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SUBROUTINE ZGEFA(A,LDA,N,IPVT,INFO)
INTEGER LDA,N,IPVT(*),INFO
COMPLEX*16 A(LDA,*)
C
C ZGEFA FACTORS A COMPLEX*16 MATRIX BY GAUSSIAN ELIMINATION.
C
C ZGEFA IS USUALLY CALLED BY ZGECO, BUT IT CAN BE CALLED
C DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED.
C (TIME FOR ZGECO) = (1 + 9/N)*(TIME FOR ZGEFA) .
C
C ON ENTRY
C
C A COMPLEX*16(LDA, N)
C THE MATRIX TO BE FACTORED.
C
C LDA INTEGER
C THE LEADING DIMENSION OF THE ARRAY A .
C
C N INTEGER
C THE ORDER OF THE MATRIX A .
C
C ON RETURN
C
C A AN UPPER TRIANGULAR MATRIX AND THE MULTIPLIERS
C WHICH WERE USED TO OBTAIN IT.
C THE FACTORIZATION CAN BE WRITTEN A = L*U WHERE
C L IS A PRODUCT OF PERMUTATION AND UNIT LOWER
C TRIANGULAR MATRICES AND U IS UPPER TRIANGULAR.
C
C IPVT INTEGER(N)
C AN INTEGER VECTOR OF PIVOT INDICES.
C
C INFO INTEGER
C = 0 NORMAL VALUE.
C = K IF U(K,K) .EQ. 0.0 . THIS IS NOT AN ERROR
C CONDITION FOR THIS SUBROUTINE, BUT IT DOES
C INDICATE THAT ZGESL OR ZGEDI WILL DIVIDE BY ZERO
C IF CALLED. USE RCOND IN ZGECO FOR A RELIABLE
C INDICATION OF SINGULARITY.
C
C LINPACK. THIS VERSION DATED 08/14/78 .
C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C SUBROUTINES AND FUNCTIONS
C
C BLAS ZAXPY,ZSCAL,IZAMAX
C FORTRAN DABS
C
C INTERNAL VARIABLES
C
COMPLEX*16 T
INTEGER IZAMAX,J,K,KP1,L,NM1
C
COMPLEX*16 ZDUM
DOUBLE PRECISION CABS1
DOUBLE PRECISION DREAL,DIMAG
COMPLEX*16 ZDUMR,ZDUMI
DREAL(ZDUMR) = ZDUMR
DIMAG(ZDUMI) = (0.0D0,-1.0D0)*ZDUMI
CABS1(ZDUM) = DABS(DREAL(ZDUM)) + DABS(DIMAG(ZDUM))
C
C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
C
INFO = 0
NM1 = N - 1
IF (NM1 .LT. 1) GO TO 70
DO 60 K = 1, NM1
KP1 = K + 1
C
C FIND L = PIVOT INDEX
C
L = IZAMAX(N-K+1,A(K,K),1) + K - 1
IPVT(K) = L
C
C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED
C
IF (CABS1(A(L,K)) .EQ. 0.0D0) GO TO 40
C
C INTERCHANGE IF NECESSARY
C
IF (L .EQ. K) GO TO 10
T = A(L,K)
A(L,K) = A(K,K)
A(K,K) = T
10 CONTINUE
C
C COMPUTE MULTIPLIERS
C
T = -(1.0D0,0.0D0)/A(K,K)
CALL ZSCAL(N-K,T,A(K+1,K),1)
C
C ROW ELIMINATION WITH COLUMN INDEXING
C
DO 30 J = KP1, N
T = A(L,J)
IF (L .EQ. K) GO TO 20
A(L,J) = A(K,J)
A(K,J) = T
20 CONTINUE
CALL ZAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1)
30 CONTINUE
GO TO 50
40 CONTINUE
INFO = K
50 CONTINUE
60 CONTINUE
70 CONTINUE
IPVT(N) = N
IF (CABS1(A(N,N)) .EQ. 0.0D0) INFO = N
RETURN
END
SUBROUTINE ZPOFA(A,LDA,N,INFO)
INTEGER LDA,N,INFO
COMPLEX*16 A(LDA,*)
C
C ZPOFA FACTORS A COMPLEX*16 HERMITIAN POSITIVE DEFINITE MATRIX.
C
C ZPOFA IS USUALLY CALLED BY ZPOCO, BUT IT CAN BE CALLED
C DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED.
C (TIME FOR ZPOCO) = (1 + 18/N)*(TIME FOR ZPOFA) .
C
C ON ENTRY
C
C A COMPLEX*16(LDA, N)
C THE HERMITIAN MATRIX TO BE FACTORED. ONLY THE
C DIAGONAL AND UPPER TRIANGLE ARE USED.
C
C LDA INTEGER
C THE LEADING DIMENSION OF THE ARRAY A .
C
C N INTEGER
C THE ORDER OF THE MATRIX A .
