double
gsl_spmatrix_get(const gsl_spmatrix *m, const size_t i, const size_t j)
{
if (i >= m->size1)
{
GSL_ERROR_VAL("first index out of range", GSL_EINVAL, 0.0);
}
else if (j >= m->size2)
{
GSL_ERROR_VAL("second index out of range", GSL_EINVAL, 0.0);
}
else
{
if (GSL_SPMATRIX_ISTRIPLET(m))
{
/* traverse binary tree to search for (i,j) element */
void *ptr = tree_find(m, i, j);
double x = ptr ? *(double *) ptr : 0.0;
return x;
}
else if (GSL_SPMATRIX_ISCCS(m))
{
const size_t *mi = m->i;
const size_t *mp = m->p;
size_t p;
/* loop over column j and search for row index i */
for (p = mp[j]; p < mp[j + 1]; ++p)
{
if (mi[p] == i)
return m->data[p];
}
}
else if (GSL_SPMATRIX_ISCRS(m))
{
const size_t *mi = m->i;
const size_t *mp = m->p;
size_t p;
/* loop over row i and search for column index j */
for (p = mp[i]; p < mp[i + 1]; ++p)
{
if (mi[p] == j)
return m->data[p];
}
}
else
{
GSL_ERROR_VAL("unknown sparse matrix type", GSL_EINVAL, 0.0);
}
/* element not found; return 0 */
return 0.0;
}
} /* gsl_spmatrix_get() */
gsl_spmatrix *
gsl_spmatrix_ccs(const gsl_spmatrix *T)
{
if (!GSL_SPMATRIX_ISTRIPLET(T))
{
GSL_ERROR_NULL("matrix must be in triplet format", GSL_EINVAL);
}
else
{
const size_t *Tj; /* column indices of triplet matrix */
size_t *Cp; /* column pointers of compressed column matrix */
size_t *w; /* copy of column pointers */
gsl_spmatrix *m;
size_t n;
m = gsl_spmatrix_alloc_nzmax(T->size1, T->size2, T->nz,
GSL_SPMATRIX_CCS);
if (!m)
return NULL;
Tj = T->p;
Cp = m->p;
/* initialize column pointers to 0 */
for (n = 0; n < m->size2 + 1; ++n)
Cp[n] = 0;
/*
* compute the number of elements in each column:
* Cp[j] = # non-zero elements in column j
*/
for (n = 0; n < T->nz; ++n)
Cp[Tj[n]]++;
/* compute column pointers: p[j] = p[j-1] + nnz[j-1] */
gsl_spmatrix_cumsum(m->size2, Cp);
/* make a copy of the column pointers */
w = (size_t *) m->work;
for (n = 0; n < m->size2; ++n)
w[n] = Cp[n];
/* transfer data from triplet format to CCS */
for (n = 0; n < T->nz; ++n)
{
size_t k = w[Tj[n]]++;
m->i[k] = T->i[n];
m->data[k] = T->data[n];
}
m->nz = T->nz;
return m;
}
}
int
gsl_spmatrix_set_zero(gsl_spmatrix *m)
{
m->nz = 0;
if (GSL_SPMATRIX_ISTRIPLET(m))
{
/* reset tree to empty state and node index pointer to 0 */
avl_empty(m->tree_data->tree, NULL);
m->tree_data->n = 0;
}
return GSL_SUCCESS;
} /* gsl_spmatrix_set_zero() */
/**
* \brief Divide each column of a compressed matrix by a vector.
*
* Divide each column of a compressed matrix by the corresponding vector element.
* \param[in] m compressed matrix to divide.
* \param[in] v vector to divide the columns of the sparse matrix.
* \param[in] tol threshold under which to avoid division by zero.
* \return Exit status.
