Annotation of rpl/lapack/lapack/zptts2.f, revision 1.13
1.12 bertrand 1: *> \brief \b ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
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 ZPTTS2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zptts2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zptts2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zptts2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER IUPLO, LDB, N, NRHS
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION D( * )
28: * COMPLEX*16 B( LDB, * ), E( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZPTTS2 solves a tridiagonal system of the form
38: *> A * X = B
39: *> using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF.
40: *> D is a diagonal matrix specified in the vector D, U (or L) is a unit
41: *> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
42: *> the vector E, and X and B are N by NRHS matrices.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] IUPLO
49: *> \verbatim
50: *> IUPLO is INTEGER
51: *> Specifies the form of the factorization and whether the
52: *> vector E is the superdiagonal of the upper bidiagonal factor
53: *> U or the subdiagonal of the lower bidiagonal factor L.
54: *> = 1: A = U**H *D*U, E is the superdiagonal of U
55: *> = 0: A = L*D*L**H, E is the subdiagonal of L
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the tridiagonal matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] NRHS
65: *> \verbatim
66: *> NRHS is INTEGER
67: *> The number of right hand sides, i.e., the number of columns
68: *> of the matrix B. NRHS >= 0.
69: *> \endverbatim
70: *>
71: *> \param[in] D
72: *> \verbatim
73: *> D is DOUBLE PRECISION array, dimension (N)
74: *> The n diagonal elements of the diagonal matrix D from the
75: *> factorization A = U**H *D*U or A = L*D*L**H.
76: *> \endverbatim
77: *>
78: *> \param[in] E
79: *> \verbatim
80: *> E is COMPLEX*16 array, dimension (N-1)
81: *> If IUPLO = 1, the (n-1) superdiagonal elements of the unit
82: *> bidiagonal factor U from the factorization A = U**H*D*U.
83: *> If IUPLO = 0, the (n-1) subdiagonal elements of the unit
84: *> bidiagonal factor L from the factorization A = L*D*L**H.
85: *> \endverbatim
86: *>
87: *> \param[in,out] B
88: *> \verbatim
89: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
90: *> On entry, the right hand side vectors B for the system of
91: *> linear equations.
92: *> On exit, the solution vectors, X.
93: *> \endverbatim
94: *>
95: *> \param[in] LDB
96: *> \verbatim
97: *> LDB is INTEGER
98: *> The leading dimension of the array B. LDB >= max(1,N).
99: *> \endverbatim
100: *
101: * Authors:
102: * ========
103: *
104: *> \author Univ. of Tennessee
105: *> \author Univ. of California Berkeley
106: *> \author Univ. of Colorado Denver
107: *> \author NAG Ltd.
108: *
1.12 bertrand 109: *> \date September 2012
1.9 bertrand 110: *
1.12 bertrand 111: *> \ingroup complex16PTcomputational
1.9 bertrand 112: *
113: * =====================================================================
1.1 bertrand 114: SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
115: *
1.12 bertrand 116: * -- LAPACK computational routine (version 3.4.2) --
1.1 bertrand 117: * -- LAPACK is a software package provided by Univ. of Tennessee, --
118: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.12 bertrand 119: * September 2012
1.1 bertrand 120: *
121: * .. Scalar Arguments ..
122: INTEGER IUPLO, LDB, N, NRHS
123: * ..
124: * .. Array Arguments ..
125: DOUBLE PRECISION D( * )
126: COMPLEX*16 B( LDB, * ), E( * )
127: * ..
128: *
129: * =====================================================================
130: *
131: * .. Local Scalars ..
132: INTEGER I, J
133: * ..
134: * .. External Subroutines ..
135: EXTERNAL ZDSCAL
136: * ..
137: * .. Intrinsic Functions ..
138: INTRINSIC DCONJG
139: * ..
140: * .. Executable Statements ..
141: *
142: * Quick return if possible
143: *
144: IF( N.LE.1 ) THEN
145: IF( N.EQ.1 )
146: $ CALL ZDSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
147: RETURN
148: END IF
149: *
150: IF( IUPLO.EQ.1 ) THEN
151: *
1.8 bertrand 152: * Solve A * X = B using the factorization A = U**H *D*U,
1.1 bertrand 153: * overwriting each right hand side vector with its solution.
154: *
155: IF( NRHS.LE.2 ) THEN
156: J = 1
157: 10 CONTINUE
158: *
1.8 bertrand 159: * Solve U**H * x = b.
1.1 bertrand 160: *
161: DO 20 I = 2, N
162: B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) )
163: 20 CONTINUE
164: *
165: * Solve D * U * x = b.
166: *
167: DO 30 I = 1, N
168: B( I, J ) = B( I, J ) / D( I )
169: 30 CONTINUE
170: DO 40 I = N - 1, 1, -1
171: B( I, J ) = B( I, J ) - B( I+1, J )*E( I )
172: 40 CONTINUE
173: IF( J.LT.NRHS ) THEN
174: J = J + 1
175: GO TO 10
176: END IF
177: ELSE
178: DO 70 J = 1, NRHS
179: *
1.8 bertrand 180: * Solve U**H * x = b.
1.1 bertrand 181: *
182: DO 50 I = 2, N
183: B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) )
184: 50 CONTINUE
185: *
186: * Solve D * U * x = b.
187: *
188: B( N, J ) = B( N, J ) / D( N )
189: DO 60 I = N - 1, 1, -1
190: B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
191: 60 CONTINUE
192: 70 CONTINUE
193: END IF
194: ELSE
195: *
1.8 bertrand 196: * Solve A * X = B using the factorization A = L*D*L**H,
1.1 bertrand 197: * overwriting each right hand side vector with its solution.
198: *
199: IF( NRHS.LE.2 ) THEN
200: J = 1
201: 80 CONTINUE
202: *
203: * Solve L * x = b.
204: *
205: DO 90 I = 2, N
206: B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
207: 90 CONTINUE
208: *
1.8 bertrand 209: * Solve D * L**H * x = b.
1.1 bertrand 210: *
211: DO 100 I = 1, N
212: B( I, J ) = B( I, J ) / D( I )
213: 100 CONTINUE
214: DO 110 I = N - 1, 1, -1
215: B( I, J ) = B( I, J ) - B( I+1, J )*DCONJG( E( I ) )
216: 110 CONTINUE
217: IF( J.LT.NRHS ) THEN
218: J = J + 1
219: GO TO 80
220: END IF
221: ELSE
222: DO 140 J = 1, NRHS
223: *
224: * Solve L * x = b.
225: *
226: DO 120 I = 2, N
227: B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
228: 120 CONTINUE
229: *
1.8 bertrand 230: * Solve D * L**H * x = b.
1.1 bertrand 231: *
232: B( N, J ) = B( N, J ) / D( N )
233: DO 130 I = N - 1, 1, -1
234: B( I, J ) = B( I, J ) / D( I ) -
235: $ B( I+1, J )*DCONJG( E( I ) )
236: 130 CONTINUE
237: 140 CONTINUE
238: END IF
239: END IF
240: *
241: RETURN
242: *
243: * End of ZPTTS2
244: *
245: END
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