Annotation of rpl/lapack/lapack/zgtsv.f, revision 1.3
1.1 bertrand 1: SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
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
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