| single_blas_level1(3) | LAPACK | single_blas_level1(3) |
single_blas_level1 - real
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
This is the group of real LEVEL 1 BLAS routines.
SASUM
Purpose:
SASUM takes the sum of the absolute values.
uses unrolled loops for increment equal to one.
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
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(*)
SAXPY
Purpose:
SAXPY constant times a vector plus a vector.
uses unrolled loops for increments equal to one.
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
Further Details:
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
SCABS1
Purpose:
SCABS1 computes |Re(.)| + |Im(.)| of a complex number
Parameters
Z is COMPLEX
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
SCASUM
Purpose:
SCASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and
returns a single precision result.
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
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(*)
SCNRM2
Purpose:
SCNRM2 returns the euclidean norm of a vector via the function
name, so that
SCNRM2 := sqrt( x**H*x )
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
Further Details:
-- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to CLASSQ.
Sven Hammarling, Nag Ltd.
SCOPY
Purpose:
SCOPY copies a vector, x, to a vector, y.
uses unrolled loops for increments equal to 1.
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
Further Details:
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
SDOT
Purpose:
SDOT forms the dot product of two vectors.
uses unrolled loops for increments equal to one.
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
Further Details:
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
SDSDOT
Purpose:
Compute the inner product of two vectors with extended
precision accumulation.
Returns S.P. result with dot product accumulated in D.P.
SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+I*INCX)*SY(LY+I*INCY),
where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
defined in a similar way using INCY.
Parameters
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
Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL)
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
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
SNRM2
Purpose:
SNRM2 returns the euclidean norm of a vector via the function
name, so that
SNRM2 := sqrt( x'*x ).
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
Further Details:
-- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to SLASSQ.
Sven Hammarling, Nag Ltd.
SROT
Purpose:
applies a plane rotation.
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
Further Details:
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
SROTG
Purpose:
SROTG construct givens plane rotation.
Parameters
SA is REAL
SB
SB is REAL
C
C is REAL
S
S is REAL
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
Further Details:
jack dongarra, linpack, 3/11/78.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
SSCAL
Purpose:
SSCAL scales a vector by a constant.
uses unrolled loops for increment equal to 1.
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
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(*)
SSWAP
Purpose:
SSWAP interchanges two vectors.
uses unrolled loops for increments equal to 1.
Parameters
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
Further Details:
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
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