Provided by: liblapack-doc_3.12.1-4_all 
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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Version 3.12.0 Sun Jul 20 2025 01:40:05 lar2v(3)