1      SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
2*
3*  -- LAPACK routine (version 3.0) --
4*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
5*     Courant Institute, Argonne National Lab, and Rice University
6*     September 30, 1994
7*
8*     .. Scalar Arguments ..
9      INTEGER            INFO, LDB, N, NRHS
10*     ..
11*     .. Array Arguments ..
12      COMPLEX*16         B( LDB, * ), D( * ), DL( * ), DU( * )
13*     ..
14*
15*  Purpose
16*  =======
17*
18*  ZGTSV  solves the equation
19*
20*     A*X = B,
21*
22*  where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
23*  partial pivoting.
24*
25*  Note that the equation  A'*X = B  may be solved by interchanging the
26*  order of the arguments DU and DL.
27*
28*  Arguments
29*  =========
30*
31*  N       (input) INTEGER
32*          The order of the matrix A.  N >= 0.
33*
34*  NRHS    (input) INTEGER
35*          The number of right hand sides, i.e., the number of columns
36*          of the matrix B.  NRHS >= 0.
37*
38*  DL      (input/output) COMPLEX*16 array, dimension (N-1)
39*          On entry, DL must contain the (n-1) subdiagonal elements of
40*          A.
41*          On exit, DL is overwritten by the (n-2) elements of the
42*          second superdiagonal of the upper triangular matrix U from
43*          the LU factorization of A, in DL(1), ..., DL(n-2).
44*
45*  D       (input/output) COMPLEX*16 array, dimension (N)
46*          On entry, D must contain the diagonal elements of A.
47*          On exit, D is overwritten by the n diagonal elements of U.
48*
49*  DU      (input/output) COMPLEX*16 array, dimension (N-1)
50*          On entry, DU must contain the (n-1) superdiagonal elements
51*          of A.
52*          On exit, DU is overwritten by the (n-1) elements of the first
53*          superdiagonal of U.
54*
55*  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
56*          On entry, the N-by-NRHS right hand side matrix B.
57*          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
58*
59*  LDB     (input) INTEGER
60*          The leading dimension of the array B.  LDB >= max(1,N).
61*
62*  INFO    (output) INTEGER
63*          = 0:  successful exit
64*          < 0:  if INFO = -i, the i-th argument had an illegal value
65*          > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
66*                has not been computed.  The factorization has not been
67*                completed unless i = N.
68*
69*  =====================================================================
70*
71*     .. Parameters ..
72      COMPLEX*16         ZERO
73      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
74*     ..
75*     .. Local Scalars ..
76      INTEGER            J, K
77      COMPLEX*16         MULT, TEMP, ZDUM
78*     ..
79*     .. Intrinsic Functions ..
80      INTRINSIC          ABS, DBLE, DIMAG, MAX
81*     ..
82*     .. External Subroutines ..
83      EXTERNAL           XERBLA
84*     ..
85*     .. Statement Functions ..
86      DOUBLE PRECISION   CABS1
87*     ..
88*     .. Statement Function definitions ..
89      CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
90*     ..
91*     .. Executable Statements ..
92*
93      INFO = 0
94      IF( N.LT.0 ) THEN
95         INFO = -1
96      ELSE IF( NRHS.LT.0 ) THEN
97         INFO = -2
98      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
99         INFO = -7
100      END IF
101      IF( INFO.NE.0 ) THEN
102         CALL XERBLA( 'ZGTSV ', -INFO )
103         RETURN
104      END IF
105*
106      IF( N.EQ.0 )
107     $   RETURN
108*
109      DO 30 K = 1, N - 1
110         IF( DL( K ).EQ.ZERO ) THEN
111*
112*           Subdiagonal is zero, no elimination is required.
113*
114            IF( D( K ).EQ.ZERO ) THEN
115*
116*              Diagonal is zero: set INFO = K and return; a unique
117*              solution can not be found.
118*
119               INFO = K
120               RETURN
121            END IF
122         ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
123*
124*           No row interchange required
125*
126            MULT = DL( K ) / D( K )
127            D( K+1 ) = D( K+1 ) - MULT*DU( K )
128            DO 10 J = 1, NRHS
129               B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
130   10       CONTINUE
131            IF( K.LT.( N-1 ) )
132     $         DL( K ) = ZERO
133         ELSE
134*
135*           Interchange rows K and K+1
136*
137            MULT = D( K ) / DL( K )
138            D( K ) = DL( K )
139            TEMP = D( K+1 )
140            D( K+1 ) = DU( K ) - MULT*TEMP
141            IF( K.LT.( N-1 ) ) THEN
142               DL( K ) = DU( K+1 )
143               DU( K+1 ) = -MULT*DL( K )
144            END IF
145            DU( K ) = TEMP
146            DO 20 J = 1, NRHS
147               TEMP = B( K, J )
148               B( K, J ) = B( K+1, J )
149               B( K+1, J ) = TEMP - MULT*B( K+1, J )
150   20       CONTINUE
151         END IF
152   30 CONTINUE
153      IF( D( N ).EQ.ZERO ) THEN
154         INFO = N
155         RETURN
156      END IF
157*
158*     Back solve with the matrix U from the factorization.
159*
160      DO 50 J = 1, NRHS
161         B( N, J ) = B( N, J ) / D( N )
162         IF( N.GT.1 )
163     $      B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
164         DO 40 K = N - 2, 1, -1
165            B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
166     $                  B( K+2, J ) ) / D( K )
167   40    CONTINUE
168   50 CONTINUE
169*
170      RETURN
171*
172*     End of ZGTSV
173*
174      END
175