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1.1 bertrand 1: SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
2: *
3: * -- LAPACK auxiliary 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 ITRANS, LDB, N, NRHS
10: * ..
11: * .. Array Arguments ..
12: INTEGER IPIV( * )
13: COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * ZGTTS2 solves one of the systems of equations
20: * A * X = B, A**T * X = B, or A**H * X = B,
21: * with a tridiagonal matrix A using the LU factorization computed
22: * by ZGTTRF.
23: *
24: * Arguments
25: * =========
26: *
27: * ITRANS (input) INTEGER
28: * Specifies the form of the system of equations.
29: * = 0: A * X = B (No transpose)
30: * = 1: A**T * X = B (Transpose)
31: * = 2: A**H * X = B (Conjugate transpose)
32: *
33: * N (input) INTEGER
34: * The order of the matrix A.
35: *
36: * NRHS (input) INTEGER
37: * The number of right hand sides, i.e., the number of columns
38: * of the matrix B. NRHS >= 0.
39: *
40: * DL (input) COMPLEX*16 array, dimension (N-1)
41: * The (n-1) multipliers that define the matrix L from the
42: * LU factorization of A.
43: *
44: * D (input) COMPLEX*16 array, dimension (N)
45: * The n diagonal elements of the upper triangular matrix U from
46: * the LU factorization of A.
47: *
48: * DU (input) COMPLEX*16 array, dimension (N-1)
49: * The (n-1) elements of the first super-diagonal of U.
50: *
51: * DU2 (input) COMPLEX*16 array, dimension (N-2)
52: * The (n-2) elements of the second super-diagonal of U.
53: *
54: * IPIV (input) INTEGER array, dimension (N)
55: * The pivot indices; for 1 <= i <= n, row i of the matrix was
56: * interchanged with row IPIV(i). IPIV(i) will always be either
57: * i or i+1; IPIV(i) = i indicates a row interchange was not
58: * required.
59: *
60: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
61: * On entry, the matrix of right hand side vectors B.
62: * On exit, B is overwritten by the solution vectors X.
63: *
64: * LDB (input) INTEGER
65: * The leading dimension of the array B. LDB >= max(1,N).
66: *
67: * =====================================================================
68: *
69: * .. Local Scalars ..
70: INTEGER I, J
71: COMPLEX*16 TEMP
72: * ..
73: * .. Intrinsic Functions ..
74: INTRINSIC DCONJG
75: * ..
76: * .. Executable Statements ..
77: *
78: * Quick return if possible
79: *
80: IF( N.EQ.0 .OR. NRHS.EQ.0 )
81: $ RETURN
82: *
83: IF( ITRANS.EQ.0 ) THEN
84: *
85: * Solve A*X = B using the LU factorization of A,
86: * overwriting each right hand side vector with its solution.
87: *
88: IF( NRHS.LE.1 ) THEN
89: J = 1
90: 10 CONTINUE
91: *
92: * Solve L*x = b.
93: *
94: DO 20 I = 1, N - 1
95: IF( IPIV( I ).EQ.I ) THEN
96: B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
97: ELSE
98: TEMP = B( I, J )
99: B( I, J ) = B( I+1, J )
100: B( I+1, J ) = TEMP - DL( I )*B( I, J )
101: END IF
102: 20 CONTINUE
103: *
104: * Solve U*x = b.
105: *
106: B( N, J ) = B( N, J ) / D( N )
107: IF( N.GT.1 )
108: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
109: $ D( N-1 )
110: DO 30 I = N - 2, 1, -1
111: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
112: $ B( I+2, J ) ) / D( I )
113: 30 CONTINUE
114: IF( J.LT.NRHS ) THEN
115: J = J + 1
116: GO TO 10
117: END IF
118: ELSE
119: DO 60 J = 1, NRHS
120: *
121: * Solve L*x = b.
