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SROT(3S)							      SROT(3S)

NAME
     SROT, DROT, CROT, ZROT - Applies a real plane rotation or complex
     coordinate rotation

SYNOPSIS
     Single precision

	  Fortran:
	       CALL SROT (n, x, incx, y, incy, c, s)

	  C/C++:
	       #include <scsl_blas.h>
	       void srotm (int n, float *x, int incx, float *y, int incy,
	       float c, float s);

     Double precision

	  Fortran:
	       CALL DROT x, incx, y, incy, c, s)

	  C/C++:
	       #include <scsl_blas.h>
	       void drot (int n, double *x, int incx, double *y, int incy,
	       double c, double s);

     Single precision complex

	  Fortran:
	       CALL CROT (n, x, incx, y, incy, c, s)

	  C/C++:
	       #include <scsl_blas.h>
	       void crot (int n, scsl_complex *x, int incx, scsl_complex *y,
	       int incy, float c, scsl_complex *s);

	  C/C++ STL:
	       #include <complex.h>
	       #include <scsl_blas.h>
	       void crot (int n, complex<float> *x, int incx, complex<float>
	       *y, int incy, float c, complex<float> *s);

     Double precision complex

	  Fortran:
	       CALL ZROT n, x, incx, y, incy, c, s)

	  C/C++:
	       #include <scsl_blas.h>
	       void zrot (int n, scsl_zomplex *x, int incx, scsl_zomplex *y,
	       int incy, double c, scsl_zomplex *s);

									Page 1

SROT(3S)							      SROT(3S)

	  C/C++ STL:
	       #include <complex.h>
	       #include <scsl_blas.h>
	       void zrot (int n, complex<double> *x, int incx, complex<double>
	       *y, int incy, double c, complex<double> *s);

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

     The C and C++ prototypes shown above are appropriate for the 4-byte
     integer version of SCSL. When using the 8-byte integer version, the
     variables of type int become long long and the <scsl_blas_i8.h> header
     file should be included.

DESCRIPTION
     SROT/DROT applies a plane rotation matrix to a real sequence of ordered
     pairs:

	  (xi, yi), for all i = 1, 2, ..., n.

     CROT/ZROT applies a complex coordinate rotation to a complex sequence of
     ordered pairs.

     These routines have the following arguments:

     n	       Integer.	 (input)
	       Number of ordered pairs (planar points in SROT) to be rotated.
	       If n <= 0, these routines return without computation.

     x	       Array of dimension (n-1) * |incx| + 1.  (input and output)
	       SROT: Single precision array.
	       DROT: Double precision array.
	       CROT: Single precision complex array.
	       ZROT: Double precision complex array.
	       On input, array x contains the x-coordinate of each planar
	       point to be rotated.  On output, array x contains the
	       x-coordinate of each rotated planar point.

     incx      Integer.	 (input)
	       Increment between elements of x.	 If incx = 0, the results will
	       be unpredictable.

									Page 2

SROT(3S)							      SROT(3S)

     y	       Array of dimension (n-1) * |incy| + 1.  (input and output)
	       SROT: Single precision array.
	       DROT: Double precision array.
	       CROT: Single precision complex array.
	       ZROT: Double precision complex array.
	       On input, array y contains the y-coordinate of each planar
	       point to be rotated.  On output, array y contains the
	       y-coordinate of each rotated planar point.

     incy      Integer.	 (input)
	       Increment between elements of y.	 If incy = 0, the results will
	       be unpredictable.

     c	       Cosine of the angle of rotation, usually calculated using
	       SROTG(3S) or CROTG(3S).	(input)
	       SROT: Single precision.
	       DROT: Double precision.
	       CROT: Single precision.
	       ZROT: Double precision.

     s	       Sine of the angle of rotation, usually calculated using SROTG.
	       (input)
	       SROT: Single precision.
	       DROT: Double precision.
	       CROT: Single precision complex.
	       ZROT: Double precision complex.

NOTES
     SROT/DROT are Level 1 Basic Linear Algebra Subprograms (Level 1 BLAS).
     CROT/ZROT are extensions to level 1 BLAS.

     SROT/DROT applies the following plane rotation to each pair of elements
     (xi, yi):

	  _    _      _	     _	   _	_
	  | x  |      | c  s |	   | x	|
	  |  i | <-   |	     |	*  |  i |
	  | y  |      |-s  c |	   | y	|
	  |  i |      |	     |	   |  i |
	  -    -      -	     -	   -	-

     for i = 1,...,n

     CROT/ZROT applies a complex coordinate rotation to each pair of elements
     (xi, yi):

	  _    _      _	     _	   _	_
	  | x  |      | c  s |	   | x	|
	  |  i | <-   | _    |	*  |  i |
	  | y  |      |-s  c |	   | y	|
	  |  i |      |	     |	   |  i |

									Page 3

SROT(3S)							      SROT(3S)

	  -    -      -	     -	   -	-
		_
	  where s represents the complex conjugate of s.

     If coefficients c and s satisfy c2 + |s|2 = 1.0, the rotation matrix is
     orthogonal, and the transformation is called a Givens plane rotation.

     To calculate the Givens coefficients c and s from a two-element vector to
     determine the angle of rotation, use SROTG(3S) or CROTG(3S).

     When working backward (incx < 0 or incy < 0), each routine starts at the
     end of the vector and moves backward, as follows:

     Fortran:

	  x(1-incx * (n-1)), x(1-incx * (n-2)), ..., x(1)

	  y(1-incy * (n-1)), y(1-incy * (n-2)), ..., y(1)

     C/C++:

	  x[-incx * (n-1)], x[-incx * (n-2)], ..., x[0]

	  y[-incy * (n-1)], x[-incy * (n-2)], ..., y[0]

   Data Types
     The following data types are described in this documentation:

	  Term Used			Data type

     Fortran:

	  Array dimensioned n		x(n)

	  Integer			INTEGER (INTEGER*8 for -lscs_i8[_mp])

	  Single precision		REAL

	  Double precision		DOUBLE PRECISION

	  Single precision complex	COMPLEX

	  Double precision complex	DOUBLE COMPLEX

     C/C++:

	  Array dimensioned n		x[n]

									Page 4

SROT(3S)							      SROT(3S)

	  Integer			int (long long for -lscs_i8[_mp])

	  Single precision		float

	  Double precision		double

	  Single precision complex	scsl_complex

	  Double precision complex	scsl_zomplex

     C++ STL:

	  Array dimensioned n		x[n]

	  Integer			int (long long for -lscs_i8[_mp])

	  Single precision		float

	  Double precision		double

	  Single precision complex	complex<float>

	  Double precision complex	complex<double>

SEE ALSO
     INTRO_SCSL(3S), INTRO_BLAS1(3S), SROTG(3S), SROTM(3S), SROTMG(3S)

     INTRO_CBLAS(3S) for information about using the C interface to Fortran 77
     Basic Linear Algebra Subprograms (legacy BLAS) set forth by the Basic
     Linear Algebra Subprograms Technical Forum.

									Page 5

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