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real(3) LAPACK real(3)

NAME

real -

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 (integerN, real, dimension(*)SX, integerINCX)

SASUM
Purpose: 
    SASUM takes the sum of the absolute values.
    uses unrolled loops for increment equal to one.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
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 (integerN, realSA, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)

SAXPY
Purpose: 
    SAXPY constant times a vector plus a vector.
    uses unrolled loops for increments equal to one.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

real function scabs1 (complexZ)

SCABS1
Purpose: 
 SCABS1 computes |Re(.)| + |Im(.)| of a complex number
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016

real function scasum (integerN, complex, dimension(*)CX, integerINCX)

SCASUM
Purpose: 
    SCASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and
    returns a single precision result.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
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 (integerN, complex, dimension(*)X, integerINCX)

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


    SCNRM2 := sqrt( x**H*x )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
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 (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)

SCOPY
Purpose: 
    SCOPY copies a vector, x, to a vector, y.
    uses unrolled loops for increments equal to 1.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

real function sdot (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)

SDOT
Purpose: 
    SDOT forms the dot product of two vectors.
    uses unrolled loops for increments equal to one.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

real function sdsdot (integerN, realSB, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)

SDSDOT
Purpose:
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016

real function snrm2 (integerN, real, dimension(*)X, integerINCX)

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


    SNRM2 := sqrt( x'*x ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
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 (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY, realC, realS)

SROT
Purpose: 
    applies a plane rotation.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

subroutine srotg (realSA, realSB, realC, realS)

SROTG
Purpose: 
    SROTG construct givens plane rotation.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
Further Details: 
     jack dongarra, linpack, 3/11/78.

subroutine srotm (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY, 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 N
         double precision vector with N elements
INCX 
          INCX is INTEGER
         storage spacing between elements of SX
SY 
          SY is REAL array, dimension N
         double precision vector with N elements
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:
December 2016

subroutine srotmg (realSD1, realSD2, realSX1, realSY1, 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:
December 2016

subroutine sscal (integerN, realSA, real, dimension(*)SX, integerINCX)

SSCAL
Purpose: 
    scales a vector by a constant.
    uses unrolled loops for increment equal to 1.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
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 (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)

SSWAP
Purpose: 
    interchanges two vectors.
    uses unrolled loops for increments equal to 1.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
December 2016
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

Author

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