C
C ON RETURN
C
C A AN UPPER TRIANGULAR MATRIX R SO THAT A =
C CTRANS(R)*R WHERE CTRANS(R) IS THE CONJUGATE
C TRANSPOSE. THE STRICT LOWER TRIANGLE IS UNALTERED.
C IF INFO .NE. 0 , THE FACTORIZATION IS NOT COMPLETE.
C
C INFO INTEGER
C = 0 FOR NORMAL RETURN.
C = K SIGNALS AN ERROR CONDITION. THE LEADING MINOR
C OF ORDER K IS NOT POSITIVE DEFINITE.
C
C LINPACK. THIS VERSION DATED 08/14/78 .
C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C SUBROUTINES AND FUNCTIONS
C
C BLAS ZDOTC
C FORTRAN DCMPLX,DCONJG,DSQRT
C
C INTERNAL VARIABLES
C
COMPLEX*16 ZDOTC,T
DOUBLE PRECISION S
INTEGER J,JM1,K
DOUBLE PRECISION DREAL,DIMAG
COMPLEX*16 ZDUMR,ZDUMI
DREAL(ZDUMR) = ZDUMR
DIMAG(ZDUMI) = (0.0D0,-1.0D0)*ZDUMI
C BEGIN BLOCK WITH ...EXITS TO 40
C
C
DO 30 J = 1, N
INFO = J
S = 0.0D0
JM1 = J - 1
IF (JM1 .LT. 1) GO TO 20
DO 10 K = 1, JM1
T = A(K,J) - ZDOTC(K-1,A(1,K),1,A(1,J),1)
T = T/A(K,K)
A(K,J) = T
S = S + DREAL(T*DCONJG(T))
10 CONTINUE
20 CONTINUE
S = DREAL(A(J,J)) - S
C ......EXIT
IF (S .LE. 0.0D0 .OR. DIMAG(A(J,J)) .NE. 0.0D0) GO TO 40
A(J,J) = DCMPLX(DSQRT(S),0.0D0)
30 CONTINUE
INFO = 0
40 CONTINUE
RETURN
END
SUBROUTINE ZGTSL(N,C,D,E,B,INFO)
INTEGER N,INFO
COMPLEX*16 C(*),D(*),E(*),B(*)
C
C ZGTSL GIVEN A GENERAL TRIDIAGONAL MATRIX AND A RIGHT HAND
C SIDE WILL FIND THE SOLUTION.
C
C ON ENTRY
C
C N INTEGER
C IS THE ORDER OF THE TRIDIAGONAL MATRIX.
C
C C COMPLEX*16(N)
C IS THE SUBDIAGONAL OF THE TRIDIAGONAL MATRIX.
C C(2) THROUGH C(N) SHOULD CONTAIN THE SUBDIAGONAL.
C ON OUTPUT C IS DESTROYED.
C
C D COMPLEX*16(N)
C IS THE DIAGONAL OF THE TRIDIAGONAL MATRIX.
C ON OUTPUT D IS DESTROYED.
C
C E COMPLEX*16(N)
C IS THE SUPERDIAGONAL OF THE TRIDIAGONAL MATRIX.
C E(1) THROUGH E(N-1) SHOULD CONTAIN THE SUPERDIAGONAL.
C ON OUTPUT E IS DESTROYED.
C
C B COMPLEX*16(N)
C IS THE RIGHT HAND SIDE VECTOR.
C
C ON RETURN
C
C B IS THE SOLUTION VECTOR.
C
C INFO INTEGER
C = 0 NORMAL VALUE.
C = K IF THE K-TH ELEMENT OF THE DIAGONAL BECOMES
C EXACTLY ZERO. THE SUBROUTINE RETURNS WHEN
C THIS IS DETECTED.
C
C LINPACK. THIS VERSION DATED 08/14/78 .
C JACK DONGARRA, ARGONNE NATIONAL LABORATORY.
