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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
         storage spacing between elements of CX

          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(*)

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
         storage spacing between elements of CX

          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(*)

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 is INTEGER
         number of elements in input vector(s)

          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX

          INCX is INTEGER
         storage spacing between elements of DX

          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(*)

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
          storage spacing between elements of SX

          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)

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
         storage spacing between elements of SX

          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(*)

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 is INTEGER
          number of elements in input vector(s)

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

          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 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

complex16 function zdotc (integer n, complex16, dimension() zx, integer incx, complex16, dimension(*) zy, integer incy)

ZDOTC

Purpose:

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

Parameters

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

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

INCX

          INCX is INTEGER
         storage spacing between elements of ZX

          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(*)

complex16 function zdotu (integer n, complex16, dimension() zx, integer incx, complex16, dimension(*) zy, integer incy)

ZDOTU

Purpose:

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

Parameters

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

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

INCX

          INCX is INTEGER
         storage spacing between elements of ZX

          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(*)

Author

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