dot - dot: x^H x and x^T x

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complexfunctioncdotc(integern,complex,dimension(*)cx,integerincx,complex,dimension(*)cy,integerincy)CDOTCPurpose: CDOTC forms the dot product of two complex vectors CDOTC = X^H * Y ParametersN 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. FurtherDetails: jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) complexfunctioncdotu(integern,complex,dimension(*)cx,integerincx,complex,dimension(*)cy,integerincy)CDOTUPurpose: CDOTU forms the dot product of two complex vectors CDOTU = X^T * Y ParametersN 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. FurtherDetails: jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) doubleprecisionfunctionddot(integern,doubleprecision,dimension(*)dx,integerincx,doubleprecision,dimension(*)dy,integerincy)DDOTPurpose: DDOT forms the dot product of two vectors. uses unrolled loops for increments equal to one. ParametersN 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. FurtherDetails: jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) doubleprecisionfunctiondsdot(integern,real,dimension(*)sx,integerincx,real,dimension(*)sy,integerincy)DSDOTPurpose: 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. ParametersN 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. FurtherDetails: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) realfunctionsdot(integern,real,dimension(*)sx,integerincx,real,dimension(*)sy,integerincy)SDOTPurpose: SDOT forms the dot product of two vectors. uses unrolled loops for increments equal to one. ParametersN 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. FurtherDetails: jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) realfunctionsdsdot(integern,realsb,real,dimension(*)sx,integerincx,real,dimension(*)sy,integerincy)SDSDOTPurpose: 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. ParametersN 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. FurtherDetails: 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*16functionzdotc(integern,complex*16,dimension(*)zx,integerincx,complex*16,dimension(*)zy,integerincy)ZDOTCPurpose: ZDOTC forms the dot product of two complex vectors ZDOTC = X^H * Y ParametersN 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. FurtherDetails: jack dongarra, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) complex*16functionzdotu(integern,complex*16,dimension(*)zx,integerincx,complex*16,dimension(*)zy,integerincy)ZDOTUPurpose: ZDOTU forms the dot product of two complex vectors ZDOTU = X^T * Y ParametersN 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. FurtherDetails: jack dongarra, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*)

dot - dot: x^H x and x^T x

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