--- name: "dot" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/dot/3" --- # dot(3) dot: x^H x and x^T x ## 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 Generated automatically by Doxygen for LAPACK from the source code.