cern.colt.matrix.doc-files.performanceNotes.html Maven / Gradle / Ivy
Show all versions of parallelcolt Show documentation
Performance Notes
Matrix Performance Notes
While the matrix interface is always identical, performance characteristics
are implementation dependent. In general, performance of a matrix operation
is a function of {data structure, density, type and kind of method arguments}.
This library takes great care about performance. When in doubt about the detailed
character of an operation, have a look at the source code.
In practice, sparse matrices are used for one of two reasons: To safe memory
or to speed up computation. Hash based sparse matrices (SparseDoubleMatrix2D)
are neither the smallest possible matrix representation nor the fastest. They
implement a reasonable trade-off between performance and memory: Very good average
performance on get/set operations at quite small memory footprint. They are
also suited for special-purpose algorithms exploiting explicit knowledge about
what regions are zero and non-zero, but not quite as good as other sparse matrix
representations. For example, sparse linear algebraic matrix multiplies, inversions,
etc. better work on sparse row compressed (RCDoubleMatrix2D).
However, alternative sparse matrix representations are really only usable for
special purposes, because their get/set performance can be very bad. In contrast,
hash based sparse matrices are more generally applicable data structures.
Here is a list describing which combinations are particularly optimized. (F
is used as shortcut for cern.jet.math.Functions)
General Remarks
Matrix-matrix and matrix-vector multiplication C = alpha*AxB + beta*C
:
For good performance B,C may have any type. For A={SparseDoubleMatrix2D,RCDoubleMatrix2D}
this is only fast if the density of A is small. For A={DenseDoubleMatrix2D}
density does not matter. If A is dense and B is sparse, this is no problem,
because even then the quick sparse mult is used.
DenseDoubleMatrix2D
Dense row major format. Essentially all methods highly optimized. This
is almost always the implementation type to go for. It is also most easily to
understand. The types below are only useful for very specific use cases.
RCDoubleMatrix2D
Sparse row-compressed format. Special-purpose implementation. Thus some
operations very efficient, others quite slow. Essentially designed to support
the fastest possible sparse matrix-matrix and matrix-vector multiplications as
well as sparse linear algebra. Efficient methods are:
Operation
Method
Comment
read
get,getQuick
always
write
set,setQuick
only fast if the matrix is really sparse and in a loop iterating upwards:
for (int i=0; i<rows; i++) { for (int j=0; j<columns; j++) {
setQuick(i,j,...) ... }}
matrix-matrix and matrix-vector multiplication
zMult
see above in Section "General"
elementwise scaling
assign(f) where f is one of {F.mult(a),F.div(a)}
x[i,j] = x[i,j] {*,/} a
elementwise scaling
assign(y,f) where f is one of {F.plus,F.minus, F.mult,F.div,
F.plusMult(a),F.minusMult(a)}
x[i,j] = x[i,j] {+,-,*,/} y[i,j]
x[i,j] = x[i,j] {+,-} y[i,j] {*,/} a
copying
assign(othermatrix)
always fast, best if othermatrix is a RCDoubleMatrix2D
iteration
forEachNonzero(function)
most of the time the preferred way for iteration and modification
SparseDoubleMatrix2D
Sparse hash format. General-purpose sparse implementation. Designed for
efficient random access to sparse structures. Thus, performance more balanced
than RCDoubleMatrix2D. Never really slow, often faster than RCDoubleMatrix2D,
sometimes slightly slower. Efficient methods are:
Operation
Method
Comment
read
get,getQuick
always
write
set,setQuick
always
matrix-matrix and matrix-vector multiplication
zMult
slightly slower than RCDoubleMatrix when size is large
elementwise scaling
assign(f) where f is one of {F.mult(a),F.div(a)}
x[i,j] = x[i,j] {*,/} a
elementwise scaling
assign(y,f) where f is one of {F.plus,F.minus, F.mult,F.div,
F.plusMult(a),F.minusMult(a)}
x[i,j] = x[i,j] {+,-,*,/} y[i,j]
x[i,j] = x[i,j] {+,-} y[i,j] {*,/} a
copying
assign(othermatrix)
best if othermatrix is a SparseDoubleMatrix2D
iteration
forEachNonzero(function)
often the preferred way for iteration and modification