LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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Functions/Subroutines
real
Level1
Collaboration diagram for real:

Functions/Subroutines

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/Subroutine 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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(*)

Definition at line 53 of file sasum.f.

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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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 53 of file saxpy.f.

REAL function scabs1 ( complex  Z)

SCABS1

Purpose: 
 SCABS1 computes absolute value of a complex number
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

Definition at line 39 of file scabs1.f.

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

SCASUM

Purpose: 
    SCASUM takes the sum of the absolute values 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:
November 2011
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(*)

Definition at line 53 of file scasum.f.

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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 )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further 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 55 of file scnrm2.f.

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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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 52 of file scopy.f.

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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 52 of file sdot.f.

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

SDSDOT

Purpose:
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

Definition at line 141 of file sdsdot.f.

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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 ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further 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 55 of file snrm2.f.

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

SROT

Purpose: 
    applies a plane rotation.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 52 of file srot.f.

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

SROTG

Purpose: 
    SROTG construct givens plane rotation.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details: 
     jack dongarra, linpack, 3/11/78.

Definition at line 47 of file srotg.f.

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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:
[in]N
          N is INTEGER
         number of elements in input vector(s)
[in,out]SX
          SX is REAL array, dimension N
         double precision vector with N elements
[in]INCX
          INCX is INTEGER
         storage spacing between elements of SX
[in,out]SY
          SY is REAL array, dimension N
         double precision vector with N elements
[in]INCY
          INCY is INTEGER
         storage spacing between elements of SY
[in,out]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 2011

Definition at line 100 of file srotm.f.

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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:
[in,out]SD1
          SD1 is REAL
[in,out]SD2
          SD2 is REAL
[in,out]SX1
          SX1 is REAL
[in]SY1
          SY1 is REAL
[in,out]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 2011

Definition at line 91 of file srotmg.f.

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

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:
November 2011
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(*)

Definition at line 54 of file sscal.f.

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

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:
November 2011
Further Details: 
     jack dongarra, linpack, 3/11/78.
     modified 12/3/93, array(1) declarations changed to array(*)

Definition at line 52 of file sswap.f.