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lar2v(3) LAPACK lar2v(3)

NAME

lar2v - lar2v: apply vector of plane rotations to 2x2 matrices

SYNOPSIS

Functions


subroutine clar2v (n, x, y, z, incx, c, s, incc)
CLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices. subroutine dlar2v (n, x, y, z, incx, c, s, incc)
DLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices. subroutine slar2v (n, x, y, z, incx, c, s, incc)
SLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices. subroutine zlar2v (n, x, y, z, incx, c, s, incc)
ZLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Detailed Description

Function Documentation

subroutine clar2v (integer n, complex, dimension( * ) x, complex, dimension( * ) y, complex, dimension( * ) z, integer incx, real, dimension( * ) c, complex, dimension( * ) s, integer incc)

CLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:

!>
!> CLAR2V applies a vector of complex plane rotations with real cosines
!> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
!> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
!>
!>    (       x(i)  z(i) ) :=
!>    ( conjg(z(i)) y(i) )
!>
!>      (  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
!>      ( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )
!>

Parameters

N 

!>          N is INTEGER
!>          The number of plane rotations to be applied.
!>

X

!>          X is COMPLEX array, dimension (1+(N-1)*INCX)
!>          The vector x; the elements of x are assumed to be real.
!>

Y

!>          Y is COMPLEX array, dimension (1+(N-1)*INCX)
!>          The vector y; the elements of y are assumed to be real.
!>

Z

!>          Z is COMPLEX array, dimension (1+(N-1)*INCX)
!>          The vector z.
!>

INCX

!>          INCX is INTEGER
!>          The increment between elements of X, Y and Z. INCX > 0.
!>

C

!>          C is REAL array, dimension (1+(N-1)*INCC)
!>          The cosines of the plane rotations.
!>

S

!>          S is COMPLEX array, dimension (1+(N-1)*INCC)
!>          The sines of the plane rotations.
!>

INCC

!>          INCC is INTEGER
!>          The increment between elements of C and S. INCC > 0.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dlar2v (integer n, double precision, dimension( * ) x, double precision, dimension( * ) y, double precision, dimension( * ) z, integer incx, double precision, dimension( * ) c, double precision, dimension( * ) s, integer incc)

DLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:

!>
!> DLAR2V applies a vector of real plane rotations from both sides to
!> a sequence of 2-by-2 real symmetric matrices, defined by the elements
!> of the vectors x, y and z. For i = 1,2,...,n
!>
!>    ( x(i)  z(i) ) := (  c(i)  s(i) ) ( x(i)  z(i) ) ( c(i) -s(i) )
!>    ( z(i)  y(i) )    ( -s(i)  c(i) ) ( z(i)  y(i) ) ( s(i)  c(i) )
!>

Parameters

N 

!>          N is INTEGER
!>          The number of plane rotations to be applied.
!>

X

!>          X is DOUBLE PRECISION array,
!>                         dimension (1+(N-1)*INCX)
!>          The vector x.
!>

Y

!>          Y is DOUBLE PRECISION array,
!>                         dimension (1+(N-1)*INCX)
!>          The vector y.
!>

Z

!>          Z is DOUBLE PRECISION array,
!>                         dimension (1+(N-1)*INCX)
!>          The vector z.
!>

INCX

!>          INCX is INTEGER
!>          The increment between elements of X, Y and Z. INCX > 0.
!>

C

!>          C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
!>          The cosines of the plane rotations.
!>

S

!>          S is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
!>          The sines of the plane rotations.
!>

INCC

!>          INCC is INTEGER
!>          The increment between elements of C and S. INCC > 0.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine slar2v (integer n, real, dimension( * ) x, real, dimension( * ) y, real, dimension( * ) z, integer incx, real, dimension( * ) c, real, dimension( * ) s, integer incc)

SLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:

!>
!> SLAR2V applies a vector of real plane rotations from both sides to
!> a sequence of 2-by-2 real symmetric matrices, defined by the elements
!> of the vectors x, y and z. For i = 1,2,...,n
!>
!>    ( x(i)  z(i) ) := (  c(i)  s(i) ) ( x(i)  z(i) ) ( c(i) -s(i) )
!>    ( z(i)  y(i) )    ( -s(i)  c(i) ) ( z(i)  y(i) ) ( s(i)  c(i) )
!>

Parameters

N 

!>          N is INTEGER
!>          The number of plane rotations to be applied.
!>

X

!>          X is REAL array,
!>                         dimension (1+(N-1)*INCX)
!>          The vector x.
!>

Y

!>          Y is REAL array,
!>                         dimension (1+(N-1)*INCX)
!>          The vector y.
!>

Z

!>          Z is REAL array,
!>                         dimension (1+(N-1)*INCX)
!>          The vector z.
!>

INCX

!>          INCX is INTEGER
!>          The increment between elements of X, Y and Z. INCX > 0.
!>

C

!>          C is REAL array, dimension (1+(N-1)*INCC)
!>          The cosines of the plane rotations.
!>

S

!>          S is REAL array, dimension (1+(N-1)*INCC)
!>          The sines of the plane rotations.
!>

INCC

!>          INCC is INTEGER
!>          The increment between elements of C and S. INCC > 0.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zlar2v (integer n, complex*16, dimension( * ) x, complex*16, dimension( * ) y, complex*16, dimension( * ) z, integer incx, double precision, dimension( * ) c, complex*16, dimension( * ) s, integer incc)

ZLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:

!>
!> ZLAR2V applies a vector of complex plane rotations with real cosines
!> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
!> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
!>
!>    (       x(i)  z(i) ) :=
!>    ( conjg(z(i)) y(i) )
!>
!>      (  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
!>      ( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )
!>

Parameters

N 

!>          N is INTEGER
!>          The number of plane rotations to be applied.
!>

X

!>          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
!>          The vector x; the elements of x are assumed to be real.
!>

Y

!>          Y is COMPLEX*16 array, dimension (1+(N-1)*INCX)
!>          The vector y; the elements of y are assumed to be real.
!>

Z

!>          Z is COMPLEX*16 array, dimension (1+(N-1)*INCX)
!>          The vector z.
!>

INCX

!>          INCX is INTEGER
!>          The increment between elements of X, Y and Z. INCX > 0.
!>

C

!>          C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
!>          The cosines of the plane rotations.
!>

S

!>          S is COMPLEX*16 array, dimension (1+(N-1)*INCC)
!>          The sines of the plane rotations.
!>

INCC

!>          INCC is INTEGER
!>          The increment between elements of C and S. INCC > 0.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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Tue Jun 30 2026 04:57:07 Version 3.12.0