?rotmg

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?rotmg

Computes the parameters for a modified Givens rotation.

Syntax

call srotmg(d1, d2, x1, y1, param)

call drotmg(d1, d2, x1, y1, param)

call rotmg(d1, d2, x1, y1, param)

Include Files

mkl.fi, mkl_blas.f90

Description

Given Cartesian coordinates \((x_1, y_1)\) of an input vector, these routines compute the components of a modified Givens transformation matrix \(H\) that zeros the y-component of the resulting vector:

\[\begin{bmatrix} x_1 \\ 0 \end{bmatrix} = H \begin{bmatrix} x_1 \, \sqrt{d_1} \\ y_1 \, \sqrt{d_2} \end{bmatrix} \]

Input Parameters

d1

REAL for srotmg
DOUBLE PRECISION for drotmg

Provides the scaling factor for the x-coordinate of the input vector.

d2

REAL for srotmg
DOUBLE PRECISION for drotmg

Provides the scaling factor for the y-coordinate of the input vector.

x1

REAL for srotmg
DOUBLE PRECISION for drotmg

Provides the x-coordinate of the input vector.

y1

REAL for srotmg
DOUBLE PRECISION for drotmg

Provides the y-coordinate of the input vector.

Output Parameters

d1

REAL for srotmg
DOUBLE PRECISION for drotmg

Provides the first diagonal element of the updated matrix.

d2

REAL for srotmg
DOUBLE PRECISION for drotmg

Provides the second diagonal element of the updated matrix.

x1

REAL for srotmg
DOUBLE PRECISION for drotmg

Provides the x-coordinate of the rotated vector before scaling.

param

REAL array for srotmg
DOUBLE PRECISION array for drotmg

The size is 5.

param(1) contains a switch. param(2) to param(5) may store the elements of the matrix \(H\), \(h_{11}\), \(h_{21}\), \(h_{12}\), and \(h_{22}\), respectively. Depending on the value of param(1), the representation of \(H\) is given as follows:

param(1) = -1.0:

\[H = \begin{bmatrix} h_{11} & h_{12} \\ h_{21} & h_{22} \end{bmatrix} \]

param(1) = 0.0:

\[H = \begin{bmatrix} 1.0 & h_{12} \\ h_{21} & 1.0 \end{bmatrix} \]

param(1) = 1.0:

\[H = \begin{bmatrix} h_{11} & 1.0 \\ -1.0 & h_{22} \end{bmatrix} \]

param(1) = -2.0:

\[H = \begin{bmatrix} 1.0 & 0.0 \\ 0.0 & 1.0 \end{bmatrix} \]

In the last three cases, the matrix entries of 1.0, -1.0, and 0.0 are assumed based on the value of param(1) and are not stored in param.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?rotmg

Syntax

Include Files

Description

Input Parameters

Output Parameters