*/
int
gsl_spmatrix_div_cols(gsl_spmatrix *m, const gsl_vector *v, const double tol)
{
size_t outerIdx, p, n;
if (GSL_SPMATRIX_ISTRIPLET(m))
{
for (n = 0; n < m->nz; n++)
{
if (gsl_pow_2(v->data[m->p[n] * v->stride]) > tol)
{
m->data[n] = m->data[n] / v->data[m->p[n] * v->stride];
}
}
}
else if (GSL_SPMATRIX_ISCCS(m))
{
for (outerIdx = 0; outerIdx < m->outerSize; outerIdx++)
{
for (p = m->p[outerIdx]; p < m->p[outerIdx + 1]; ++p)
{
if (gsl_pow_2(v->data[outerIdx * v->stride]) > tol)
{
m->data[p] /= v->data[outerIdx * v->stride];
}
}
}
}
else if (GSL_SPMATRIX_ISCRS(m))
{
for (outerIdx = 0; outerIdx < m->outerSize; outerIdx++)
{
for (p = m->p[outerIdx]; p < m->p[outerIdx + 1]; ++p)
{
if (gsl_pow_2(v->data[m->i[p] * v->stride]) > tol)
{
m->data[p] /= v->data[m->i[p] * v->stride];
}
}
}
}
else
{
GSL_ERROR("unknown sparse matrix type", GSL_EINVAL);
}
return GSL_SUCCESS;
}
int
gsl_spmatrix_realloc(const size_t nzmax, gsl_spmatrix *m)
{
int s = GSL_SUCCESS;
void *ptr;
if (nzmax < m->nz)
{
GSL_ERROR("new nzmax is less than current nz", GSL_EINVAL);
}
ptr = realloc(m->i, nzmax * sizeof(size_t));
if (!ptr)
{
GSL_ERROR("failed to allocate space for row indices", GSL_ENOMEM);
}
m->i = (size_t *) ptr;
if (GSL_SPMATRIX_ISTRIPLET(m))
{
ptr = realloc(m->p, nzmax * sizeof(size_t));
if (!ptr)
{
GSL_ERROR("failed to allocate space for column indices", GSL_ENOMEM);
}
m->p = (size_t *) ptr;
}
ptr = realloc(m->data, nzmax * sizeof(double));
if (!ptr)
{
GSL_ERROR("failed to allocate space for data", GSL_ENOMEM);
}
m->data = (double *) ptr;
m->nzmax = nzmax;
return s;
} /* gsl_spmatrix_realloc() */
/** \brief Get the sum of the elements of a compressed matrix over each column.
*
* Get the sum of the elements of a compressed matrix over each column.
* \param[out] sum Resulting vector of the sum of the columns.
* \param[in] m Compressed matrix over which to sum.
* \return Exit status.
*/
int
gsl_spmatrix_get_colsum(gsl_vector *sum, const gsl_spmatrix *m)
{
size_t outerIdx, p, n;
if (GSL_SPMATRIX_ISTRIPLET(m))
{
for (n = 0; n < m->nz; n++)
{
sum->data[m->p[n] * sum->stride] += m->data[n];
}
}
else if (GSL_SPMATRIX_ISCCS(m))
{
for (outerIdx = 0; outerIdx < m->outerSize; outerIdx++)
{
for (p = m->p[outerIdx]; p < m->p[outerIdx + 1]; ++p)
{
sum->data[outerIdx * sum->stride] += m->data[p];
}
}
}
else if (GSL_SPMATRIX_ISCRS(m))
{
for (outerIdx = 0; outerIdx < m->outerSize; outerIdx++)
{
for (p = m->p[outerIdx]; p < m->p[outerIdx + 1]; ++p)
{
sum->data[m->i[p] * sum->stride] += m->data[p];
}
}
}
else
{
GSL_ERROR("unknown sparse matrix type", GSL_EINVAL);
}
return GSL_SUCCESS;
}
int
gsl_spmatrix_set(gsl_spmatrix *m, const size_t i, const size_t j,
const double x, const int sum_duplicate)
{
if (!GSL_SPMATRIX_ISTRIPLET(m))
{
GSL_ERROR("matrix not in triplet representation", GSL_EINVAL);