C
C NO EXTERNALS
C FORTRAN DABS
C
C INTERNAL VARIABLES
C
INTEGER K,KB,KP1,NM1,NM2
COMPLEX*16 T
COMPLEX*16 ZDUM
DOUBLE PRECISION CABS1
DOUBLE PRECISION DREAL,DIMAG
COMPLEX*16 ZDUMR,ZDUMI
DREAL(ZDUMR) = ZDUMR
DIMAG(ZDUMI) = (0.0D0,-1.0D0)*ZDUMI
CABS1(ZDUM) = DABS(DREAL(ZDUM)) + DABS(DIMAG(ZDUM))
C BEGIN BLOCK PERMITTING ...EXITS TO 100
C
INFO = 0
C(1) = D(1)
NM1 = N - 1
IF (NM1 .LT. 1) GO TO 40
D(1) = E(1)
E(1) = (0.0D0,0.0D0)
E(N) = (0.0D0,0.0D0)
C
DO 30 K = 1, NM1
KP1 = K + 1
C
C FIND THE LARGEST OF THE TWO ROWS
C
IF (CABS1(C(KP1)) .LT. CABS1(C(K))) GO TO 10
C
C INTERCHANGE ROW
C
T = C(KP1)
C(KP1) = C(K)
C(K) = T
T = D(KP1)
D(KP1) = D(K)
D(K) = T
T = E(KP1)
E(KP1) = E(K)
E(K) = T
T = B(KP1)
B(KP1) = B(K)
B(K) = T
10 CONTINUE
C
C ZERO ELEMENTS
C
IF (CABS1(C(K)) .NE. 0.0D0) GO TO 20
INFO = K
C ............EXIT
GO TO 100
20 CONTINUE
T = -C(KP1)/C(K)
C(KP1) = D(KP1) + T*D(K)
D(KP1) = E(KP1) + T*E(K)
E(KP1) = (0.0D0,0.0D0)
B(KP1) = B(KP1) + T*B(K)
30 CONTINUE
40 CONTINUE
IF (CABS1(C(N)) .NE. 0.0D0) GO TO 50
INFO = N
GO TO 90
50 CONTINUE
C
C BACK SOLVE
C
NM2 = N - 2
B(N) = B(N)/C(N)
IF (N .EQ. 1) GO TO 80
B(NM1) = (B(NM1) - D(NM1)*B(N))/C(NM1)
IF (NM2 .LT. 1) GO TO 70
DO 60 KB = 1, NM2
K = NM2 - KB + 1
B(K) = (B(K) - D(K)*B(K+1) - E(K)*B(K+2))/C(K)
60 CONTINUE
70 CONTINUE
80 CONTINUE
90 CONTINUE
100 CONTINUE
C
RETURN
END
SUBROUTINE ZPTSL(N,D,E,B)
INTEGER N
COMPLEX*16 D(*),E(*),B(*)
C
C ZPTSL GIVEN A POSITIVE DEFINITE TRIDIAGONAL MATRIX AND A RIGHT
C HAND SIDE WILL FIND THE SOLUTION.
C
C ON ENTRY
C
C N INTEGER
C IS THE ORDER OF THE TRIDIAGONAL MATRIX.
C
C D COMPLEX*16(N)
C IS THE DIAGONAL OF THE TRIDIAGONAL MATRIX.
C ON OUTPUT D IS DESTROYED.
C
C E COMPLEX*16(N)
C IS THE OFFDIAGONAL OF THE TRIDIAGONAL MATRIX.
C E(1) THROUGH E(N-1) SHOULD CONTAIN THE
C OFFDIAGONAL.
C
C B COMPLEX*16(N)
C IS THE RIGHT HAND SIDE VECTOR.
C
C ON RETURN
C
C B CONTAINS THE SOULTION.
C
C LINPACK. THIS VERSION DATED 08/14/78 .
C JACK DONGARRA, ARGONNE NATIONAL LABORATORY.
C
C NO EXTERNALS
C FORTRAN DCONJG,MOD
C
C INTERNAL VARIABLES
C
INTEGER K,KBM1,KE,KF,KP1,NM1,NM1D2
COMPLEX*16 T1,T2
C
C CHECK FOR 1 X 1 CASE
C
IF (N .NE. 1) GO TO 10
B(1) = B(1)/D(1)
GO TO 70
10 CONTINUE
NM1 = N - 1
NM1D2 = NM1/2
IF (N .EQ. 2) GO TO 30
KBM1 = N - 1
C
C ZERO TOP HALF OF SUBDIAGONAL AND BOTTOM HALF OF
C SUPERDIAGONAL
C
DO 20 K = 1, NM1D2
T1 = DCONJG(E(K))/D(K)
D(K+1) = D(K+1) - T1*E(K)
B(K+1) = B(K+1) - T1*B(K)
T2 = E(KBM1)/D(KBM1+1)
D(KBM1) = D(KBM1) - T2*DCONJG(E(KBM1))
B(KBM1) = B(KBM1) - T2*B(KBM1+1)
KBM1 = KBM1 - 1
20 CONTINUE
30 CONTINUE
KP1 = NM1D2 + 1
C
C CLEAN UP FOR POSSIBLE 2 X 2 BLOCK AT CENTER
C
IF (MOD(N,2) .NE. 0) GO TO 40
T1 = DCONJG(E(KP1))/D(KP1)
D(KP1+1) = D(KP1+1) - T1*E(KP1)
B(KP1+1) = B(KP1+1) - T1*B(KP1)
KP1 = KP1 + 1
40 CONTINUE
C
C BACK SOLVE STARTING AT THE CENTER, GOING TOWARDS THE TOP
C AND BOTTOM
C
B(KP1) = B(KP1)/D(KP1)
IF (N .EQ. 2) GO TO 60
K = KP1 - 1
KE = KP1 + NM1D2 - 1
DO 50 KF = KP1, KE
B(K) = (B(K) - E(K)*B(K+1))/D(K)
B(KF+1) = (B(KF+1) - DCONJG(E(KF))*B(KF))/D(KF+1)
K = K - 1
50 CONTINUE
60 CONTINUE
IF (MOD(N,2) .EQ. 0) B(1) = (B(1) - E(1)*B(2))/D(1)
70 CONTINUE
RETURN
END
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