122: *
123: DO 40 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: 40 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 50 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: 50 CONTINUE
143: 60 CONTINUE
144: END IF
145: ELSE IF( ITRANS.EQ.1 ) THEN
146: *
147: * Solve A**T * X = B.
148: *
149: IF( NRHS.LE.1 ) THEN
150: J = 1
151: 70 CONTINUE
152: *
153: * Solve U**T * x = b.
154: *
155: B( 1, J ) = B( 1, J ) / D( 1 )
156: IF( N.GT.1 )
157: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
158: DO 80 I = 3, N
159: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
160: $ B( I-2, J ) ) / D( I )
161: 80 CONTINUE
162: *
163: * Solve L**T * x = b.
164: *
165: DO 90 I = N - 1, 1, -1
166: IF( IPIV( I ).EQ.I ) THEN
167: B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
168: ELSE
169: TEMP = B( I+1, J )
170: B( I+1, J ) = B( I, J ) - DL( I )*TEMP
171: B( I, J ) = TEMP
172: END IF
173: 90 CONTINUE
174: IF( J.LT.NRHS ) THEN
175: J = J + 1
176: GO TO 70
177: END IF
178: ELSE
179: DO 120 J = 1, NRHS
180: *
181: * Solve U**T * x = b.
182: *
183: B( 1, J ) = B( 1, J ) / D( 1 )
184: IF( N.GT.1 )
185: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
186: DO 100 I = 3, N
187: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
188: $ DU2( I-2 )*B( I-2, J ) ) / D( I )
189: 100 CONTINUE
190: *
191: * Solve L**T * x = b.
192: *
193: DO 110 I = N - 1, 1, -1
194: IF( IPIV( I ).EQ.I ) THEN
195: B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
196: ELSE
197: TEMP = B( I+1, J )
198: B( I+1, J ) = B( I, J ) - DL( I )*TEMP
199: B( I, J ) = TEMP
200: END IF
201: 110 CONTINUE
202: 120 CONTINUE
203: END IF
204: ELSE
205: *
206: * Solve A**H * X = B.
207: *
208: IF( NRHS.LE.1 ) THEN
209: J = 1
210: 130 CONTINUE
211: *
212: * Solve U**H * x = b.
213: *
214: B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) )
215: IF( N.GT.1 )
216: $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) /
217: $ DCONJG( D( 2 ) )
218: DO 140 I = 3, N
219: B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*B( I-1, J )-
220: $ DCONJG( DU2( I-2 ) )*B( I-2, J ) ) /
221: $ DCONJG( D( I ) )
222: 140 CONTINUE
223: *
224: * Solve L**H * x = b.
225: *
226: DO 150 I = N - 1, 1, -1
227: IF( IPIV( I ).EQ.I ) THEN
228: B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*B( I+1, J )
229: ELSE
230: TEMP = B( I+1, J )
231: B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP
232: B( I, J ) = TEMP
233: END IF
234: 150 CONTINUE
235: IF( J.LT.NRHS ) THEN
236: J = J + 1
237: GO TO 130
238: END IF
239: ELSE
240: DO 180 J = 1, NRHS
241: *
242: * Solve U**H * x = b.
243: *
244: B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) )
245: IF( N.GT.1 )
246: $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) )
247: $ / DCONJG( D( 2 ) )
248: DO 160 I = 3, N
249: B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*
250: $ B( I-1, J )-DCONJG( DU2( I-2 ) )*
251: $ B( I-2, J ) ) / DCONJG( D( I ) )
252: 160 CONTINUE
253: *
254: * Solve L**H * x = b.
255: *
256: DO 170 I = N - 1, 1, -1
257: IF( IPIV( I ).EQ.I ) THEN
258: B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*
259: $ B( I+1, J )
260: ELSE
261: TEMP = B( I+1, J )
262: B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP
263: B( I, J ) = TEMP
264: END IF
265: 170 CONTINUE
266: 180 CONTINUE
267: END IF
268: END IF
269: *
270: * End of ZGTTS2
271: *
272: END