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#ifndef __Teuchos_MatrixMarket_Raw_Adder_hpp
#define __Teuchos_MatrixMarket_Raw_Adder_hpp
#include "Teuchos_ConfigDefs.hpp"
#include "Teuchos_ArrayRCP.hpp"
#include "Teuchos_CommHelpers.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_MatrixMarket_Banner.hpp"
#include "Teuchos_MatrixMarket_CoordDataReader.hpp"
#include <algorithm>
#include <fstream>
#include <iostream>
#include <iterator>
#include <vector>
#include <stdexcept>
namespace Teuchos {
namespace MatrixMarket {
namespace Raw {
/// \class Element
/// \author Mark Hoemmen
/// \brief Stores one entry of a sparse matrix.
///
/// \tparam Scalar The type of entries of the sparse matrix.
/// \tparam Ordinal The type of indices of the sparse matrix.
///
/// This class is mainly useful as an implementation detail of
/// Adder. We expose it to users only if they wish to convert
/// the sparse matrix read in by Adder into a storage format
/// other than CSR (compressed sparse row).
///
/// An array of Elements implements the so-called "array of
/// structs" representation of a coordinate format sparse
/// matrix. An Element has a row and column index (each of type
/// Ordinal) and a value (of type Scalar). Elements also have
/// equality and ordering comparisons. The equality comparison
/// only tests the row and column index, and is intended to
/// simplify merging matrix entries with the same row and column
/// indices. The ordering comparison means that std::sort of a
/// sequence of Elements will put them in an order suitable for
/// extracting the CSR (compressed sparse row) representation of
/// the sparse matrix.
template<class Scalar, class Ordinal>
class Element {
public:
//! Default constructor: an invalid entry of the matrix.
Element () :
rowIndex_ (Teuchos::OrdinalTraits<Ordinal>::invalid ()),
colIndex_ (Teuchos::OrdinalTraits<Ordinal>::invalid ()),
value_ (Teuchos::ScalarTraits<Scalar>::zero ())
{}
//! Create a sparse matrix entry at (i,j) with value Aij.
Element (const Ordinal i, const Ordinal j, const Scalar& Aij) :
rowIndex_ (i), colIndex_ (j), value_ (Aij) {}
//! Ignore the matrix value for comparisons.
bool operator== (const Element& rhs) {
return rowIndex_ == rhs.rowIndex_ && colIndex_ == rhs.colIndex_;
}
//! Ignore the matrix value for comparisons.
bool operator!= (const Element& rhs) {
return ! (*this == rhs);
}
//! Lexicographic order first by row index, then by column index.
bool operator< (const Element& rhs) const {
if (rowIndex_ < rhs.rowIndex_)
return true;
else if (rowIndex_ > rhs.rowIndex_)
return false;
else { // equal
return colIndex_ < rhs.colIndex_;
}
}
/// \brief Merge rhs into this Element, using custom binary function.
///
/// This replaces the current value Aij with f(rhs.value_,
/// Aij). The object f must be a binary function that takes
/// two Scalar arguments and returns a Scalar.
template<class BinaryFunction>
void merge (const Element& rhs, const BinaryFunction& f) {
TEUCHOS_TEST_FOR_EXCEPTION(
rowIndex() != rhs.rowIndex() || colIndex() != rhs.colIndex(),
std::invalid_argument,
"Attempt to merge elements at different locations in the sparse "
"matrix. The current element is at (" << rowIndex() << ", "
<< colIndex() << ") and the element you asked me to merge with it "
"is at (" << rhs.rowIndex() << ", " << rhs.colIndex() << "). This "
"probably indicates a bug in the sparse matrix reader.");
value_ = f (rhs.value_, value_);
}
/// \brief Merge rhs into this Element, either by addition or replacement.
///
/// \param rhs [in] Element to merge in.
/// \param replace [in] If true, replace this Element's value
/// with that of rhs. If false, add rhs to this Element's
/// value.
void merge (const Element& rhs, const bool replace=false) {
TEUCHOS_TEST_FOR_EXCEPTION(
rowIndex() != rhs.rowIndex() || colIndex() != rhs.colIndex(),
std::invalid_argument,
"Attempt to merge elements at different locations in the sparse "
"matrix. The current element is at (" << rowIndex() << ", "
<< colIndex() << ") and the element you asked me to merge with it "
"is at (" << rhs.rowIndex() << ", " << rhs.colIndex() << "). This "
"probably indicates a bug in the sparse matrix reader.");
if (replace) {
value_ = rhs.value_;
}
else {
value_ += rhs.value_;
}
}
//! Row index (zero-based) of this Element.
