|
5164
|
1 SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, |
|
|
2 $ INFO ) |
|
|
3 * |
|
|
4 * -- LAPACK routine (version 2.0) -- |
|
|
5 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
|
|
6 * Courant Institute, Argonne National Lab, and Rice University |
|
|
7 * September 30, 1994 |
|
|
8 * |
|
|
9 * .. Scalar Arguments .. |
|
|
10 CHARACTER TRANS |
|
|
11 INTEGER INFO, LDB, N, NRHS |
|
|
12 * .. |
|
|
13 * .. Array Arguments .. |
|
|
14 INTEGER IPIV( * ) |
|
|
15 DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) |
|
|
16 * .. |
|
|
17 * |
|
|
18 * Purpose |
|
|
19 * ======= |
|
|
20 * |
|
|
21 * DGTTRS solves one of the systems of equations |
|
|
22 * A*X = B or A'*X = B, |
|
|
23 * with a tridiagonal matrix A using the LU factorization computed |
|
|
24 * by DGTTRF. |
|
|
25 * |
|
|
26 * Arguments |
|
|
27 * ========= |
|
|
28 * |
|
|
29 * TRANS (input) CHARACTER |
|
|
30 * Specifies the form of the system of equations: |
|
|
31 * = 'N': A * X = B (No transpose) |
|
|
32 * = 'T': A'* X = B (Transpose) |
|
|
33 * = 'C': A'* X = B (Conjugate transpose = Transpose) |
|
|
34 * |
|
|
35 * N (input) INTEGER |
|
|
36 * The order of the matrix A. N >= 0. |
|
|
37 * |
|
|
38 * NRHS (input) INTEGER |
|
|
39 * The number of right hand sides, i.e., the number of columns |
|
|
40 * of the matrix B. NRHS >= 0. |
|
|
41 * |
|
|
42 * DL (input) DOUBLE PRECISION array, dimension (N-1) |
|
|
43 * The (n-1) multipliers that define the matrix L from the |
|
|
44 * LU factorization of A. |
|
|
45 * |
|
|
46 * D (input) DOUBLE PRECISION array, dimension (N) |
|
|
47 * The n diagonal elements of the upper triangular matrix U from |
|
|
48 * the LU factorization of A. |
|
|
49 * |
|
|
50 * DU (input) DOUBLE PRECISION array, dimension (N-1) |
|
|
51 * The (n-1) elements of the first superdiagonal of U. |
|
|
52 * |
|
|
53 * DU2 (input) DOUBLE PRECISION array, dimension (N-2) |
|
|
54 * The (n-2) elements of the second superdiagonal of U. |
|
|
55 * |
|
|
56 * IPIV (input) INTEGER array, dimension (N) |
|
|
57 * The pivot indices; for 1 <= i <= n, row i of the matrix was |
|
|
58 * interchanged with row IPIV(i). IPIV(i) will always be either |
|
|
59 * i or i+1; IPIV(i) = i indicates a row interchange was not |
|
|
60 * required. |
|
|
61 * |
|
|
62 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
|
|
63 * On entry, the right hand side matrix B. |
|
|
64 * On exit, B is overwritten by the solution matrix X. |
|
|
65 * |
|
|
66 * LDB (input) INTEGER |
|
|
67 * The leading dimension of the array B. LDB >= max(1,N). |
|
|
68 * |
|
|
69 * INFO (output) INTEGER |
|
|
70 * = 0: successful exit |
|
|
71 * < 0: if INFO = -i, the i-th argument had an illegal value |
|
|
72 * |
|
|
73 * ===================================================================== |
|
|
74 * |
|
|
