single_blas_level1(3)

NAME
single_blas_level1 - real

SYNOPSIS

  Functions
real function sasum (n, sx, incx)
SASUM
subroutine saxpy (n, sa, sx, incx, sy, incy)
SAXPY
real function scabs1 (z)
SCABS1
real function scasum (n, cx, incx)
SCASUM
subroutine scopy (n, sx, incx, sy, incy)
SCOPY
real function sdot (n, sx, incx, sy, incy)
SDOT
real function sdsdot (n, sb, sx, incx, sy, incy)
SDSDOT
subroutine srot (n, sx, incx, sy, incy, c, s)
SROT
subroutine srotm (n, sx, incx, sy, incy, sparam)
SROTM
subroutine srotmg (sd1, sd2, sx1, sy1, sparam)
SROTMG
subroutine sscal (n, sa, sx, incx)
SSCAL
subroutine sswap (n, sx, incx, sy, incy)
SSWAP

Detailed Description

This is the group of real LEVEL 1 BLAS routines.

Function Documentation

  real function sasum (integer n, real, dimension(*) sx, integer incx)

SASUM

Purpose:

        SASUM takes the sum of the absolute values.
        uses unrolled loops for increment equal to one.

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

         jack dongarra, linpack, 3/11/78.
         modified 3/93 to return if incx .le. 0.
         modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 71 of file sasum.f.

  subroutine saxpy (integer n, real sa, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy)

SAXPY

Purpose:

        SAXPY constant times a vector plus a vector.
        uses unrolled loops for increments equal to one.

Parameters
    N

              N is INTEGER
             number of elements in input vector(s)

    SA

              SA is REAL
               On entry, SA specifies the scalar alpha.

    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

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(*)

Definition at line 88 of file saxpy.f.

  real function scabs1 (complex z)

SCABS1

Purpose:

     SCABS1 computes |Re(.)| + |Im(.)| of a complex number

Parameters
    Z

              Z is COMPLEX

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 45 of file scabs1.f.

  real function scasum (integer n, complex, dimension(*) cx, integer incx)

SCASUM

Purpose:

        SCASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and
        returns a single precision result.

Parameters
    N

              N is INTEGER
             number of elements in input vector(s)

    CX

              CX is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

    INCX

              INCX is INTEGER
             storage spacing between elements of SX

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

         jack dongarra, linpack, 3/11/78.
         modified 3/93 to return if incx .le. 0.
         modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 71 of file scasum.f.

  subroutine scopy (integer n, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy)

SCOPY

Purpose:

        SCOPY copies a vector, x, to a vector, y.
        uses unrolled loops for increments equal to 1.

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

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(*)

Definition at line 81 of file scopy.f.

  real function sdot (integer n, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy)

SDOT

Purpose:

        SDOT forms the dot product of two vectors.
        uses unrolled loops for increments equal to one.

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

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(*)

Definition at line 81 of file sdot.f.

  real function sdsdot (integer n, real sb, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy)

SDSDOT

Purpose:

       Compute the inner product of two vectors with extended
       precision accumulation.
       Returns S.P. result with dot product accumulated in D.P.
       SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+I*INCX)*SY(LY+I*INCY),
       where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
       defined in a similar way using INCY.

Parameters
    N

              N is INTEGER
              number of elements in input vector(s)

    SB

              SB is REAL
              single precision scalar to be added to inner product

    SX

              SX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
              single precision vector with N elements

    INCX

              INCX is INTEGER
              storage spacing between elements of SX

    SY

              SY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
              single precision vector with N elements

    INCY

              INCY is INTEGER
              storage spacing between elements of SY

Author
    Lawson, C. L., (JPL), Hanson, R. J., (SNLA),

    Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL)

    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

        REFERENCES
        C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
        Krogh, Basic linear algebra subprograms for Fortran
        usage, Algorithm No. 539, Transactions on Mathematical
        Software 5, 3 (September 1979), pp. 308-323.
        REVISION HISTORY  (YYMMDD)
        791001  DATE WRITTEN
        890531  Changed all specific intrinsics to generic.  (WRB)
        890831  Modified array declarations.  (WRB)
        890831  REVISION DATE from Version 3.2
        891214  Prologue converted to Version 4.0 format.  (BAB)
        920310  Corrected definition of LX in DESCRIPTION.  (WRB)
        920501  Reformatted the REFERENCES section.  (WRB)
        070118  Reformat to LAPACK coding style

Definition at line 112 of file sdsdot.f.

  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(*)

Definition at line 91 of file srot.f.

  subroutine srotm (integer n, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy, real, dimension(5) sparam)

SROTM

Purpose:

        APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
        (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN
        (SX**T)
        SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
        LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY.
        WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS..
        SFLAG=-1.E0     SFLAG=0.E0        SFLAG=1.E0     SFLAG=-2.E0
          (SH11  SH12)    (1.E0  SH12)    (SH11  1.E0)    (1.E0  0.E0)
        H=(          )    (          )    (          )    (          )
          (SH21  SH22),   (SH21  1.E0),   (-1.E0 SH22),   (0.E0  1.E0).
        SEE  SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM.

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

    SPARAM

              SPARAM is REAL array, dimension (5)
         SPARAM(1)=SFLAG
         SPARAM(2)=SH11
         SPARAM(3)=SH21
         SPARAM(4)=SH12
         SPARAM(5)=SH22

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 96 of file srotm.f.

  subroutine srotmg (real sd1, real sd2, real sx1, real sy1, real, dimension(5) sparam)

SROTMG

Purpose:

        CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
        THE SECOND COMPONENT OF THE 2-VECTOR  (SQRT(SD1)*SX1,SQRT(SD2)*>    SY2)**T.
        WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS..
        SFLAG=-1.E0     SFLAG=0.E0        SFLAG=1.E0     SFLAG=-2.E0
          (SH11  SH12)    (1.E0  SH12)    (SH11  1.E0)    (1.E0  0.E0)
        H=(          )    (          )    (          )    (          )
          (SH21  SH22),   (SH21  1.E0),   (-1.E0 SH22),   (0.E0  1.E0).
        LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22
        RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE
        VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.)
        THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE
        INEXACT.  THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
        OF SD1 AND SD2.  ALL ACTUAL SCALING OF DATA IS DONE USING GAM.

Parameters
    SD1

              SD1 is REAL

    SD2

              SD2 is REAL

    SX1

              SX1 is REAL

    SY1

              SY1 is REAL

    SPARAM

              SPARAM is REAL array, dimension (5)
         SPARAM(1)=SFLAG
         SPARAM(2)=SH11
         SPARAM(3)=SH21
         SPARAM(4)=SH12
         SPARAM(5)=SH22

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 89 of file srotmg.f.

  subroutine sscal (integer n, real sa, real, dimension(*) sx, integer incx)

SSCAL

Purpose:

        SSCAL scales a vector by a constant.
        uses unrolled loops for increment equal to 1.

Parameters
    N

              N is INTEGER
             number of elements in input vector(s)

    SA

              SA is REAL
               On entry, SA specifies the scalar alpha.

    SX

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

    INCX

              INCX is INTEGER
             storage spacing between elements of SX

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

         jack dongarra, linpack, 3/11/78.
         modified 3/93 to return if incx .le. 0.
         modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 78 of file sscal.f.

  subroutine sswap (integer n, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy)

SSWAP

Purpose:

        SSWAP interchanges two vectors.
        uses unrolled loops for increments equal to 1.

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

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(*)

Definition at line 81 of file sswap.f.

Author

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