Ordinal rowIndex() const { return rowIndex_; }
//! Column index (zero-based) of this Element.
Ordinal colIndex() const { return colIndex_; }
//! Value (A(rowIndex(), colIndex()) of this Element.
Scalar value() const { return value_; }
private:
Ordinal rowIndex_, colIndex_;
Scalar value_;
};
/// \brief Print out an Element to the given output stream.
///
/// This method is suitable for printing a sparse matrix to a
/// Matrix Market file. We try to print out floating-point
/// values with enough digits to reproduce the results, but in
/// general this routine does not promise that the matrix entry
/// later read in from this printing will be bitwise identical
/// to the matrix entry supplied as input. There _are_ printing
/// algorithms that make this guarantee; we just haven't
/// implemented them yet here.
template<class Scalar, class Ordinal>
std::ostream&
operator<< (std::ostream& out, const Element<Scalar, Ordinal>& elt)
{
typedef ScalarTraits<Scalar> STS;
std::ios::fmtflags f( out.flags() );
// Non-Ordinal types are floating-point types. In order not to
// lose information when we print a floating-point type, we have
// to set the number of digits to print. C++ standard behavior
// in the default locale seems to be to print only five decimal
// digits after the decimal point; this does not suffice for
// double precision. We solve the problem of how many digits to
// print more generally below. It's a rough solution so please
// feel free to audit and revise it.
//
// FIXME (mfh 01 Feb 2011)
// This really calls for the following approach:
//
// Guy L. Steele and Jon L. White, "How to print floating-point
// numbers accurately", 20 Years of the ACM/SIGPLAN Conference
// on Programming Language Design and Implementation
// (1979-1999): A Selection, 2003.
if (! STS::isOrdinal) {
// std::scientific, std::fixed, and default are the three
// output states for floating-point numbers. A reasonable
// user-defined floating-point type should respect these
// flags; hopefully it does.
out << std::scientific;
// Decimal output is standard for Matrix Market format.
out << std::setbase (10);
// Compute the number of decimal digits required for expressing
// a Scalar, by comparing with IEEE 754 double precision (16
// decimal digits, 53 binary digits). This would be easier if
// Teuchos exposed std::numeric_limits<T>::digits10, alas.
const double numDigitsAsDouble =
16 * ((double) STS::t() / (double) ScalarTraits<double>::t());
// Adding 0.5 and truncating is a portable "floor".
const int numDigits = static_cast<int> (numDigitsAsDouble + 0.5);
// Precision to which a Scalar should be written. Add one
// for good measure, since 17 is necessary for IEEE 754
// doubles.
out << std::setprecision (numDigits + 1);
}
out << elt.rowIndex () << " " << elt.colIndex () << " ";
if (STS::isComplex) {
out << STS::real (elt.value ()) << " " << STS::imag (elt.value ());
}
else {
out << elt.value ();
}
// Restore flags
out.flags( f );
return out;
}
/// \class Adder
/// \brief To be used with Checker for "raw" sparse matrix input.
///
/// \tparam Scalar The type of entries in the sparse matrix.
/// \tparam Ordinal The type of indices in the sparse matrix.
///
/// This class implements the following interface, which is
/// required by the Callback template parameter of
/// Teuchos::MatrixMarket::CoordDataReader:
/// \code
/// class AdderType {
/// public:
/// typedef ... index_type; // Ellipsis represents the actual type
/// typedef ... value_type; // Ellipsis represents the actual type
/// void operator() (const index_type, const index_type, const value_type&);
/// };
/// \endcode
/// For Adder, the Scalar template parameter is value_type, and
/// the Ordinal template parameter is index_type. Adder
/// provides a simple implementation of the above interface
/// which is useful for things like printing out a sparse
/// matrix's entries, or converting between storage formats.
