single_blas_level1(3) LAPACK single_blas_level1(3) NAME single_blas_level1 SYNOPSISFunctionsreal functionsasum(N, SX, INCX)SASUMsubroutinesaxpy(N, SA, SX, INCX, SY, INCY)SAXPYreal functionscabs1(Z)SCABS1real functionscasum(N, CX, INCX)SCASUMreal functionscnrm2(N, X, INCX)SCNRM2subroutinescopy(N, SX, INCX, SY, INCY)SCOPYreal functionsdot(N, SX, INCX, SY, INCY)SDOTreal functionsdsdot(N, SB, SX, INCX, SY, INCY)SDSDOTreal functionsnrm2(N, X, INCX)SNRM2subroutinesrot(N, SX, INCX, SY, INCY, C, S)SROTsubroutinesrotg(SA, SB, C, S)SROTGsubroutinesrotm(N, SX, INCX, SY, INCY, SPARAM)SROTMsubroutinesrotmg(SD1, SD2, SX1, SY1, SPARAM)SROTMGsubroutinesscal(N, SA, SX, INCX)SSCALsubroutinesswap(N, SX, INCX, SY, INCY)SSWAPDetailed Description This is the group of real LEVEL 1 BLAS routines. Function Documentationreal function sasum (integer N, real, dimension(*) SX, integer INCX)SASUMPurpose:SASUM takes the sum of the absolute values. uses unrolled loops for increment equal to one.ParametersNN is INTEGER number of elements in input vector(s)SXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Definition at line 74 of file sasum.f.subroutine saxpy (integer N, real SA, real, dimension(*) SX, integer INCX,real, dimension(*) SY, integer INCY)SAXPYPurpose:SAXPY constant times a vector plus a vector. uses unrolled loops for increments equal to one.ParametersNN is INTEGER number of elements in input vector(s)SASA is REAL On entry, SA specifies the scalar alpha.SXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXSYSY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )INCYINCY is INTEGER storage spacing between elements of SYAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Definition at line 91 of file saxpy.f.real function scabs1 (complex Z)SCABS1Purpose:SCABS1 computes |Re(.)| + |Im(.)| of a complex numberParametersZZ is COMPLEXAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017 Definition at line 48 of file scabs1.f.real function scasum (integer N, complex, dimension(*) CX, integer INCX)SCASUMPurpose:SCASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and returns a single precision result.ParametersNN is INTEGER number of elements in input vector(s)CXCX is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Definition at line 74 of file scasum.f.real function scnrm2 (integer N, complex, dimension(*) X, integer INCX)SCNRM2Purpose:SCNRM2 returns the euclidean norm of a vector via the function name, so that SCNRM2 := sqrt( x**H*x )ParametersNN is INTEGER number of elements in input vector(s)XX is COMPLEX array, dimension (N) complex vector with N elementsINCXINCX is INTEGER storage spacing between elements of XAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:-- This version written on 25-October-1982. Modified on 14-October-1993 to inline the call to CLASSQ. Sven Hammarling, Nag Ltd. Definition at line 77 of file scnrm2.f.subroutine scopy (integer N, real, dimension(*) SX, integer INCX, real,dimension(*) SY, integer INCY)SCOPYPurpose:SCOPY copies a vector, x, to a vector, y. uses unrolled loops for increments equal to 1.ParametersNN is INTEGER number of elements in input vector(s)SXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXSYSY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )INCYINCY is INTEGER storage spacing between elements of SYAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Definition at line 84 of file scopy.f.real function sdot (integer N, real, dimension(*) SX, integer INCX, real,dimension(*) SY, integer INCY)SDOTPurpose:SDOT forms the dot product of two vectors. uses unrolled loops for increments equal to one.ParametersNN is INTEGER number of elements in input vector(s)SXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXSYSY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )INCYINCY is INTEGER storage spacing between elements of SYAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Definition at line 84 of file sdot.f.real function sdsdot (integer N, real SB, real, dimension(*) SX, integerINCX, real, dimension(*) SY, integer INCY)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.ParametersNN is INTEGER number of elements in input vector(s)SBSB is REAL single precision scalar to be added to inner productSXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) single precision vector with N elementsINCXINCX is INTEGER storage spacing between elements of SXSYSY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) single precision vector with N elementsINCYINCY is INTEGER storage spacing between elements of SYAuthorLawson, 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.DateNovember 2017Further 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 115 of file sdsdot.f.real function snrm2 (integer N, real, dimension(*) X, integer INCX)SNRM2Purpose:SNRM2 returns the euclidean norm of a vector via the function name, so that SNRM2 := sqrt( x'*x ).ParametersNN is INTEGER number of elements in input vector(s)XX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:-- This version written on 25-October-1982. Modified on 14-October-1993 to inline the call to SLASSQ. Sven Hammarling, Nag Ltd. Definition at line 76 of file snrm2.f.subroutine srot (integer N, real, dimension(*) SX, integer INCX, real,dimension(*) SY, integer INCY, real C, real S)SROTPurpose:applies a plane rotation.ParametersNN is INTEGER number of elements in input vector(s)SXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXSYSY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )INCYINCY is INTEGER storage spacing between elements of SYCC is REALSS is REALAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Definition at line 94 of file srot.f.subroutine srotg (real SA, real SB, real C, real S)SROTGPurpose:SROTG construct givens plane rotation.ParametersSASA is REALSBSB is REALCC is REALSS is REALAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. Definition at line 71 of file srotg.f.subroutine srotm (integer N, real, dimension(*) SX, integer INCX, real,dimension(*) SY, integer INCY, real,dimension(5)SPARAM)SROTMPurpose:APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN (SX**T) SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY. WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) H=( ) ( ) ( ) ( ) (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). SEE SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM.ParametersNN is INTEGER number of elements in input vector(s)SXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXSYSY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )INCYINCY is INTEGER storage spacing between elements of SYSPARAMSPARAM is REAL array, dimension (5) SPARAM(1)=SFLAG SPARAM(2)=SH11 SPARAM(3)=SH21 SPARAM(4)=SH12 SPARAM(5)=SH22AuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017 Definition at line 99 of file srotm.f.subroutine srotmg (real SD1, real SD2, real SX1, real SY1, real,dimension(5)SPARAM)SROTMGPurpose:CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)*> SY2)**T. WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) H=( ) ( ) ( ) ( ) (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22 RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.) THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE OF SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM.ParametersSD1SD1 is REALSD2SD2 is REALSX1SX1 is REALSY1SY1 is REALSPARAMSPARAM is REAL array, dimension (5) SPARAM(1)=SFLAG SPARAM(2)=SH11 SPARAM(3)=SH21 SPARAM(4)=SH12 SPARAM(5)=SH22AuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017 Definition at line 92 of file srotmg.f.subroutine sscal (integer N, real SA, real, dimension(*) SX, integer INCX)SSCALPurpose:SSCAL scales a vector by a constant. uses unrolled loops for increment equal to 1.ParametersNN is INTEGER number of elements in input vector(s)SASA is REAL On entry, SA specifies the scalar alpha.SXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Definition at line 81 of file sscal.f.subroutine sswap (integer N, real, dimension(*) SX, integer INCX, real,dimension(*) SY, integer INCY)SSWAPPurpose:SSWAP interchanges two vectors. uses unrolled loops for increments equal to 1.ParametersNN is INTEGER number of elements in input vector(s)SXSX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )INCXINCX is INTEGER storage spacing between elements of SXSYSY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )INCYINCY is INTEGER storage spacing between elements of SYAuthorUniv. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.DateNovember 2017Further Details:jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Definition at line 84 of file sswap.f. 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