1 SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
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**H *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
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
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**H *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