///
/// It is possible to nest classes that implement the above
/// interface, in order to modify the definition of inserting
/// values into a sparse matrix. (If you are familiar with
/// Emacs Lisp, this is called "advising" (the insertion
/// function, in this case). See the
/// <a href="http://www.gnu.org/software/emacs/manual/html_node/elisp/Advising-Functions.html">Emacs Lisp Manual</a>
/// for details.) If you are building a chain of classes, each
/// of which implements the above interface by calling the next
/// lower class' operator() beneath it, this class is a good
/// start, since it implements insertion of values directly.
/// SymmetrizingAdder is an example; it "advises" Adder by
/// inserting an entry at (j,i) whenever Adder inserts an entry
/// at (i,j) with i != j.
template<class Scalar, class Ordinal>
class Adder {
public:
typedef Ordinal index_type;
typedef Scalar value_type;
typedef Element<Scalar, Ordinal> element_type;
typedef typename std::vector<element_type>::size_type size_type;
/// \brief Default constructor.
///
/// If you call the default constructor, we assume that you
/// want tolerant mode (in which the Adder tries to infer the
/// matrix dimensions and number of entries from the actual
/// matrix data, not from any metadata). Tolerant mode is
/// similar to what Matlab does if you give it an ASCII file
/// of (i,j,Aij) triples. It may get the matrix dimensions
/// (m,n) wrong if the lower right entry of the matrix is zero
/// and is not supplied explicitly by calling operator().
Adder () :
expectedNumRows_(0),
expectedNumCols_(0),
expectedNumEntries_(0),
seenNumRows_(0),
seenNumCols_(0),
seenNumEntries_(0),
tolerant_ (true),
debug_ (false)
{}
/// \brief Standard constructor.
///
/// \param expectedNumRows [in] Number of rows in the matrix,
/// as specified by the matrix metadata.
///
/// \param expectedNumCols [in] Number of columns in the
/// matrix, as specified by the matrix metadata.
///
/// \param expectedNumEntries [in] Number of entries in the
/// matrix, as specified by the matrix metadata.
///
/// \param tolerant [in] Whether the "expected" metadata is
/// required to match what the read-in matrix entries tell
/// us.
///
/// \param debug [in] If true, we may print copious status
/// output for debugging purposes.
Adder (const Ordinal expectedNumRows,
const Ordinal expectedNumCols,
const Ordinal expectedNumEntries,
const bool tolerant=false,
const bool debug=false) :
expectedNumRows_(expectedNumRows),
expectedNumCols_(expectedNumCols),
expectedNumEntries_(expectedNumEntries),
seenNumRows_(0),
seenNumCols_(0),
seenNumEntries_(0),
tolerant_ (tolerant),
debug_ (debug)
{}
/// \brief Add an entry to the sparse matrix.
///
/// If tolerant==false, this method will perform error
/// checking to ensure that the matrix data matches the
/// metadata. For example, it will check that i and j are in
/// bounds. If countAgainstTotal is true, it will also check
/// to make sure you haven't added more than the expected
/// number of matrix entries. Regardless, this method will
/// update the "actual" metadata.
///
/// \param i [in] (1-based) row index
/// \param j [in] (1-based) column index
/// \param Aij [in] Value of the entry A(i,j)
/// \param countAgainstTotal [in] Whether to count the entry
/// to insert against the total expected number of entries.
/// The default is true. Make this false if you are
/// inserting an entry that wasn't stored in the original
/// Matrix Market file, which you're adding in order to
/// preserve symmetry or some other related structural
/// property of the matrix.
void
operator() (const Ordinal i,
const Ordinal j,
const Scalar& Aij,
const bool countAgainstTotal=true)
{
if (! tolerant_) {
const bool indexPairOutOfRange = i < 1 || j < 1 ||
i > expectedNumRows_ || j > expectedNumCols_;
TEUCHOS_TEST_FOR_EXCEPTION(indexPairOutOfRange,
std::invalid_argument, "Matrix is " << expectedNumRows_ << " x "
<< expectedNumCols_ << ", so entry A(" << i << "," << j << ") = "
<< Aij << " is out of range.");
if (countAgainstTotal) {
TEUCHOS_TEST_FOR_EXCEPTION(seenNumEntries_ >= expectedNumEntries_,
std::invalid_argument, "Cannot add entry A(" << i << "," << j
<< ") = " << Aij << " to matrix; already have expected number "
"of entries " << expectedNumEntries_ << ".");
}
}
// i and j are 1-based indices, but we store them as 0-based.
elts_.push_back (element_type (i-1, j-1, Aij));
// Keep track of the rightmost column containing a matrix
// entry, and the bottommost row containing a matrix entry.
