lartv(3)

NAME
lartv - lartv: apply vector of plane rotations to vectors

SYNOPSIS

  Functions

subroutine clartv (n, x, incx, y, incy, c, s, incc)
CLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.
subroutine dlartv (n, x, incx, y, incy, c, s, incc)
DLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.
subroutine slartv (n, x, incx, y, incy, c, s, incc)
SLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.
subroutine zlartv (n, x, incx, y, incy, c, s, incc)
ZLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

Detailed Description

Function Documentation

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

CLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

Purpose:

    !>
    !> CLARTV applies a vector of complex plane rotations with real cosines
    !> to elements of the complex vectors x and y. For i = 1,2,...,n
    !>
    !>    ( x(i) ) := (        c(i)   s(i) ) ( x(i) )
    !>    ( y(i) )    ( -conjg(s(i))  c(i) ) ( y(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.
    !>

    INCX

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

    Y

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

    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.
    !>

    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 dlartv (integer n, double precision, dimension( * ) x, integer incx, double precision, dimension( * ) y, integer incy, double precision, dimension( * ) c, double precision, dimension( * ) s, integer incc)

DLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.

Purpose:

    !>
    !> DLARTV applies a vector of real plane rotations to elements of the
    !> real vectors x and y. For i = 1,2,...,n
    !>
    !>    ( x(i) ) := (  c(i)  s(i) ) ( x(i) )
    !>    ( y(i) )    ( -s(i)  c(i) ) ( y(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.
    !>

    INCX

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

    Y

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

    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.
    !>

    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 slartv (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real, dimension( * ) c, real, dimension( * ) s, integer incc)

SLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.

Purpose:

    !>
    !> SLARTV applies a vector of real plane rotations to elements of the
    !> real vectors x and y. For i = 1,2,...,n
    !>
    !>    ( x(i) ) := (  c(i)  s(i) ) ( x(i) )
    !>    ( y(i) )    ( -s(i)  c(i) ) ( y(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.
    !>

    INCX

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

    Y

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

    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.
    !>

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

ZLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

Purpose:

    !>
    !> ZLARTV applies a vector of complex plane rotations with real cosines
    !> to elements of the complex vectors x and y. For i = 1,2,...,n
    !>
    !>    ( x(i) ) := (        c(i)   s(i) ) ( x(i) )
    !>    ( y(i) )    ( -conjg(s(i))  c(i) ) ( y(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.
    !>

    INCX

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

    Y

    !>          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
    !>          The vector y.
    !>

    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.
    !>

    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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