Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 12/16/2022
Public

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Vector Arguments in Vector Math

Vector arguments of classic VM mathematical functions are passed in one-dimensional arrays with unit vector increment. It means that a vector of length n is passed contiguously in an array a whose values are defined as

a(1), a(2), ..., a(n)

.

Strided VM mathematical functions allow using positive increments for all input and output vector arguments.

To accommodate for arrays with other increments, or more complicated indexing, VM contains auxiliary Pack/Unpack functions that gather the array elements into a contiguous vector and then scatter them after the computation is complete.

Generally, if the vector elements are stored in a one-dimensional array a as

a(m1), a(m2), ..., a(mn)

and need to be regrouped into an array y as

y(k1), y(k2), ..., y(kn),

.

VM Pack/Unpack functions can use one of the following indexing methods:

Positive Increment Indexing

kj = 1 + incy * (j - 1), mj = 1 + inca * (j - 1), j = 1, ..., n.

.

Constraint: incy > 0 and inca > 0.

For example, setting incy = 1 specifies gathering array elements into a contiguous vector.

This method is similar to that used in BLAS, with the exception that negative and zero increments are not permitted.

Index Vector Indexing

kj = iy(j), mj = ia(j), j = 1 ,..., n .

.

where ia and iy are arrays of length n that contain index vectors for the input and output arrays a and y, respectively.

Mask Vector Indexing

Indices kj , mj are such that:

my(kj)  0, ma(mj)  0 , j = 1,..., n .

.

where ma and my are arrays that contain mask vectors for the input and output arrays a and y, respectively.

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