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(*)

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 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(*)

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 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(*)

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 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)

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 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(*)

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 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

Definition at line 112 of file sdsdot.f.

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(*)

Definition at line 82 of file zdotc.f.

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(*)

Definition at line 82 of file zdotu.f.

Author

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