Provided by: liblapack-doc_3.12.0-3build1.1_all bug

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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