single_blas_level1(3)

NAME
single_blas_level1

SYNOPSIS

  Functions
real function sasum (N, SX, INCX)
SASUM
subroutine saxpy (N, SA, SX, INCX, SY, INCY)
SAXPY
real function scabs1 (Z)
SCABS1
real function scasum (N, CX, INCX)
SCASUM
real function scnrm2 (N, X, INCX)
SCNRM2
subroutine scopy (N, SX, INCX, SY, INCY)
SCOPY
real function sdot (N, SX, INCX, SY, INCY)
SDOT
real function sdsdot (N, SB, SX, INCX, SY, INCY)
SDSDOT
real function snrm2 (N, X, INCX)
SNRM2
subroutine srot (N, SX, INCX, SY, INCY, C, S)
SROT
subroutine srotg (SA, SB, C, S)
SROTG
subroutine srotm (N, SX, INCX, SY, INCY, SPARAM)
SROTM
subroutine srotmg (SD1, SD2, SX1, SY1, SPARAM)
SROTMG
subroutine sscal (N, SA, SX, INCX)
SSCAL
subroutine sswap (N, SX, INCX, SY, INCY)
SSWAP

Detailed Description

This is the group of real LEVEL 1 BLAS routines.

Function Documentation

  real function sasum (integer N, real, dimension(*) SX, integer INCX)

SASUM

Purpose: @verbatim

SASUM takes the sum of the absolute values. uses unrolled loops for increment 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

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Further Details: @verbatim

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)

SAXPY

Purpose: @verbatim

SAXPY constant times a vector plus a vector. uses unrolled loops for increments equal to one.

Parameters:
    N

              N is INTEGER
             number of elements in input vector(s)

    SA

              SA is REAL
               On entry, SA specifies the scalar alpha.

    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.

Date:
    November 2017

Further Details: @verbatim

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)

SCABS1

Purpose: @verbatim

SCABS1 computes |Re(.)| + |Im(.)| of a complex number

Parameters:
    Z

              Z is COMPLEX

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Definition at line 48 of file scabs1.f.

  real function scasum (integer N, complex, dimension(*) CX, integer INCX)

SCASUM

Purpose: @verbatim

SCASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and returns a single precision result.

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 SX

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Further Details: @verbatim

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)

SCNRM2

Purpose: @verbatim

SCNRM2 returns the euclidean norm of a vector via the function name, so that

SCNRM2 := sqrt( x**H*x )

Parameters:
    N

              N is INTEGER
             number of elements in input vector(s)

    X

              X is COMPLEX array, dimension (N)
             complex vector with N elements

    INCX

              INCX is INTEGER
             storage spacing between elements of X

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Further Details: @verbatim

-- 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)

SCOPY

Purpose: @verbatim

SCOPY copies a vector, x, to a vector, y. uses unrolled loops for increments equal to 1.

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.

Date:
    November 2017

Further Details: @verbatim

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)

SDOT

Purpose: @verbatim

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.

Date:
    November 2017

Further Details: @verbatim

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, integer INCX, real, dimension(*) SY, integer INCY)

SDSDOT

Purpose: @verbatim \endverbatim @param [in] N

              N is INTEGER
              number of elements in input vector(s)

Parameters:
    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)

Further Details: @verbatim

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

Purpose: @verbatim

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Definition at line 166 of file sdsdot.f.

  real function snrm2 (integer N, real, dimension(*) X, integer INCX)

SNRM2

Purpose: @verbatim

SNRM2 returns the euclidean norm of a vector via the function name, so that

SNRM2 := sqrt( x'*x ).

Parameters:
    N

              N is INTEGER
             number of elements in input vector(s)

    X

              X is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

    INCX

              INCX is INTEGER
             storage spacing between elements of SX

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Further Details: @verbatim

-- 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)

SROT

Purpose: @verbatim

applies a plane rotation.

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

    C

              C is REAL

    S

              S is REAL

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Further Details: @verbatim

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)

SROTG

Purpose: @verbatim

SROTG construct givens plane rotation.

Parameters:
    SA

              SA is REAL

    SB

              SB is REAL

    C

              C is REAL

    S

              S is REAL

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Further Details: @verbatim

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)

SROTM

Purpose: @verbatim

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.

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

    SPARAM

              SPARAM is REAL array, dimension (5)
         SPARAM(1)=SFLAG
         SPARAM(2)=SH11
         SPARAM(3)=SH21
         SPARAM(4)=SH12
         SPARAM(5)=SH22

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Definition at line 99 of file srotm.f.

  subroutine srotmg (real SD1, real SD2, real SX1, real SY1, real, dimension(5) SPARAM)

SROTMG

Purpose: @verbatim

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.

Parameters:
    SD1

              SD1 is REAL

    SD2

              SD2 is REAL

    SX1

              SX1 is REAL

    SY1

              SY1 is REAL

    SPARAM

              SPARAM is REAL array, dimension (5)
         SPARAM(1)=SFLAG
         SPARAM(2)=SH11
         SPARAM(3)=SH21
         SPARAM(4)=SH12
         SPARAM(5)=SH22

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Definition at line 92 of file srotmg.f.

  subroutine sscal (integer N, real SA, real, dimension(*) SX, integer INCX)

SSCAL

Purpose: @verbatim

SSCAL scales a vector by a constant. uses unrolled loops for increment equal to 1.

Parameters:
    N

              N is INTEGER
             number of elements in input vector(s)

    SA

              SA is REAL
               On entry, SA specifies the scalar alpha.

    SX

              SX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

    INCX

              INCX is INTEGER
             storage spacing between elements of SX

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Further Details: @verbatim

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)

SSWAP

Purpose: @verbatim

SSWAP interchanges two vectors. uses unrolled loops for increments equal to 1.

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.

Date:
    November 2017

Further Details: @verbatim

jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 84 of file sswap.f.

Author

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