dot(3)

NAME
dot - dot: x^H x and x^T x

SYNOPSIS

  Functions
complex function cdotc (n, cx, incx, cy, incy)
CDOTC
complex function cdotu (n, cx, incx, cy, incy)
CDOTU
double precision function ddot (n, dx, incx, dy, incy)
DDOT
double precision function dsdot (n, sx, incx, sy, incy)
DSDOT
real function sdot (n, sx, incx, sy, incy)
SDOT
real function sdsdot (n, sb, sx, incx, sy, incy)
SDSDOT
complex *16 function zdotc (n, zx, incx, zy, incy)
ZDOTC
complex *16 function zdotu (n, zx, incx, zy, incy)
ZDOTU

Detailed Description

Function Documentation

  complex function cdotc (integer n, complex, dimension(*) cx, integer incx, complex, dimension(*) cy, integer incy)

CDOTC

Purpose:

     CDOTC forms the dot product of two complex vectors
          CDOTC = X^H * Y

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 CX

    CY

              CY is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

    INCY

              INCY is INTEGER
             storage spacing between elements of CY

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 82 of file cdotc.f.

  complex function cdotu (integer n, complex, dimension(*) cx, integer incx, complex, dimension(*) cy, integer incy)

CDOTU

Purpose:

     CDOTU forms the dot product of two complex vectors
          CDOTU = X^T * Y

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 CX

    CY

              CY is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

    INCY

              INCY is INTEGER
             storage spacing between elements of CY

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 82 of file cdotu.f.

  double precision function ddot (integer n, double precision, dimension(*) dx, integer incx, double precision, dimension(*) dy, integer incy)

DDOT

Purpose:

        DDOT 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)

    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

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 ddot.f.

  double precision function dsdot (integer n, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy)

DSDOT

Purpose:

     Compute the inner product of two vectors with extended
     precision accumulation and result.
     Returns D.P. dot product accumulated in D.P., for S.P. SX and SY
     DSDOT = 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)

    SX

              SX is REAL array, dimension(N)
             single precision vector with N elements

    INCX

              INCX is INTEGER
              storage spacing between elements of SX

    SY

              SY is REAL array, dimension(N)
             single precision vector with N elements

    INCY

              INCY is INTEGER
             storage spacing between elements of SY

Returns
    DSDOT

              DSDOT is DOUBLE PRECISION
             DSDOT  double precision dot product (zero if N.LE.0)

Author
    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
      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 style (JL)

Definition at line 118 of file dsdot.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.

  complex*16 function zdotc (integer n, complex*16, dimension(*) zx, integer incx, complex*16, dimension(*) zy, integer incy)

ZDOTC

Purpose:

     ZDOTC forms the dot product of two complex vectors
          ZDOTC = X^H * Y

Parameters
    N

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

    ZX

              ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

    INCX

              INCX is INTEGER
             storage spacing between elements of ZX

    ZY

              ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

    INCY

              INCY is INTEGER
             storage spacing between elements of ZY

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

         jack dongarra, 3/11/78.
         modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 82 of file zdotc.f.

  complex*16 function zdotu (integer n, complex*16, dimension(*) zx, integer incx, complex*16, dimension(*) zy, integer incy)

ZDOTU

Purpose:

     ZDOTU forms the dot product of two complex vectors
          ZDOTU = X^T * Y

Parameters
    N

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

    ZX

              ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

    INCX

              INCX is INTEGER
             storage spacing between elements of ZX

    ZY

              ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

    INCY

              INCY is INTEGER
             storage spacing between elements of ZY

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

         jack dongarra, 3/11/78.
         modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 82 of file zdotu.f.

Author

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