75 * .. Local Scalars .. |
|
|
76 LOGICAL NOTRAN |
|
|
77 INTEGER I, J |
|
|
78 DOUBLE PRECISION TEMP |
|
|
79 * .. |
|
|
80 * .. External Functions .. |
|
|
81 LOGICAL LSAME |
|
|
82 EXTERNAL LSAME |
|
|
83 * .. |
|
|
84 * .. External Subroutines .. |
|
|
85 EXTERNAL XERBLA |
|
|
86 * .. |
|
|
87 * .. Intrinsic Functions .. |
|
|
88 INTRINSIC MAX |
|
|
89 * .. |
|
|
90 * .. Executable Statements .. |
|
|
91 * |
|
|
92 INFO = 0 |
|
|
93 NOTRAN = LSAME( TRANS, 'N' ) |
|
|
94 IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. |
|
|
95 $ LSAME( TRANS, 'C' ) ) THEN |
|
|
96 INFO = -1 |
|
|
97 ELSE IF( N.LT.0 ) THEN |
|
|
98 INFO = -2 |
|
|
99 ELSE IF( NRHS.LT.0 ) THEN |
|
|
100 INFO = -3 |
|
|
101 ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN |
|
|
102 INFO = -10 |
|
|
103 END IF |
|
|
104 IF( INFO.NE.0 ) THEN |
|
|
105 CALL XERBLA( 'DGTTRS', -INFO ) |
|
|
106 RETURN |
|
|
107 END IF |
|
|
108 * |
|
|
109 * Quick return if possible |
|
|
110 * |
|
|
111 IF( N.EQ.0 .OR. NRHS.EQ.0 ) |
|
|
112 $ RETURN |
|
|
113 * |
|
|
114 IF( NOTRAN ) THEN |
|
|
115 * |
|
|
116 * Solve A*X = B using the LU factorization of A, |
|
|
117 * overwriting each right hand side vector with its solution. |
|
|
118 * |
|
|
119 DO 30 J = 1, NRHS |
|
|
120 * |
|
|
121 * Solve L*x = b. |
|
|
122 * |
|
|
123 DO 10 I = 1, N - 1 |
|
|
124 IF( IPIV( I ).EQ.I ) THEN |
|
|
125 B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J ) |
|
|
126 ELSE |
|
|
127 TEMP = B( I, J ) |
|
|
128 B( I, J ) = B( I+1, J ) |
|
|
129 B( I+1, J ) = TEMP - DL( I )*B( I, J ) |
|
|
130 END IF |
|
|
131 10 CONTINUE |
|
|
132 * |
|
|
133 * Solve U*x = b. |
|
|
134 * |
|
|
135 B( N, J ) = B( N, J ) / D( N ) |
|
|
136 IF( N.GT.1 ) |
|
|
137 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / |
|
|
138 $ D( N-1 ) |
|
|
139 DO 20 I = N - 2, 1, -1 |
|
|
140 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )* |
|
|
141 $ B( I+2, J ) ) / D( I ) |
|
|
142 20 CONTINUE |
|
|
143 30 CONTINUE |
|
|
144 ELSE |
|
|
145 * |
|
|
146 * Solve A' * X = B. |
|
|
147 * |
|
|
148 DO 60 J = 1, NRHS |
|
|
149 * |
|
|
150 * Solve U'*x = b. |
|
|
151 * |
|
|
152 B( 1, J ) = B( 1, J ) / D( 1 ) |
|
|
153 IF( N.GT.1 ) |
|
|
154 $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 ) |
|
|
155 DO 40 I = 3, N |
|
|
156 B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )* |
|
|
157 $ B( I-2, J ) ) / D( I ) |
|
|
158 40 CONTINUE |
|
|
159 * |
|
|
160 * Solve L'*x = b. |
|
|
161 * |
|
|
162 DO 50 I = N - 1, 1, -1 |
|
|
163 IF( IPIV( I ).EQ.I ) THEN |
|
|
164 B( I, J ) = B( I, J ) - DL( I )*B( I+1, J ) |
|
|
165 ELSE |
|
|
166 TEMP = B( I+1, J ) |
|
|
167 B( I+1, J ) = B( I, J ) - DL( I )*TEMP |
|
|
168 B( I, J ) = TEMP |
|
|
169 END IF |
|
|
170 50 CONTINUE |
|
|
171 60 CONTINUE |
|
|
172 END IF |
|
|
173 * |
|
|
174 * End of DGTTRS |
|
|
175 * |
|
|
176 END |
