DASUM takes the sum of the absolute values.

     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(*)

    DAXPY constant times a vector plus a vector.
    uses unrolled loops for increments equal to one.

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

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

    DCOPY copies a vector, x, to a vector, y.
    uses unrolled loops for increments equal to one.

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

    DDOT forms the dot product of two vectors.
    uses unrolled loops for increments equal to one.

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

 DNRM2 returns the euclidean norm of a vector via the function
 name, so that

    DNRM2 := sqrt( x'*x )

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

    DROT applies a plane rotation.

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

    DROTG construct givens plane rotation.

     jack dongarra, linpack, 3/11/78.

    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.

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

          DX is DOUBLE PRECISION array, dimension N
         double precision vector with N elements

          INCX is INTEGER
         storage spacing between elements of DX

          DY is DOUBLE PRECISION array, dimension N
         double precision vector with N elements

          INCY is INTEGER
         storage spacing between elements of DY

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

    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.

          DD1 is DOUBLE PRECISION

          DD2 is DOUBLE PRECISION

          DX1 is DOUBLE PRECISION

          DY1 is DOUBLE PRECISION

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

    DSCAL scales a vector by a constant.
    uses unrolled loops for increment equal to one.

     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(*)

 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.

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

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

          INCX is INTEGER
          storage spacing between elements of SX

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

          INCY is INTEGER
         storage spacing between elements of SY

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

  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)

    interchanges two vectors.
    uses unrolled loops for increments equal one.

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

 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.

          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 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 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 of 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 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 of 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 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.

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

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

 DZNRM2 returns the euclidean norm of a vector via the function
 name, so that

    DZNRM2 := sqrt( x**H*x )

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