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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