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 is INTEGER
         number of elements in input vector(s)

          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(*)

Definition at line 70 of file dasum.f.

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 is INTEGER
         number of elements in input vector(s)

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

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

INCX

          INCX is INTEGER
         storage spacing between elements of DX

          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(*)

Definition at line 88 of file daxpy.f.

double precision function dcabs1 (complex*16 Z)

DCABS1

Purpose:

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

Parameters

          Z is COMPLEX*16

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 46 of file dcabs1.f.

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
         storage spacing between elements of DX

          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(*)

Definition at line 81 of file dcopy.f.

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
         storage spacing between elements of DX

          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(*)

Definition at line 81 of file ddot.f.

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
         storage spacing between elements of DX

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

INCY

          INCY is INTEGER
         storage spacing between elements of DY

          C is DOUBLE PRECISION

          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(*)

Definition at line 91 of file drot.f.

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
         storage spacing between elements of DX

          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.

Definition at line 95 of file drotm.f.

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.

Definition at line 89 of file drotmg.f.

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 is INTEGER
         number of elements in input vector(s)

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

          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(*)

Definition at line 78 of file dscal.f.

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
          storage spacing between elements of SX

          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)

Definition at line 118 of file dsdot.f.

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 is INTEGER
         number of elements in input vector(s)

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

INCX

          INCX is INTEGER
         storage spacing between elements of DX

          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(*)

Definition at line 81 of file dswap.f.

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

          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 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.

Definition at line 142 of file dtrsv.f.

double precision function dzasum (integer N, complex16, 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 is INTEGER
         number of elements in input vector(s)

          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(*)

Definition at line 71 of file dzasum.f.

Author

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