Provided by: liblapack-doc_3.8.0-2_all bug

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:

               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:

                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(*)

   subroutine saxpy (integer N, real SA, real, dimension(*) SX, integer INCX, real, dimension(*)
       SY, integer INCY)
       SAXPY

       Purpose:

               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:

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

   real function scabs1 (complex Z)
       SCABS1

       Purpose:

            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

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

       Purpose:

               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:

                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(*)

   real function scnrm2 (integer N, complex, dimension(*) X, integer INCX)
       SCNRM2

       Purpose:

            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:

             -- This version written on 25-October-1982.
                Modified on 14-October-1993 to inline the call to CLASSQ.
                Sven Hammarling, Nag Ltd.

   subroutine scopy (integer N, real, dimension(*) SX, integer INCX, real, dimension(*) SY,
       integer INCY)
       SCOPY

       Purpose:

               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:

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

   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.

       Date:
           November 2017

       Further Details:

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

   real function sdsdot (integer N, real SB, real, dimension(*) SX, integer INCX, real,
       dimension(*) SY, integer INCY)
       SDSDOT

       Purpose:

       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)

       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

       Purpose:

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   real function snrm2 (integer N, real, dimension(*) X, integer INCX)
       SNRM2

       Purpose:

            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:

             -- This version written on 25-October-1982.
                Modified on 14-October-1993 to inline the call to SLASSQ.
                Sven Hammarling, Nag Ltd.

   subroutine srot (integer N, real, dimension(*) SX, integer INCX, real, dimension(*) SY,
       integer INCY, real C, real S)
       SROT

       Purpose:

               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:

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

   subroutine srotg (real SA, real SB, real C, real S)
       SROTG

       Purpose:

               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:

                jack dongarra, linpack, 3/11/78.

   subroutine srotm (integer N, real, dimension(*) SX, integer INCX, real, dimension(*) SY,
       integer INCY, real, dimension(5) SPARAM)
       SROTM

       Purpose:

               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

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

       Purpose:

               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

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

       Purpose:

               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:

                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(*)

   subroutine sswap (integer N, real, dimension(*) SX, integer INCX, real, dimension(*) SY,
       integer INCY)
       SSWAP

       Purpose:

               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:

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

Author

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