 LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
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## 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.```
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.```
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`
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.```
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 )```
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.```
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.```
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:
` `
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 ).```
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.`
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.`
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```
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```
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.```
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.```
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.