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 cvxopt.h header
file in the src directory of the distribution.
Before the C API can be used in an extension module it must be initialized
by calling the macro import_cvxopt. As an example we show the
module initialization from the cvxopt.blas module, which itself uses
the API:
As can be seen from the header file cvxopt.h, a matrix is
essentially a structure with four fields. The fields nrows and
ncols are two integers that specify the dimensions. The
id field controls the type of the matrix and can have values
DOUBLE, INT, and COMPLEX. The 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.
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 nrows and 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 cvxopt.uniform function
described in the section Randomly Generated Matrices.
PyObject*uniform(PyObject*self,PyObject*args,PyObject*kwrds){matrix*obj;inti,nrows,ncols=1;doublea=0,b=1;char*kwlist[]={"nrows","ncols","a","b",NULL};if(!PyArg_ParseTupleAndKeywords(args,kwrds,"i|idd",kwlist,&nrows,&ncols,&a,&b))returnNULL;if((nrows<0)||(ncols<0)){PyErr_SetString(PyExc_TypeError,"dimensions must be non-negative");returnNULL;}if(!(obj=Matrix_New(nrows,ncols,DOUBLE)))returnPyErr_NoMemory();for(i=0;i<nrows*ncols;i++)MAT_BUFD(obj)[i]=Uniform(a,b);return(PyObject*)obj;}
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:
values
An array of floating-point numbers of length nnz with the
nonzero entries of the matrix stored columnwise.
rowind
An array of integers of length nnz containing the row indices of
the nonzero entries, stored in the same order as values.
colptr
An array of integers of length ncols + 1 with for each column of the
matrix the index of the first element in values from that
column. More precisely, colptr[0] is 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
the elements of values, rowind, and colptr
are:
values:
1.0, 2.0, 3.0, 4.0, 5.0, 6.0
rowind:
0, 1,3, 1, 0, 2
colptr:
0, 3, 3, 4, 6.
It is crucial that for each column the row indices in rowind are
sorted; the equivalent representation
values:
3.0, 2.0, 1.0, 4.0, 5.0, 6.0
rowind:
3, 1, 0, 1, 0, 2
colptr:
0, 3, 3, 4, 6
is not allowed (and will likely cause the program to crash).
The nzmax field specifies the number of non-zero elements the
matrix can store. It is equal to the length of rowind and
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 nzmax field
can safely be ignored, however, since it will always be adjusted
automatically as the number of non-zero elements grows.
The id field controls the type of the matrix and can have
values DOUBLE and COMPLEX.
Sparse matrices are created using the following functions from the API.
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 values and rowind fields).
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 NULL. If V is
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 real method, which returns the real part of
a sparse matrix: