1: *> \brief \b ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGTTS2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgtts2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgtts2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgtts2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER ITRANS, LDB, N, NRHS
25: * ..
26: * .. Array Arguments ..
27: * INTEGER IPIV( * )
28: * COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZGTTS2 solves one of the systems of equations
38: *> A * X = B, A**T * X = B, or A**H * X = B,
39: *> with a tridiagonal matrix A using the LU factorization computed
40: *> by ZGTTRF.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] ITRANS
47: *> \verbatim
48: *> ITRANS is INTEGER
49: *> Specifies the form of the system of equations.
50: *> = 0: A * X = B (No transpose)
51: *> = 1: A**T * X = B (Transpose)
52: *> = 2: A**H * X = B (Conjugate transpose)
53: *> \endverbatim
54: *>
55: *> \param[in] N
56: *> \verbatim
57: *> N is INTEGER
58: *> The order of the matrix A.
59: *> \endverbatim
60: *>
61: *> \param[in] NRHS
62: *> \verbatim
63: *> NRHS is INTEGER
64: *> The number of right hand sides, i.e., the number of columns
65: *> of the matrix B. NRHS >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in] DL
69: *> \verbatim
70: *> DL is COMPLEX*16 array, dimension (N-1)
71: *> The (n-1) multipliers that define the matrix L from the
72: *> LU factorization of A.
73: *> \endverbatim
74: *>
75: *> \param[in] D
76: *> \verbatim
77: *> D is COMPLEX*16 array, dimension (N)
78: *> The n diagonal elements of the upper triangular matrix U from
79: *> the LU factorization of A.
80: *> \endverbatim
81: *>
82: *> \param[in] DU
83: *> \verbatim
84: *> DU is COMPLEX*16 array, dimension (N-1)
85: *> The (n-1) elements of the first super-diagonal of U.
86: *> \endverbatim
87: *>
88: *> \param[in] DU2
89: *> \verbatim
90: *> DU2 is COMPLEX*16 array, dimension (N-2)
91: *> The (n-2) elements of the second super-diagonal of U.
92: *> \endverbatim
93: *>
94: *> \param[in] IPIV
95: *> \verbatim
96: *> IPIV is INTEGER array, dimension (N)
97: *> The pivot indices; for 1 <= i <= n, row i of the matrix was
98: *> interchanged with row IPIV(i). IPIV(i) will always be either
99: *> i or i+1; IPIV(i) = i indicates a row interchange was not
100: *> required.
101: *> \endverbatim
102: *>
103: *> \param[in,out] B
104: *> \verbatim
105: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
106: *> On entry, the matrix of right hand side vectors B.
107: *> On exit, B is overwritten by the solution vectors X.
108: *> \endverbatim
109: *>
110: *> \param[in] LDB
111: *> \verbatim
112: *> LDB is INTEGER
113: *> The leading dimension of the array B. LDB >= max(1,N).
114: *> \endverbatim
115: *
116: * Authors:
117: * ========
118: *
119: *> \author Univ. of Tennessee
120: *> \author Univ. of California Berkeley
121: *> \author Univ. of Colorado Denver
122: *> \author NAG Ltd.
123: *
124: *> \date September 2012
125: *
126: *> \ingroup complex16GTcomputational
127: *
128: * =====================================================================
129: SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
130: *
131: * -- LAPACK computational routine (version 3.4.2) --
132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134: * September 2012
135: *
136: * .. Scalar Arguments ..
137: INTEGER ITRANS, LDB, N, NRHS
138: * ..
139: * .. Array Arguments ..
140: INTEGER IPIV( * )
141: COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
142: * ..
143: *
144: * =====================================================================
145: *
146: * .. Local Scalars ..
147: INTEGER I, J
148: COMPLEX*16 TEMP
149: * ..
150: * .. Intrinsic Functions ..
151: INTRINSIC DCONJG
152: * ..
153: * .. Executable Statements ..
154: *
155: * Quick return if possible
156: *
157: IF( N.EQ.0 .OR. NRHS.EQ.0 )
158: $ RETURN
159: *
160: IF( ITRANS.EQ.0 ) THEN
161: *
162: * Solve A*X = B using the LU factorization of A,
163: * overwriting each right hand side vector with its solution.
164: *
165: IF( NRHS.LE.1 ) THEN
166: J = 1
167: 10 CONTINUE
168: *
169: * Solve L*x = b.
170: *
171: DO 20 I = 1, N - 1
172: IF( IPIV( I ).EQ.I ) THEN
173: B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
174: ELSE
175: TEMP = B( I, J )
176: B( I, J ) = B( I+1, J )
177: B( I+1, J ) = TEMP - DL( I )*B( I, J )
178: END IF
179: 20 CONTINUE
180: *
181: * Solve U*x = b.
