Geology Reference
In-Depth Information
real part of matrix is,
-0.63681D+03 -0.54262D+03 0.00000D+00 0.00000D+00 0.00000D+00
0.00000D+00 0.47353D-01 -0.20383D-02 0.77597D-02 -0.24832D-01
0.00000D+00 0.41176D-01 0.41669D-02 -0.12093D-01 -0.20853D-01
0.00000D+00 0.14868D+00 -0.19657D-02 0.50075D-01 -0.41175D-01
0.00000D+00 -0.36038D+00 -0.10301D-02 -0.33330D-01
0.15153D+00
imaginary part of matrix is,
0.00000D+00
0.11524D+04
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00 -0.70684D-02 -0.44649D-02
0.95123D-02
0.58349D-02
0.00000D+00
0.82013D-01
0.19453D-02
0.12739D-01 -0.26964D-01
0.00000D+00 -0.18263D+00
0.28303D-02
0.58515D-03
0.79070D-01
0.00000D+00 -0.89162D-01 -0.10635D-02 -0.65263D-01
0.63077D-03.
These operations are repeated for the second column, second row, and so on,
until the final operation is on the second to last column. The matrix is left in the
complex upper bidiagonal form
real part of matrix is,
-0.63681D+03 -0.54262D+03
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00 -0.44672D+00 -0.12538D+00
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00 -0.85026D-04 -0.25365D-02
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00 -0.38416D-02
0.51173D-02
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00
0.17430D-02
imaginary part of matrix is,
0.00000D+00
0.11524D+04
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00
0.66681D-01 -0.15867D+00
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00
0.10496D-01
0.41533D-02
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00 -0.34631D-02
0.50654D-02
0.00000D+00
0.00000D+00
0.00000D+00
0.00000D+00
0.25834D-02.
The basis of the foregoing operations is the subroutine HHOLDER that anni-
hilates the components of the M -length vector v beyond the n th component for
n < M . It calculates the vector u required to construct the Householder matrix P
and replaces the vector v with the transformed vector w .
SUBROUTINE HHOLDER(V,U,N,M,MMAX)
C
C The subroutine HHOLDER annihilates the components of the vector V(M)
C beyond the Nth component for N<M. The Householder vector U is calculated
C and the annihilated vector W replaces V on return.
C
DOUBLE COMPLEX U(MMAX),V(MMAX),W(MMAX)
DOUBLE PRECISION ETA,AMAG,VWMAG,VR,VI
C No modification for N=M.
IF(N.EQ.M) GO TO 10
C Find value of ETA.
ETA=0.D0
DO 11 I=N,M
ETA=ETA+DREAL(V(I)*DCONJG(V(I)))
11 CONTINUE
ETA=DSQRT(ETA)
C Find magnitude and real and imaginary parts of V(N).
AMAG=CDABS(V(N))
VR=DREAL(V(N))
VI=DIMAG(V(N))
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