srotg(3S)

NAME
     SROTG, DROTG, CROTG, ZROTG - Constructs a Givens plane rotation

SYNOPSIS
     Single precision

          Fortran:
               CALL SROTG (a, b, c, s)

          C/C++:
               #include <scsl_blas.h>
               void srotg (float *a, float *b, float *c, float *s);

     Double precision

          Fortran:
               CALL DROTG (a, b, c, s)

          C/C++:
               #include <scsl_blas.h>
               void drotg (double *a, double *b, double *c, double *s);

     Single precision complex

          Fortran:
               CALL CROTG (a, b, c, s)

          C/C++:
               #include <scsl_blas.h>
               void crotg (scsl_complex *a, scsl_complex *b, float *c,
               scsl_complex *s);

          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void crotg (complex<float> *a, complex<float> *b, float *c,
               complex<float> *s);

     Double precision complex

          Fortran:
               CALL ZROTG (a, b, c, s)

          C/C++:
               #include <scsl_blas.h>
               void zrotg (scsl_zomplex *a, scsl_zomplex *b, double *c,
               scsl_zomplex *s);

          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void zrotg (complex<double> *a, complex<double> *b, 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
     DROTG/SROTG computes the elements of a rotation matrix such that:

          _      _     _   _    _   _
          | c  s |     | a |    | r |
          |-s  c | *   | b | =  | 0 |
          -      -     -   -    -   -


     where

                   2    2       2    2
     r = +- sqrt (a  + b ) and c  + s  = 1


     CROTG/ZROTG computes the elements of a rotation matrix such that:


          _      _    _   _    _   _
          | c  s |    | a |    | r |
          | _    |    |   |    |   |
          |-s  c | *  | b | =  | 0 |
          -      -    -   -    -   -


     where

                        _             _      _
          r = (a / sqrt(aa)) * sqrt ((aa) + (bb))

     and the notation

          -
          z


     represents the complex conjugate of z.

     See the NOTES section of this man page for information about the
     interpretation of the data types described in the following arguments.

     These routines have the following arguments:

     a      First vector component.  (input and output)

            SROTG (Single precision), DROTG (Double precision):
            On input, the first component of the vector to be rotated.  On
            output, a is overwritten by by r, the first component of the
            vector in the rotated coordinate system where:

                                2    2
                 r = sign(sqrt(a  + b ,a), if |a| > |b|



                           2    2
            r = sign(sqrt(a  + b ,b), if |a| <= |b|


            CROTG (Single precision complex), ZROTG (Double precision
            complex):
            On output, a is overwritten by the unique complex number r, whose
            size in the complex plane is the Euclidean norm of the complex
            vector (a,b), and whose direction in the complex plane is the same
            as that of the original complex element a.

            For C/C++, a pointer to this value is passed.

     b      Second vector component. (input and output)
            SROTG: Single precision.
            DROTG: Double precision.
            CROTG: Single precision complex.
            ZROTG: Double precision complex.
            On input, the second component of the vector to be rotated.  On
            output, b contains z, where:

                 z=s     if |a| > |b|
                 z=1c    if |a| <= |b| and c / 0
                 z=1     if c = 0.

            For C/C++, a pointer to this value is passed.

     c      Cosine of the angle of rotation. (output)
            SROTG: Single precision.
            DROTG: Double precision.
            CROTG: Single precision.
            ZROTG: Double precision.

            For C/C++, a pointer to this value is passed.

     s      Sine of the angle of rotation. (output)
            SROTG: Single precision.
            DROTG: Double precision.
            CROTG: Single precision complex.
            ZROTG: Double precision complex.

            For C/C++, a pointer to this value is passed.

NOTES
     SROTG/DROTG routines are Level 1 Basic Linear Algebra Subprograms (Level
     1 BLAS).

     CROTG and ZROTG, are extensions to the Level 1 Basic Linear Algebra
     Subprograms (Level 1 BLAS).

     The value of z, returned in b by SROTG, gives a compact representation of
     the rotation matrix, which can be used later to reconstruct c and s as in
     the following example:

          IF (B .EQ. 1. ) THEN
             C = 0.
             S = 1.
          ELSEIF( ABS( B) .LT. 1) THEN
             C = SQRT( 1. - B * B)
             S = B
          ELSE
             C = 1. / B
             S = SQRT( 1 - C * C)
          ENDIF



   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]

          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), SROT(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.