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.
    !>

  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.

  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.

  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.
    !>

Author

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