Annotation of rpl/lapack/lapack/zgtsv.f, revision 1.19
1.16 bertrand 1: *> \brief <b> ZGTSV computes the solution to system of linear equations A * X = B for GT matrices </b>
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 9: *> Download ZGTSV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgtsv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgtsv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgtsv.f">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
1.16 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDB, N, NRHS
25: * ..
26: * .. Array Arguments ..
27: * COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )
28: * ..
1.16 bertrand 29: *
1.9 bertrand 30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> ZGTSV solves the equation
37: *>
38: *> A*X = B,
39: *>
40: *> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
41: *> partial pivoting.
42: *>
43: *> Note that the equation A**T *X = B may be solved by interchanging the
44: *> order of the arguments DU and DL.
45: *> \endverbatim
46: *
47: * Arguments:
48: * ==========
49: *
50: *> \param[in] N
51: *> \verbatim
52: *> N is INTEGER
53: *> The order of the matrix A. N >= 0.
54: *> \endverbatim
55: *>
56: *> \param[in] NRHS
57: *> \verbatim
58: *> NRHS is INTEGER
59: *> The number of right hand sides, i.e., the number of columns
60: *> of the matrix B. NRHS >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in,out] DL
64: *> \verbatim
65: *> DL is COMPLEX*16 array, dimension (N-1)
66: *> On entry, DL must contain the (n-1) subdiagonal elements of
67: *> A.
68: *> On exit, DL is overwritten by the (n-2) elements of the
69: *> second superdiagonal of the upper triangular matrix U from
70: *> the LU factorization of A, in DL(1), ..., DL(n-2).
71: *> \endverbatim
72: *>
73: *> \param[in,out] D
74: *> \verbatim
75: *> D is COMPLEX*16 array, dimension (N)
76: *> On entry, D must contain the diagonal elements of A.
77: *> On exit, D is overwritten by the n diagonal elements of U.
78: *> \endverbatim
79: *>
80: *> \param[in,out] DU
81: *> \verbatim
82: *> DU is COMPLEX*16 array, dimension (N-1)
83: *> On entry, DU must contain the (n-1) superdiagonal elements
84: *> of A.
85: *> On exit, DU is overwritten by the (n-1) elements of the first
86: *> superdiagonal of U.
87: *> \endverbatim
88: *>
89: *> \param[in,out] B
90: *> \verbatim
91: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
92: *> On entry, the N-by-NRHS right hand side matrix B.
93: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
94: *> \endverbatim
95: *>
96: *> \param[in] LDB
97: *> \verbatim
98: *> LDB is INTEGER
99: *> The leading dimension of the array B. LDB >= max(1,N).
100: *> \endverbatim
101: *>
102: *> \param[out] INFO
103: *> \verbatim
104: *> INFO is INTEGER
105: *> = 0: successful exit
106: *> < 0: if INFO = -i, the i-th argument had an illegal value
107: *> > 0: if INFO = i, U(i,i) is exactly zero, and the solution
108: *> has not been computed. The factorization has not been
109: *> completed unless i = N.
110: *> \endverbatim
111: *
112: * Authors:
113: * ========
114: *
1.16 bertrand 115: *> \author Univ. of Tennessee
116: *> \author Univ. of California Berkeley
117: *> \author Univ. of Colorado Denver
118: *> \author NAG Ltd.
1.9 bertrand 119: *
1.12 bertrand 120: *> \ingroup complex16GTsolve
1.9 bertrand 121: *
122: * =====================================================================
1.1 bertrand 123: SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
124: *
1.19 ! bertrand 125: * -- LAPACK driver routine --
1.1 bertrand 126: * -- LAPACK is a software package provided by Univ. of Tennessee, --
127: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128: *
129: * .. Scalar Arguments ..
130: INTEGER INFO, LDB, N, NRHS
131: * ..
132: * .. Array Arguments ..
133: COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )
134: * ..
135: *
136: * =====================================================================
137: *
138: * .. Parameters ..
139: COMPLEX*16 ZERO
140: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
141: * ..
142: * .. Local Scalars ..
143: INTEGER J, K
144: COMPLEX*16 MULT, TEMP, ZDUM
145: * ..
146: * .. Intrinsic Functions ..
147: INTRINSIC ABS, DBLE, DIMAG, MAX
148: * ..
149: * .. External Subroutines ..
150: EXTERNAL XERBLA
151: * ..
152: * .. Statement Functions ..
153: DOUBLE PRECISION CABS1
154: * ..
155: * .. Statement Function definitions ..
156: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
157: * ..
158: * .. Executable Statements ..
159: *
160: INFO = 0
161: IF( N.LT.0 ) THEN
162: INFO = -1
163: ELSE IF( NRHS.LT.0 ) THEN
164: INFO = -2
165: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
166: INFO = -7
167: END IF
168: IF( INFO.NE.0 ) THEN
169: CALL XERBLA( 'ZGTSV ', -INFO )
170: RETURN
171: END IF
172: *
173: IF( N.EQ.0 )
174: $ RETURN
175: *
176: DO 30 K = 1, N - 1
177: IF( DL( K ).EQ.ZERO ) THEN
178: *
179: * Subdiagonal is zero, no elimination is required.
180: *
181: IF( D( K ).EQ.ZERO ) THEN
182: *
183: * Diagonal is zero: set INFO = K and return; a unique
184: * solution can not be found.
185: *
186: INFO = K
187: RETURN
188: END IF
189: ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
190: *
191: * No row interchange required
192: *
193: MULT = DL( K ) / D( K )
194: D( K+1 ) = D( K+1 ) - MULT*DU( K )
195: DO 10 J = 1, NRHS
196: B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
197: 10 CONTINUE
198: IF( K.LT.( N-1 ) )
199: $ DL( K ) = ZERO
200: ELSE
201: *
202: * Interchange rows K and K+1
203: *
204: MULT = D( K ) / DL( K )
205: D( K ) = DL( K )
206: TEMP = D( K+1 )
207: D( K+1 ) = DU( K ) - MULT*TEMP
208: IF( K.LT.( N-1 ) ) THEN
209: DL( K ) = DU( K+1 )
210: DU( K+1 ) = -MULT*DL( K )
211: END IF
212: DU( K ) = TEMP
213: DO 20 J = 1, NRHS
214: TEMP = B( K, J )
215: B( K, J ) = B( K+1, J )
216: B( K+1, J ) = TEMP - MULT*B( K+1, J )
217: 20 CONTINUE
218: END IF
219: 30 CONTINUE
220: IF( D( N ).EQ.ZERO ) THEN
221: INFO = N
222: RETURN
223: END IF
224: *
225: * Back solve with the matrix U from the factorization.
226: *
227: DO 50 J = 1, NRHS
228: B( N, J ) = B( N, J ) / D( N )
229: IF( N.GT.1 )
230: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
231: DO 40 K = N - 2, 1, -1
232: B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
233: $ B( K+2, J ) ) / D( K )
234: 40 CONTINUE
235: 50 CONTINUE
236: *
237: RETURN
238: *
239: * End of ZGTSV
240: *
241: END
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