Provided by: liblapack-doc_3.12.0-3build1.1_all bug

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(*)

   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(*)

   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(*)

   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)

   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(*)

   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

   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(*)

   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(*)

Author

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