Man page - lar2v(3)

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Manual

lar2v

NAME
SYNOPSIS
Functions
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)
subroutine dlar2v (integer n, double precision, dimension( * ) x, doubleprecision, dimension( * ) y, double precision, dimension( * ) z,integer incx, double precision, dimension( * ) c, double precision,dimension( * ) s, integer incc)
subroutine slar2v (integer n, real, dimension( * ) x, real, dimension( * )y, real, dimension( * ) z, integer incx, real, dimension( * ) c, real,dimension( * ) s, integer incc)
subroutine zlar2v (integer n, complex*16, dimension( * ) x, complex*16,dimension( * ) y, complex*16, dimension( * ) z, integer incx, doubleprecision, dimension( * ) c, complex*16, dimension( * ) s, integerincc)
Author

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, doubleprecision, 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, doubleprecision, dimension( * ) c, complex*16, dimension( * ) s, integerincc)

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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