?roti

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?roti

Applies Givens rotation to sparse vectors one of which is in compressed form.

Syntax

call sroti ( nz, x, indx, y, c, s )

call droti ( nz, x, indx, y, c, s )

call roti ( x, indx, y, c, s )

Include Files

mkl.fi , mkl_blas.f90

Description

sroti droti roti

The ?roti routines apply the Givens rotation to elements of two real vectors, x (in compressed form nz , x , indx ) and y (in full storage form):

\[\left(\begin{array}{c} x_{i} \\ y_{indx_{i}}\end{array}\right) \leftarrow \left(\begin{array}{cc} c & s\\ -s & c\end{array}\right) \left(\begin{array}{c} x_{i} \\ y_{indx_{i}}\end{array}\right)\text{, for } i = 1, \dots, nz\]

or in other words,

do i = 1, nz
    xval = x(i)
    yval = y(indx(i))
    x(i) = c*xval + s*yval
    y(indx(i)) = c*yval - s*xval
end do

The routines reference only the elements of y whose indices are listed in the array indx . The values in indx must be distinct.

Input Parameters

nz

INTEGER .

The number of elements in x and indx.

x

`REAL`	for `sroti`
`DOUBLE PRECISION`	for `droti`

Array, size at least nz .

indx

INTEGER.

Specifies the indices for the elements of x. Array, size at least nz .

y

`REAL`	for `sroti`
`DOUBLE PRECISION`	for `droti`

Array, size at least \(\max(\text{indx}(i))\).

c

`REAL`	for `sroti`
`DOUBLE PRECISION`	for `droti`

A scalar.

s

`REAL`	for `sroti`
`DOUBLE PRECISION`	for `droti`

A scalar.

Output Parameters

x and y: The updated arrays.

BLAS 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see BLAS 95 Interface Conventions .

Specific details for the routine roti interface are the following:

x: Holds the vector with the number of elements nz .
indx: Holds the vector with the number of elements nz .
y: Holds the vector with the number of elements nz .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?roti

Syntax

Include Files

Description

Input Parameters

Output Parameters

BLAS 95 Interface Notes