}
else if (x == 0.0)
{
/* traverse binary tree to search for (i,j) element */
void *ptr = tree_find(m, i, j);
/*
* just set the data element to 0; it would be easy to
* delete the node from the tree with avl_delete(), but
* we'd also have to delete it from the data arrays which
* is less simple
*/
if (ptr != NULL)
*(double *) ptr = 0.0;
return GSL_SUCCESS;
}
else
{
int s = GSL_SUCCESS;
void *ptr;
/* check if matrix needs to be realloced */
if (m->nz >= m->nzmax)
{
s = gsl_spmatrix_realloc(2 * m->nzmax, m);
if (s)
return s;
}
/* store the triplet (i, j, x) */
m->i[m->nz] = i;
m->p[m->nz] = j;
m->data[m->nz] = x;
ptr = avl_insert(m->tree_data->tree, &m->data[m->nz]);
if (ptr != NULL)
{
/* AT: found duplicate entry (i,j) */
if (sum_duplicate)
{
/* sum it with new x */
*((double *) ptr) += x;
}
else
{
/* replace with new x */
*((double *) ptr) = x;
}
}
else
{
/* no duplicate (i,j) found, update indices as needed */
/* increase matrix dimensions if needed */
m->size1 = GSL_MAX(m->size1, i + 1);
m->size2 = GSL_MAX(m->size2, j + 1);
++(m->nz);
}
return s;
}
} /* gsl_spmatrix_set() */
int
gsl_spmatrix_equal(const gsl_spmatrix *a, const gsl_spmatrix *b)
{
const size_t M = a->size1;
const size_t N = a->size2;
if (b->size1 != M || b->size2 != N)
{
GSL_ERROR_VAL("matrices must have same dimensions", GSL_EBADLEN, 0);
}
else if (a->sptype != b->sptype)
{
GSL_ERROR_VAL("trying to compare different sparse matrix types", GSL_EINVAL, 0);
}
else
{
const size_t nz = a->nz;
size_t n;
if (nz != b->nz)
return 0; /* different number of non-zero elements */
if (GSL_SPMATRIX_ISTRIPLET(a))
{
/*
* triplet formats could be out of order but identical, so use
* gsl_spmatrix_get() on b for each aij
*/
for (n = 0; n < nz; ++n)
{
double bij = gsl_spmatrix_get(b, a->i[n], a->p[n]);
if (a->data[n] != bij)
return 0;
}
}
else if (GSL_SPMATRIX_ISCCS(a))
{
/*
* for compressed column, both matrices should have everything
* in the same order
*/
/* check row indices and data */
for (n = 0; n < nz; ++n)
{
if ((a->i[n] != b->i[n]) || (a->data[n] != b->data[n]))
return 0;
}
/* check column pointers */
for (n = 0; n < a->size2 + 1; ++n)
{
if (a->p[n] != b->p[n])
return 0;
}
}
else
{
GSL_ERROR_VAL("unknown sparse matrix type", GSL_EINVAL, 0);
}
return 1;
}
} /* gsl_spmatrix_equal() */
int
gsl_spmatrix_realloc(const size_t nzmax, gsl_spmatrix *m)
{
int s = GSL_SUCCESS;
void *ptr;
if (nzmax < m->nz)
{
GSL_ERROR("new nzmax is less than current nz", GSL_EINVAL);
}
ptr = realloc(m->i, nzmax * sizeof(size_t));
if (!ptr)
{
GSL_ERROR("failed to allocate space for row indices", GSL_ENOMEM);
}
m->i = (size_t *) ptr;
if (GSL_SPMATRIX_ISTRIPLET(m))
{
ptr = realloc(m->p, nzmax * sizeof(size_t));
if (!ptr)
{
GSL_ERROR("failed to allocate space for column indices", GSL_ENOMEM);