// This gives us a lower bound for the dimensions of the
// matrix, and a check for the reported dimensions of the
// matrix in the Matrix Market file.
seenNumRows_ = std::max (seenNumRows_, i);
seenNumCols_ = std::max (seenNumCols_, j);
if (countAgainstTotal) {
++seenNumEntries_;
}
}
/// \brief Print the sparse matrix data.
///
/// We always print the data sorted. You may also merge
/// duplicate entries if you prefer.
///
/// \param out [out] Output stream to which to print
/// \param doMerge [in] Whether to merge entries before printing
/// \param replace [in] If merging, whether to replace duplicate
/// entries; otherwise their values are added together.
void
print (std::ostream& out, const bool doMerge, const bool replace=false)
{
if (doMerge) {
merge (replace);
} else {
std::sort (elts_.begin(), elts_.end());
}
// Print out the results, delimited by newlines.
typedef std::ostream_iterator<element_type> iter_type;
std::copy (elts_.begin(), elts_.end(), iter_type (out, "\n"));
}
/// \brief Merge duplicate elements.
///
/// Merge elements of the sparse matrix that have the same row
/// and column indices ("duplicates"). Resize the array of
/// elements to fit just the "unique" (not duplicate)
/// elements.
///
/// \param replace [in] If true, replace each duplicate
/// element with the next element sharing the same row and
/// column index. This means that results will depend on
/// the order in which the duplicate elements were added.
/// Otherwise, duplicate elements have their values added
/// together; in that case, the result is independent (in
/// exact arithmetic, not in finite-precision arithmetic) of
/// their order.
///
/// \return (# unique elements, # removed elements)
///
/// \note This method does not change the "expected" or "seen"
/// numbers of entries, since both of those count entries
/// with the same row and column indices as separate
/// entries.
std::pair<size_type, size_type>
merge (const bool replace=false)
{
typedef typename std::vector<element_type>::iterator iter_type;
// Start with a sorted container. Element objects sort in
// lexicographic order of their (row, column) indices, for
// easy conversion to CSR format. If you expect that the
// elements will usually be sorted in the desired order, you
// can check first whether they are already sorted. We have
// no such expectation, so we don't even bother to spend the
// extra O(# entries) operations to check.
std::sort (elts_.begin(), elts_.end());
// Walk through the array of elements in place, merging
// duplicates and pushing unique elements up to the front of
// the array. We can't use std::unique for this because it
// doesn't let us merge duplicate elements; it only removes
// them from the sequence.
size_type numUnique = 0;
iter_type cur = elts_.begin();
if (cur == elts_.end()) { // No elements to merge
return std::make_pair (numUnique, size_type (0));
}
else {
iter_type next = cur;
++next; // There is one unique element
++numUnique;
while (next != elts_.end()) {
if (*cur == *next) {
// Merge in the duplicated element *next
cur->merge (*next, replace);
} else {
// *cur is already a unique element. Move over one to
// *make space for the new unique element.
++cur;
*cur = *next; // Add the new unique element
++numUnique;
}
// Look at the "next" not-yet-considered element
++next;
}
// Remember how many elements we removed before resizing.
const size_type numRemoved = elts_.size() - numUnique;
elts_.resize (numUnique);
return std::make_pair (numUnique, numRemoved);
}
}
/// \brief Merge duplicate elements and convert to zero-based CSR.
///
/// Merge elements of the sparse matrix that have the same row
/// and column indices ("duplicates"). Resize the array of
/// elements to fit just the "unique" (not duplicate)
/// elements. Return a CSR (compressed sparse row) version of
/// the data, with zero-based indices.
///
/// We combine merge and conversion to CSR because the latter
/// requires the former.
///
/// \param numUniqueElts [out] Same as the first return value
/// of merge().
///
/// \param numRemovedElts [out] Same as the second return
/// value of merge().
///
/// \param rowptr [out] Array of numRows+1 offsets, where
/// numRows is the number of rows in the sparse matrix. For
/// row i (zero-based indexing), the entries of that row are
/// in indices rowptr[i] .. rowptr[i+1]-1 of colind and
/// values.
