rot(3) LAPACK rot(3)

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


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.

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.

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.

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(*)

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(*)

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.

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.

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