}
m->p = (size_t *) ptr;
}
ptr = realloc(m->data, nzmax * sizeof(double));
if (!ptr)
{
GSL_ERROR("failed to allocate space for data", GSL_ENOMEM);
}
m->data = (double *) ptr;
/* rebuild binary tree */
if (GSL_SPMATRIX_ISTRIPLET(m))
{
size_t n;
/* reset tree to empty state, but don't free root tree ptr */
avl_empty(m->tree_data->tree, NULL);
m->tree_data->n = 0;
ptr = realloc(m->tree_data->node_array, nzmax * sizeof(struct avl_node));
if (!ptr)
{
GSL_ERROR("failed to allocate space for AVL tree nodes", GSL_ENOMEM);
}
m->tree_data->node_array = ptr;
/*
* need to reinsert all tree elements since the m->data addresses
* have changed
*/
for (n = 0; n < m->nz; ++n)
{
ptr = avl_insert(m->tree_data->tree, &m->data[n]);
if (ptr != NULL)
{
GSL_ERROR("detected duplicate entry", GSL_EINVAL);
}
}
}
/* update to new nzmax */
m->nzmax = nzmax;
return s;
} /* gsl_spmatrix_realloc() */
int
gsl_spblas_dgemv(const CBLAS_TRANSPOSE_t TransA, const double alpha,
const gsl_spmatrix *A, const gsl_vector *x,
const double beta, gsl_vector *y)
{
const size_t M = A->size1;
const size_t N = A->size2;
if ((TransA == CblasNoTrans && N != x->size) ||
(TransA == CblasTrans && M != x->size))
{
GSL_ERROR("invalid length of x vector", GSL_EBADLEN);
}
else if ((TransA == CblasNoTrans && M != y->size) ||
(TransA == CblasTrans && N != y->size))
{
GSL_ERROR("invalid length of y vector", GSL_EBADLEN);
}
else
{
size_t j, p;
size_t incX, incY;
size_t lenX, lenY;
double *X, *Y;
double *Ad;
size_t *Ap, *Ai, *Aj;
if (TransA == CblasNoTrans)
{
lenX = N;
lenY = M;
}
else
{
lenX = M;
lenY = N;
}
/* form y := beta*y */
Y = y->data;
incY = y->stride;
if (beta == 0.0)
{
size_t jy = 0;
for (j = 0; j < lenY; ++j)
{
Y[jy] = 0.0;
jy += incY;
}
}
else if (beta != 1.0)
{
size_t jy = 0;
for (j = 0; j < lenY; ++j)
{
Y[jy] *= beta;
jy += incY;
}
}
if (alpha == 0.0)
return GSL_SUCCESS;
/* form y := alpha*op(A)*x + y */
Ap = A->p;
Ad = A->data;
X = x->data;
incX = x->stride;
if ((GSL_SPMATRIX_ISCCS(A) && (TransA == CblasNoTrans)) ||
(GSL_SPMATRIX_ISCRS(A) && (TransA == CblasTrans)))
{
Ai = A->i;
for (j = 0; j < lenX; ++j)
{
for (p = Ap[j]; p < Ap[j + 1]; ++p)
{
Y[Ai[p] * incY] += alpha * Ad[p] * X[j * incX];
}
}
}
else if ((GSL_SPMATRIX_ISCCS(A) && (TransA == CblasTrans)) ||
(GSL_SPMATRIX_ISCRS(A) && (TransA == CblasNoTrans)))
{
Ai = A->i;
for (j = 0; j < lenY; ++j)
{
for (p = Ap[j]; p < Ap[j + 1]; ++p)
{
Y[j * incY] += alpha * Ad[p] * X[Ai[p] * incX];
}
}
}
else if (GSL_SPMATRIX_ISTRIPLET(A))
{
if (TransA == CblasNoTrans)
{
Ai = A->i;
Aj = A->p;
}
else
{
Ai = A->p;
Aj = A->i;
}
for (p = 0; p < A->nz; ++p)
{
Y[Ai[p] * incY] += alpha * Ad[p] * X[Aj[p] * incX];
}
}
else
{
GSL_ERROR("unsupported matrix type", GSL_EINVAL);
}
return GSL_SUCCESS;
}
} /* gsl_spblas_dgemv() */