MKL or BLAS routine to multiply vector by a scalar out-of-place

Question

I work in simulation software and one of the many operations done on arrays is scaling a vector by a number.

I have code like this:

//Just some initialization code, don't bother about this part
int n = 10000;
std::vector<double> input(n, 42.0);
std::vector<double> output(input.size());

double alpha = 69.0;

//the actual calculation:
for (size_t i = 0; i < n; ++i) {
    output[i] = input[i] * alpha;
}

I have the MKL library available, so if my calculations are done "in-place" the following can be written:

cblas_dscal(n, alpha, &input[0], 1);

However, this will change the input variable, which is not what I want.

I tried using the mkl_domatcopy() but it is very slow for this operation.

Answer 1

The solution I came up with was calling cblas_dcopy() then cblas_dscal().

It is not the best of all worlds but it is still faster than the raw loop.

Answer 2

From MKL reference:

The cblas_?axpy routines perform a vector-vector operation defined as

y := a * x + y where: a is a scalar, x and y are vectors each with a number of elements that equals n.

Answer 3

There is a routine within the BLAS-like extensions called cblas_?axpby

Here is an excerpt from the documentation:

Scales two vectors, adds them to one another and stores result in the vector.

The difference to cblas_?axpy is that you have second scaling parameter on the result vector y. In your case, you could just set b := 0.0 and thus have your out of place scaling in one call, instead of the two cblas_dcopy() and cblas_dscal().

Your code could look like this:

//Just some initialization code, don't bother about this part
int n = 10000;
std::vector<double> input(n, 42.0);
std::vector<double> output(input.size());

double alpha = 69.0;

//the actual calculation:
cblas_daxpby (output.size(), alpha, input.data(), 1, 0.0, output.data(), 1);