///
/// \param colind [out] Column indices of the matrix. Same
/// number of entries as values. colind[k] is the column
/// index of values[k].
///
/// \param values [out] Values stored in the matrix.
///
/// \param replace [in] If true, replace each duplicate
/// element with the next element sharing the same row and
/// column index. This means that results will depend on
/// the order in which the duplicate elements were added.
/// Otherwise, duplicate elements have their values added
/// together; in that case, the result is independent (in
/// exact arithmetic, not in finite-precision arithmetic) of
/// their order.
///
/// \note This method does not change the "expected" or "seen"
/// numbers of entries, since both of those count entries
/// with the same row and column indices as separate
/// entries.
void
mergeAndConvertToCSR (size_type& numUniqueElts,
size_type& numRemovedElts,
Teuchos::ArrayRCP<Ordinal>& rowptr,
Teuchos::ArrayRCP<Ordinal>& colind,
Teuchos::ArrayRCP<Scalar>& values,
const bool replace=false)
{
using Teuchos::arcp;
using Teuchos::ArrayRCP;
std::pair<size_type, size_type> mergeResult = merge (replace);
// At this point, elts_ is already in CSR order.
// Now we can allocate and fill the ind and val arrays.
ArrayRCP<Ordinal> ind = arcp<Ordinal> (elts_.size ());
ArrayRCP<Scalar> val = arcp<Scalar> (elts_.size ());
// Number of rows in the matrix.
const Ordinal nrows = tolerant_ ? seenNumRows_ : expectedNumRows_;
ArrayRCP<Ordinal> ptr = arcp<Ordinal> (nrows + 1);
// Copy over the elements, and fill in the ptr array with
// offsets. Note that merge() sorted the entries by row
// index, so we can assume the row indices are increasing in
// the list of entries.
Ordinal curRow = 0;
Ordinal curInd = 0;
typedef typename std::vector<element_type>::const_iterator iter_type;
ptr[0] = 0; // ptr always has at least one entry.
for (iter_type it = elts_.begin(); it != elts_.end(); ++it) {
const Ordinal i = it->rowIndex ();
const Ordinal j = it->colIndex ();
const Scalar Aij = it->value ();
TEUCHOS_TEST_FOR_EXCEPTION(i < curRow, std::logic_error, "The "
"current matrix entry's row index " << i << " is less then what "
"should be the current row index lower bound " << curRow << ".");
for (Ordinal k = curRow+1; k <= i; ++k) {
ptr[k] = curInd;
}
curRow = i;
TEUCHOS_TEST_FOR_EXCEPTION(
static_cast<size_t> (curInd) >= elts_.size (),
std::logic_error, "The current index " << curInd << " into ind "
"and val is >= the number of matrix entries " << elts_.size ()
<< ".");
ind[curInd] = j;
val[curInd] = Aij;
++curInd;
}
for (Ordinal k = curRow+1; k <= nrows; ++k) {
ptr[k] = curInd;
}
// Assign to outputs here, to ensure the strong exception
// guarantee (assuming that ArrayRCP's operator= doesn't
// throw).
rowptr = ptr;
colind = ind;
values = val;
numUniqueElts = mergeResult.first;
numRemovedElts = mergeResult.second;
}
//! A temporary const view of the entries of the matrix.
const std::vector<element_type>& getEntries() const {
return elts_;
}
//! Clear all the added matrix entries and reset metadata.
void clear() {
seenNumRows_ = 0;
seenNumCols_ = 0;
seenNumEntries_ = 0;
elts_.resize (0);
}
/// \brief Computed number of rows.
///
/// "Computed" means "as seen from the matrix data."
const Ordinal numRows() const { return seenNumRows_; }
/// \brief Computed number of columns.
///
/// "Computed" means "as seen from the matrix data."
const Ordinal numCols() const { return seenNumCols_; }
private:
Ordinal expectedNumRows_, expectedNumCols_, expectedNumEntries_;
Ordinal seenNumRows_, seenNumCols_, seenNumEntries_;
bool tolerant_;
bool debug_;
//! The actual matrix entries, stored as an array of structs.
std::vector<element_type> elts_;
};
} // namespace Raw
} // namespace MatrixMarket
} // namespace Teuchos
#endif // #ifndef __Teuchos_MatrixMarket_Raw_Adder_hpp
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