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largv(3) Library Functions Manual largv(3)

NAME

largv - largv: generate vector of plane rotations

SYNOPSIS

Functions


subroutine CLARGV (n, x, incx, y, incy, c, incc)
CLARGV generates a vector of plane rotations with real cosines and complex sines. subroutine DLARGV (n, x, incx, y, incy, c, incc)
DLARGV generates a vector of plane rotations with real cosines and real sines. subroutine SLARGV (n, x, incx, y, incy, c, incc)
SLARGV generates a vector of plane rotations with real cosines and real sines. subroutine ZLARGV (n, x, incx, y, incy, c, incc)
ZLARGV generates a vector of plane rotations with real cosines and complex sines.

Detailed Description

Function Documentation

subroutine CLARGV (integer n, complex, dimension( * ) x, integer incx, complex, dimension( * ) y, integer incy, real, dimension( * ) c, integer incc)

CLARGV generates a vector of plane rotations with real cosines and complex sines.

Purpose:

!>
!> CLARGV generates a vector of complex plane rotations with real
!> cosines, determined by elements of the complex vectors x and y.
!> For i = 1,2,...,n
!>
!>    (        c(i)   s(i) ) ( x(i) ) = ( r(i) )
!>    ( -conjg(s(i))  c(i) ) ( y(i) ) = (   0  )
!>
!>    where c(i)**2 + ABS(s(i))**2 = 1
!>
!> The following conventions are used (these are the same as in CLARTG,
!> but differ from the BLAS1 routine CROTG):
!>    If y(i)=0, then c(i)=1 and s(i)=0.
!>    If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
!>

Parameters

N 

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

X

!>          X is COMPLEX array, dimension (1+(N-1)*INCX)
!>          On entry, the vector x.
!>          On exit, x(i) is overwritten by r(i), for i = 1,...,n.
!>

INCX

!>          INCX is INTEGER
!>          The increment between elements of X. INCX > 0.
!>

Y

!>          Y is COMPLEX array, dimension (1+(N-1)*INCY)
!>          On entry, the vector y.
!>          On exit, the sines of the plane rotations.
!>

INCY

!>          INCY is INTEGER
!>          The increment between elements of Y. INCY > 0.
!>

C

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

INCC

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
!>
!>  This version has a few statements commented out for thread safety
!>  (machine parameters are computed on each entry). 10 feb 03, SJH.
!>

Definition at line 121 of file clargv.f.

subroutine DLARGV (integer n, double precision, dimension( * ) x, integer incx, double precision, dimension( * ) y, integer incy, double precision, dimension( * ) c, integer incc)

DLARGV generates a vector of plane rotations with real cosines and real sines.

Purpose:

!>
!> DLARGV generates a vector of real plane rotations, determined by
!> elements of the real vectors x and y. For i = 1,2,...,n
!>
!>    (  c(i)  s(i) ) ( x(i) ) = ( a(i) )
!>    ( -s(i)  c(i) ) ( y(i) ) = (   0  )
!>

Parameters

N 

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

X

!>          X is DOUBLE PRECISION array,
!>                         dimension (1+(N-1)*INCX)
!>          On entry, the vector x.
!>          On exit, x(i) is overwritten by a(i), for i = 1,...,n.
!>

INCX

!>          INCX is INTEGER
!>          The increment between elements of X. INCX > 0.
!>

Y

!>          Y is DOUBLE PRECISION array,
!>                         dimension (1+(N-1)*INCY)
!>          On entry, the vector y.
!>          On exit, the sines of the plane rotations.
!>

INCY

!>          INCY is INTEGER
!>          The increment between elements of Y. INCY > 0.
!>

C

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

INCC

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 103 of file dlargv.f.

subroutine SLARGV (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real, dimension( * ) c, integer incc)

SLARGV generates a vector of plane rotations with real cosines and real sines.

Purpose:

!>
!> SLARGV generates a vector of real plane rotations, determined by
!> elements of the real vectors x and y. For i = 1,2,...,n
!>
!>    (  c(i)  s(i) ) ( x(i) ) = ( a(i) )
!>    ( -s(i)  c(i) ) ( y(i) ) = (   0  )
!>

Parameters

N 

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

X

!>          X is REAL array,
!>                         dimension (1+(N-1)*INCX)
!>          On entry, the vector x.
!>          On exit, x(i) is overwritten by a(i), for i = 1,...,n.
!>

INCX

!>          INCX is INTEGER
!>          The increment between elements of X. INCX > 0.
!>

Y

!>          Y is REAL array,
!>                         dimension (1+(N-1)*INCY)
!>          On entry, the vector y.
!>          On exit, the sines of the plane rotations.
!>

INCY

!>          INCY is INTEGER
!>          The increment between elements of Y. INCY > 0.
!>

C

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

INCC

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 103 of file slargv.f.

subroutine ZLARGV (integer n, complex*16, dimension( * ) x, integer incx, complex*16, dimension( * ) y, integer incy, double precision, dimension( * ) c, integer incc)

ZLARGV generates a vector of plane rotations with real cosines and complex sines.

Purpose:

!>
!> ZLARGV generates a vector of complex plane rotations with real
!> cosines, determined by elements of the complex vectors x and y.
!> For i = 1,2,...,n
!>
!>    (        c(i)   s(i) ) ( x(i) ) = ( r(i) )
!>    ( -conjg(s(i))  c(i) ) ( y(i) ) = (   0  )
!>
!>    where c(i)**2 + ABS(s(i))**2 = 1
!>
!> The following conventions are used (these are the same as in ZLARTG,
!> but differ from the BLAS1 routine ZROTG):
!>    If y(i)=0, then c(i)=1 and s(i)=0.
!>    If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
!>

Parameters

N 

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

X

!>          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
!>          On entry, the vector x.
!>          On exit, x(i) is overwritten by r(i), for i = 1,...,n.
!>

INCX

!>          INCX is INTEGER
!>          The increment between elements of X. INCX > 0.
!>

Y

!>          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
!>          On entry, the vector y.
!>          On exit, the sines of the plane rotations.
!>

INCY

!>          INCY is INTEGER
!>          The increment between elements of Y. INCY > 0.
!>

C

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

INCC

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
!>
!>  This version has a few statements commented out for thread safety
!>  (machine parameters are computed on each entry). 10 feb 03, SJH.
!>

Definition at line 121 of file zlargv.f.

Author

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