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double_blas_level1(3) LAPACK double_blas_level1(3)

NAME

double_blas_level1 - double

SYNOPSIS

Functions


double precision function dasum (N, DX, INCX)
DASUM subroutine daxpy (N, DA, DX, INCX, DY, INCY)
DAXPY double precision function dcabs1 (Z)
DCABS1 subroutine dcopy (N, DX, INCX, DY, INCY)
DCOPY double precision function ddot (N, DX, INCX, DY, INCY)
DDOT subroutine drot (N, DX, INCX, DY, INCY, C, S)
DROT subroutine drotm (N, DX, INCX, DY, INCY, DPARAM)
DROTM subroutine drotmg (DD1, DD2, DX1, DY1, DPARAM)
DROTMG subroutine dscal (N, DA, DX, INCX)
DSCAL double precision function dsdot (N, SX, INCX, SY, INCY)
DSDOT subroutine dswap (N, DX, INCX, DY, INCY)
DSWAP subroutine dtrsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRSV double precision function dzasum (N, ZX, INCX)
DZASUM

Detailed Description

This is the group of double LEVEL 1 BLAS routines.

Function Documentation

double precision function dasum (integer N, double precision, dimension(*) DX, integer INCX)

DASUM

Purpose:


DASUM takes the sum of the absolute values.

Parameters

N


N is INTEGER
number of elements in input vector(s)

DX


DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of DX

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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 daxpy (integer N, double precision DA, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY)

DAXPY

Purpose:


DAXPY 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)

DA


DA is DOUBLE PRECISION
On entry, DA specifies the scalar alpha.

DX


DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of DX

DY


DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

INCY


INCY is INTEGER
storage spacing between elements of DY

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:


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

double precision function dcabs1 (complex*16 Z)

DCABS1

Purpose:


DCABS1 computes |Re(.)| + |Im(.)| of a double complex number

Parameters

Z


Z is COMPLEX*16

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dcopy (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY)

DCOPY

Purpose:


DCOPY 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)

DX


DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of DX

DY


DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

INCY


INCY is INTEGER
storage spacing between elements of DY

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:


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

double precision function ddot (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY)

DDOT

Purpose:


DDOT 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)

DX


DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of DX

DY


DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

INCY


INCY is INTEGER
storage spacing between elements of DY

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:


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

subroutine drot (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY, double precision C, double precision S)

DROT

Purpose:


DROT applies a plane rotation.

Parameters

N


N is INTEGER
number of elements in input vector(s)

DX


DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of DX

DY


DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

INCY


INCY is INTEGER
storage spacing between elements of DY

C


C is DOUBLE PRECISION

S


S is DOUBLE PRECISION

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:


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

subroutine drotm (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY, double precision, dimension(5) DPARAM)

DROTM

Purpose:


APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
(DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN
(DY**T)
DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY.
WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0
(DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0)
H=( ) ( ) ( ) ( )
(DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0).
SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM.

Parameters

N


N is INTEGER
number of elements in input vector(s)

DX


DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of DX

DY


DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

INCY


INCY is INTEGER
storage spacing between elements of DY

DPARAM


DPARAM is DOUBLE PRECISION array, dimension (5)
DPARAM(1)=DFLAG
DPARAM(2)=DH11
DPARAM(3)=DH21
DPARAM(4)=DH12
DPARAM(5)=DH22

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine drotmg (double precision DD1, double precision DD2, double precision DX1, double precision DY1, double precision, dimension(5) DPARAM)

DROTMG

Purpose:


CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)*> DY2)**T.
WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0
(DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0)
H=( ) ( ) ( ) ( )
(DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0).
LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22
RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE
VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.)
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 DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM.

Parameters

DD1


DD1 is DOUBLE PRECISION

DD2


DD2 is DOUBLE PRECISION

DX1


DX1 is DOUBLE PRECISION

DY1


DY1 is DOUBLE PRECISION

DPARAM


DPARAM is DOUBLE PRECISION array, dimension (5)
DPARAM(1)=DFLAG
DPARAM(2)=DH11
DPARAM(3)=DH21
DPARAM(4)=DH12
DPARAM(5)=DH22

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dscal (integer N, double precision DA, double precision, dimension(*) DX, integer INCX)

DSCAL

Purpose:


DSCAL 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)

DA


DA is DOUBLE PRECISION
On entry, DA specifies the scalar alpha.

DX


DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of DX

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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(*)

double precision function dsdot (integer N, real, dimension(*) SX, integer INCX, real, dimension(*) SY, integer INCY)

DSDOT

Purpose:


Compute the inner product of two vectors with extended
precision accumulation and result.
Returns D.P. dot product accumulated in D.P., for S.P. SX and SY
DSDOT = 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


N is INTEGER
number of elements in input vector(s)

SX


SX is REAL array, dimension(N)
single precision vector with N elements

INCX


INCX is INTEGER
storage spacing between elements of SX

SY


SY is REAL array, dimension(N)
single precision vector with N elements

INCY


INCY is INTEGER
storage spacing between elements of SY

Returns

DSDOT


DSDOT is DOUBLE PRECISION
DSDOT double precision dot product (zero if N.LE.0)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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
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 style (JL)

subroutine dswap (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY)

DSWAP

Purpose:


DSWAP interchanges two vectors.
uses unrolled loops for increments equal to 1.

Parameters

N


N is INTEGER
number of elements in input vector(s)

DX


DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of DX

DY


DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )

INCY


INCY is INTEGER
storage spacing between elements of DY

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:


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

subroutine dtrsv (character UPLO, character TRANS, character DIAG, integer N, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX)

DTRSV

Purpose:


DTRSV solves one of the systems of equations
A*x = b, or A**T*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.

Parameters

UPLO


UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.

TRANS


TRANS is CHARACTER*1
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n' A*x = b.
TRANS = 'T' or 't' A**T*x = b.
TRANS = 'C' or 'c' A**T*x = b.

DIAG


DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.

N


N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.

A


A is DOUBLE PRECISION array, dimension ( LDA, N )
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.

LDA


LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).

X


X is DOUBLE PRECISION array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.

INCX


INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function dzasum (integer N, complex*16, dimension(*) ZX, integer INCX)

DZASUM

Purpose:


DZASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and
returns a double precision result.

Parameters

N


N is INTEGER
number of elements in input vector(s)

ZX


ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

INCX


INCX is INTEGER
storage spacing between elements of ZX

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:


jack dongarra, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)

Author

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