Annotation of rpl/lapack/lapack/dgtts2.f, revision 1.15
1.12 bertrand 1: *> \brief \b DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DGTTS2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgtts2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgtts2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgtts2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGTTS2( 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: * DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DGTTS2 solves one of the systems of equations
38: *> A*X = B or A**T*X = B,
39: *> with a tridiagonal matrix A using the LU factorization computed
40: *> by DGTTRF.
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**T* X = B (Conjugate transpose = 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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: *
1.12 bertrand 124: *> \date September 2012
1.9 bertrand 125: *
1.12 bertrand 126: *> \ingroup doubleGTcomputational
1.9 bertrand 127: *
128: * =====================================================================
1.1 bertrand 129: SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
130: *
1.12 bertrand 131: * -- LAPACK computational routine (version 3.4.2) --
1.1 bertrand 132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.12 bertrand 134: * September 2012
1.1 bertrand 135: *
136: * .. Scalar Arguments ..
137: INTEGER ITRANS, LDB, N, NRHS
138: * ..
139: * .. Array Arguments ..
140: INTEGER IPIV( * )
141: DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
142: * ..
143: *
144: * =====================================================================
145: *
146: * .. Local Scalars ..
147: INTEGER I, IP, J
148: DOUBLE PRECISION TEMP
149: * ..
150: * .. Executable Statements ..
151: *
152: * Quick return if possible
153: *
154: IF( N.EQ.0 .OR. NRHS.EQ.0 )
155: $ RETURN
156: *
157: IF( ITRANS.EQ.0 ) THEN
158: *
159: * Solve A*X = B using the LU factorization of A,
160: * overwriting each right hand side vector with its solution.
161: *
162: IF( NRHS.LE.1 ) THEN
163: J = 1
164: 10 CONTINUE
165: *
166: * Solve L*x = b.
167: *
168: DO 20 I = 1, N - 1
169: IP = IPIV( I )
170: TEMP = B( I+1-IP+I, J ) - DL( I )*B( IP, J )
171: B( I, J ) = B( IP, J )
172: B( I+1, J ) = TEMP
173: 20 CONTINUE
174: *
175: * Solve U*x = b.
176: *
177: B( N, J ) = B( N, J ) / D( N )
178: IF( N.GT.1 )
179: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
180: $ D( N-1 )
181: DO 30 I = N - 2, 1, -1
182: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
183: $ B( I+2, J ) ) / D( I )
184: 30 CONTINUE
185: IF( J.LT.NRHS ) THEN
186: J = J + 1
187: GO TO 10
188: END IF
189: ELSE
190: DO 60 J = 1, NRHS
191: *
192: * Solve L*x = b.
193: *
194: DO 40 I = 1, N - 1
195: IF( IPIV( I ).EQ.I ) THEN
196: B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
197: ELSE
198: TEMP = B( I, J )
199: B( I, J ) = B( I+1, J )
200: B( I+1, J ) = TEMP - DL( I )*B( I, J )
201: END IF
202: 40 CONTINUE
203: *
204: * Solve U*x = b.
205: *
206: B( N, J ) = B( N, J ) / D( N )
207: IF( N.GT.1 )
208: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
209: $ D( N-1 )
210: DO 50 I = N - 2, 1, -1
211: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
212: $ B( I+2, J ) ) / D( I )
213: 50 CONTINUE
214: 60 CONTINUE
215: END IF
216: ELSE
217: *
1.8 bertrand 218: * Solve A**T * X = B.
1.1 bertrand 219: *
220: IF( NRHS.LE.1 ) THEN
221: *
1.8 bertrand 222: * Solve U**T*x = b.
1.1 bertrand 223: *
224: J = 1
225: 70 CONTINUE
226: B( 1, J ) = B( 1, J ) / D( 1 )
227: IF( N.GT.1 )
228: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
229: DO 80 I = 3, N
230: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
231: $ B( I-2, J ) ) / D( I )
232: 80 CONTINUE
233: *
1.8 bertrand 234: * Solve L**T*x = b.
1.1 bertrand 235: *
236: DO 90 I = N - 1, 1, -1
237: IP = IPIV( I )
238: TEMP = B( I, J ) - DL( I )*B( I+1, J )
239: B( I, J ) = B( IP, J )
240: B( IP, J ) = TEMP
241: 90 CONTINUE
242: IF( J.LT.NRHS ) THEN
243: J = J + 1
244: GO TO 70
245: END IF
246: *
247: ELSE
248: DO 120 J = 1, NRHS
249: *
1.8 bertrand 250: * Solve U**T*x = b.
1.1 bertrand 251: *
252: B( 1, J ) = B( 1, J ) / D( 1 )
253: IF( N.GT.1 )
254: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
255: DO 100 I = 3, N
256: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
257: $ DU2( I-2 )*B( I-2, J ) ) / D( I )
258: 100 CONTINUE
259: DO 110 I = N - 1, 1, -1
260: IF( IPIV( I ).EQ.I ) THEN
261: B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
262: ELSE
263: TEMP = B( I+1, J )
264: B( I+1, J ) = B( I, J ) - DL( I )*TEMP
265: B( I, J ) = TEMP
266: END IF
267: 110 CONTINUE
268: 120 CONTINUE
269: END IF
270: END IF
271: *
272: * End of DGTTS2
273: *
274: END
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