatrix_real(spmatrix *self) {

      if (SP_ID(self) != COMPLEX) 
        return (PyObject *)SpMatrix_NewFromMatrix(self, 0, SP_ID(self));
      
      spmatrix *ret = SpMatrix_New(SP_NROWS(self), SP_NCOLS(self), 
          SP_NNZ(self), DOUBLE);
      if (!ret) return PyErr_NoMemory();

      int i;
      for (i=0; i < SP_NNZ(self); i++) 
        SP_VALD(ret)[i] = creal(SP_VALZ(self)[i]);
      
      memcpy(SP_COL(ret), SP_COL(self), (SP_NCOLS(self)+1)*sizeof(int_t));
      memcpy(SP_ROW(ret), SP_ROW(self), SP_NNZ(self)*sizeof(int_t));
      return (PyObject *)ret;
    }
