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rot(3) LAPACK rot(3)

NAME

rot - rot: apply plane rotation ([cz]rot in LAPACK)

SYNOPSIS

Functions


subroutine csrot (n, cx, incx, cy, incy, c, s)
CSROT subroutine drot (n, dx, incx, dy, incy, c, s)
DROT subroutine srot (n, sx, incx, sy, incy, c, s)
SROT subroutine zdrot (n, zx, incx, zy, incy, c, s)
ZDROT subroutine crot (n, cx, incx, cy, incy, c, s)
CROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors. subroutine zrot (n, cx, incx, cy, incy, c, s)
ZROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors.

Detailed Description

Function Documentation

subroutine crot (integer n, complex, dimension( * ) cx, integer incx, complex, dimension( * ) cy, integer incy, real c, complex s)

CROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors.

Purpose:



 CROT applies a plane rotation, where the cos (C) is real and the


 sin (S) is complex, and the vectors CX and CY are complex.

Parameters

N 



          N is INTEGER


          The number of elements in the vectors CX and CY.

CX



          CX is COMPLEX array, dimension (N)


          On input, the vector X.


          On output, CX is overwritten with C*X + S*Y.

INCX



          INCX is INTEGER


          The increment between successive values of CX.  INCX <> 0.

CY



          CY is COMPLEX array, dimension (N)


          On input, the vector Y.


          On output, CY is overwritten with -CONJG(S)*X + C*Y.

INCY



          INCY is INTEGER


          The increment between successive values of CY.  INCX <> 0.

C



          C is REAL

S



          S is COMPLEX


          C and S define a rotation


             [  C          S  ]


             [ -conjg(S)   C  ]


          where C*C + S*CONJG(S) = 1.0.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine csrot (integer n, complex, dimension( * ) cx, integer incx, complex, dimension( * ) cy, integer incy, real c, real s)

CSROT

Purpose:



 CSROT applies a plane rotation, where the cos and sin (c and s) are real


 and the vectors cx and cy are complex.


 jack dongarra, linpack, 3/11/78.

Parameters

N 



          N is INTEGER


           On entry, N specifies the order of the vectors cx and cy.


           N must be at least zero.

CX



          CX is COMPLEX array, dimension at least


           ( 1 + ( N - 1 )*abs( INCX ) ).


           Before entry, the incremented array CX must contain the n


           element vector cx. On exit, CX is overwritten by the updated


           vector cx.

INCX



          INCX is INTEGER


           On entry, INCX specifies the increment for the elements of


           CX. INCX must not be zero.

CY



          CY is COMPLEX array, dimension at least


           ( 1 + ( N - 1 )*abs( INCY ) ).


           Before entry, the incremented array CY must contain the n


           element vector cy. On exit, CY is overwritten by the updated


           vector cy.

INCY



          INCY is INTEGER


           On entry, INCY specifies the increment for the elements of


           CY. INCY must not be zero.

C



          C is REAL


           On entry, C specifies the cosine, cos.

S



          S is REAL


           On entry, S specifies the sine, sin.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine drot (integer n, double precision, dimension(*) dx, integer incx, double precision, dimension(*) dy, integer incy, double precision c, double precision s)

DROT

Purpose:



    DROT applies a plane rotation.

Parameters

N 



          N is INTEGER


         number of elements in input vector(s)

DX



          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX



          INCX is INTEGER


         storage spacing between elements of DX

DY



          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

INCY



          INCY is INTEGER


         storage spacing between elements of DY

C



          C is DOUBLE PRECISION

S



          S is DOUBLE PRECISION

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



     jack dongarra, linpack, 3/11/78.


     modified 12/3/93, array(1) declarations changed to array(*)

subroutine srot (integer n, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy, real c, real s)

SROT

Purpose:



    applies a plane rotation.

Parameters

N 



          N is INTEGER


         number of elements in input vector(s)

SX



          SX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX



          INCX is INTEGER


         storage spacing between elements of SX

SY



          SY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

INCY



          INCY is INTEGER


         storage spacing between elements of SY

C



          C is REAL

S



          S is REAL

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



     jack dongarra, linpack, 3/11/78.


     modified 12/3/93, array(1) declarations changed to array(*)

subroutine zdrot (integer n, complex*16, dimension( * ) zx, integer incx, complex*16, dimension( * ) zy, integer incy, double precision c, double precision s)

ZDROT

Purpose:



 Applies a plane rotation, where the cos and sin (c and s) are real


 and the vectors cx and cy are complex.


 jack dongarra, linpack, 3/11/78.

Parameters

N 



          N is INTEGER


           On entry, N specifies the order of the vectors cx and cy.


           N must be at least zero.

ZX



          ZX is COMPLEX*16 array, dimension at least


           ( 1 + ( N - 1 )*abs( INCX ) ).


           Before entry, the incremented array ZX must contain the n


           element vector cx. On exit, ZX is overwritten by the updated


           vector cx.

INCX



          INCX is INTEGER


           On entry, INCX specifies the increment for the elements of


           ZX. INCX must not be zero.

ZY



          ZY is COMPLEX*16 array, dimension at least


           ( 1 + ( N - 1 )*abs( INCY ) ).


           Before entry, the incremented array ZY must contain the n


           element vector cy. On exit, ZY is overwritten by the updated


           vector cy.

INCY



          INCY is INTEGER


           On entry, INCY specifies the increment for the elements of


           ZY. INCY must not be zero.

C



          C is DOUBLE PRECISION


           On entry, C specifies the cosine, cos.

S



          S is DOUBLE PRECISION


           On entry, S specifies the sine, sin.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zrot (integer n, complex*16, dimension( * ) cx, integer incx, complex*16, dimension( * ) cy, integer incy, double precision c, complex*16 s)

ZROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors.

Purpose:



 ZROT applies a plane rotation, where the cos (C) is real and the


 sin (S) is complex, and the vectors CX and CY are complex.

Parameters

N 



          N is INTEGER


          The number of elements in the vectors CX and CY.

CX



          CX is COMPLEX*16 array, dimension (N)


          On input, the vector X.


          On output, CX is overwritten with C*X + S*Y.

INCX



          INCX is INTEGER


          The increment between successive values of CX.  INCX <> 0.

CY



          CY is COMPLEX*16 array, dimension (N)


          On input, the vector Y.


          On output, CY is overwritten with -CONJG(S)*X + C*Y.

INCY



          INCY is INTEGER


          The increment between successive values of CY.  INCX <> 0.

C



          C is DOUBLE PRECISION

S



          S is COMPLEX*16


          C and S define a rotation


             [  C          S  ]


             [ -conjg(S)   C  ]


          where C*C + S*CONJG(S) = 1.0.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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