182: *
183: B( N, J ) = B( N, J ) / D( N )
184: IF( N.GT.1 )
185: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
186: $ D( N-1 )
187: DO 30 I = N - 2, 1, -1
188: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
189: $ B( I+2, J ) ) / D( I )
190: 30 CONTINUE
191: IF( J.LT.NRHS ) THEN
192: J = J + 1
193: GO TO 10
194: END IF
195: ELSE
196: DO 60 J = 1, NRHS
197: *
198: * Solve L*x = b.
199: *
200: DO 40 I = 1, N - 1
201: IF( IPIV( I ).EQ.I ) THEN
202: B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
203: ELSE
204: TEMP = B( I, J )
205: B( I, J ) = B( I+1, J )
206: B( I+1, J ) = TEMP - DL( I )*B( I, J )
207: END IF
208: 40 CONTINUE
209: *
210: * Solve U*x = b.
211: *
212: B( N, J ) = B( N, J ) / D( N )
213: IF( N.GT.1 )
214: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
215: $ D( N-1 )
216: DO 50 I = N - 2, 1, -1
217: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
218: $ B( I+2, J ) ) / D( I )
219: 50 CONTINUE
220: 60 CONTINUE
221: END IF
222: ELSE IF( ITRANS.EQ.1 ) THEN
223: *
224: * Solve A**T * X = B.
225: *
226: IF( NRHS.LE.1 ) THEN
227: J = 1
228: 70 CONTINUE
229: *
230: * Solve U**T * x = b.
231: *
232: B( 1, J ) = B( 1, J ) / D( 1 )
233: IF( N.GT.1 )
234: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
235: DO 80 I = 3, N
236: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
237: $ B( I-2, J ) ) / D( I )
238: 80 CONTINUE
239: *
240: * Solve L**T * x = b.
241: *
242: DO 90 I = N - 1, 1, -1
243: IF( IPIV( I ).EQ.I ) THEN
244: B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
245: ELSE
246: TEMP = B( I+1, J )
247: B( I+1, J ) = B( I, J ) - DL( I )*TEMP
248: B( I, J ) = TEMP
249: END IF
250: 90 CONTINUE
251: IF( J.LT.NRHS ) THEN
252: J = J + 1
253: GO TO 70
254: END IF
255: ELSE
256: DO 120 J = 1, NRHS
257: *
258: * Solve U**T * x = b.
259: *
260: B( 1, J ) = B( 1, J ) / D( 1 )
261: IF( N.GT.1 )
262: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
263: DO 100 I = 3, N
264: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
265: $ DU2( I-2 )*B( I-2, J ) ) / D( I )
266: 100 CONTINUE
267: *
268: * Solve L**T * x = b.
269: *
270: DO 110 I = N - 1, 1, -1
271: IF( IPIV( I ).EQ.I ) THEN
272: B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
273: ELSE
274: TEMP = B( I+1, J )
275: B( I+1, J ) = B( I, J ) - DL( I )*TEMP
276: B( I, J ) = TEMP
277: END IF
278: 110 CONTINUE
279: 120 CONTINUE
280: END IF
281: ELSE
282: *
283: * Solve A**H * X = B.
284: *
285: IF( NRHS.LE.1 ) THEN
286: J = 1
287: 130 CONTINUE
288: *
289: * Solve U**H * x = b.
290: *
291: B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) )
292: IF( N.GT.1 )
293: $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) /
294: $ DCONJG( D( 2 ) )
295: DO 140 I = 3, N
296: B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*B( I-1, J )-
297: $ DCONJG( DU2( I-2 ) )*B( I-2, J ) ) /
298: $ DCONJG( D( I ) )
299: 140 CONTINUE
300: *
301: * Solve L**H * x = b.
302: *
303: DO 150 I = N - 1, 1, -1
304: IF( IPIV( I ).EQ.I ) THEN
305: B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*B( I+1, J )
306: ELSE
307: TEMP = B( I+1, J )
308: B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP
309: B( I, J ) = TEMP
310: END IF
311: 150 CONTINUE
312: IF( J.LT.NRHS ) THEN
313: J = J + 1
314: GO TO 130
315: END IF
316: ELSE
317: DO 180 J = 1, NRHS
318: *
319: * Solve U**H * x = b.
320: *
321: B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) )
322: IF( N.GT.1 )
323: $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) )
324: $ / DCONJG( D( 2 ) )
325: DO 160 I = 3, N
326: B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*
327: $ B( I-1, J )-DCONJG( DU2( I-2 ) )*
328: $ B( I-2, J ) ) / DCONJG( D( I ) )
329: 160 CONTINUE
330: *
331: * Solve L**H * x = b.
332: *
333: DO 170 I = N - 1, 1, -1
334: IF( IPIV( I ).EQ.I ) THEN
335: B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*
336: $ B( I+1, J )
337: ELSE
338: TEMP = B( I+1, J )
339: B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP
340: B( I, J ) = TEMP
341: END IF
342: 170 CONTINUE
343: 180 CONTINUE
344: END IF
345: END IF
346: *
347: * End of ZGTTS2
348: *
349: END
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