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double_blas_level1(3) LAPACK double_blas_level1(3)

NAME

double_blas_level1

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 double precision function dnrm2 (N, X, INCX)
DNRM2 subroutine drot (N, DX, INCX, DY, INCY, C, S)
DROT subroutine drotg (DA, DB, C, S)
DROTG 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 double precision function dznrm2 (N, X, INCX)
DZNRM2

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.

Date:

November 2017

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.

Date:

November 2017

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.

Date:

November 2017

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.

Date:

November 2017

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.

Date:

November 2017

Further Details:

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

double precision function dnrm2 (integer N, double precision, dimension(*) X, integer INCX)

DNRM2

Purpose:

 DNRM2 returns the euclidean norm of a vector via the function
 name, so that
    DNRM2 := sqrt( x'*x )

Parameters:

N

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

X

          X 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.

Date:

November 2017

Further Details:

  -- This version written on 25-October-1982.
     Modified on 14-October-1993 to inline the call to DLASSQ.
     Sven Hammarling, Nag Ltd.

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.

Date:

November 2017

Further Details:

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

subroutine drotg (double precision DA, double precision DB, double precision C, double precision S)

DROTG

Purpose:

    DROTG construct givens plane rotation.

Parameters:

DA

          DA is DOUBLE PRECISION

DB

          DB is DOUBLE PRECISION

C

          C is DOUBLE PRECISION

S

          S is DOUBLE PRECISION

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2017

Further Details:

     jack dongarra, linpack, 3/11/78.

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.

Date:

November 2017

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.

Date:

November 2017

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.

Date:

November 2017

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.

Date:

December 2016

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.

Date:

November 2017

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.

Date:

December 2016

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 single 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.

Date:

November 2017

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(*)

double precision function dznrm2 (integer N, complex*16, dimension(*) X, integer INCX)

DZNRM2

Purpose:

 DZNRM2 returns the euclidean norm of a vector via the function
 name, so that
    DZNRM2 := sqrt( x**H*x )

Parameters:

N

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

X

          X is COMPLEX*16 array, dimension (N)
         complex vector with N elements

INCX

          INCX is INTEGER
         storage spacing between elements of X

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2017

Further Details:

  -- This version written on 25-October-1982.
     Modified on 14-October-1993 to inline the call to ZLASSQ.
     Sven Hammarling, Nag Ltd.

Author

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