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() */
/**
* \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;
}
/** \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_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_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() */
