Annotation of rpl/lapack/lapack/zpbtrs.f, revision 1.18
1.9 bertrand 1: *> \brief \b ZPBTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download ZPBTRS + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpbtrs.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpbtrs.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpbtrs.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
1.15 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, KD, LDAB, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 AB( LDAB, * ), B( LDB, * )
29: * ..
1.15 bertrand 30: *
1.9 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZPBTRS solves a system of linear equations A*X = B with a Hermitian
38: *> positive definite band matrix A using the Cholesky factorization
39: *> A = U**H *U or A = L*L**H computed by ZPBTRF.
40: *> \endverbatim
41: *
42: * Arguments:
43: * ==========
44: *
45: *> \param[in] UPLO
46: *> \verbatim
47: *> UPLO is CHARACTER*1
48: *> = 'U': Upper triangular factor stored in AB;
49: *> = 'L': Lower triangular factor stored in AB.
50: *> \endverbatim
51: *>
52: *> \param[in] N
53: *> \verbatim
54: *> N is INTEGER
55: *> The order of the matrix A. N >= 0.
56: *> \endverbatim
57: *>
58: *> \param[in] KD
59: *> \verbatim
60: *> KD is INTEGER
61: *> The number of superdiagonals of the matrix A if UPLO = 'U',
62: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] NRHS
66: *> \verbatim
67: *> NRHS is INTEGER
68: *> The number of right hand sides, i.e., the number of columns
69: *> of the matrix B. NRHS >= 0.
70: *> \endverbatim
71: *>
72: *> \param[in] AB
73: *> \verbatim
74: *> AB is COMPLEX*16 array, dimension (LDAB,N)
75: *> The triangular factor U or L from the Cholesky factorization
76: *> A = U**H *U or A = L*L**H of the band matrix A, stored in the
77: *> first KD+1 rows of the array. The j-th column of U or L is
78: *> stored in the j-th column of the array AB as follows:
79: *> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
80: *> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
81: *> \endverbatim
82: *>
83: *> \param[in] LDAB
84: *> \verbatim
85: *> LDAB is INTEGER
86: *> The leading dimension of the array AB. LDAB >= KD+1.
87: *> \endverbatim
88: *>
89: *> \param[in,out] B
90: *> \verbatim
91: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
92: *> On entry, the right hand side matrix B.
93: *> On exit, the 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: *> \endverbatim
108: *
109: * Authors:
110: * ========
111: *
1.15 bertrand 112: *> \author Univ. of Tennessee
113: *> \author Univ. of California Berkeley
114: *> \author Univ. of Colorado Denver
115: *> \author NAG Ltd.
1.9 bertrand 116: *
117: *> \ingroup complex16OTHERcomputational
118: *
119: * =====================================================================
1.1 bertrand 120: SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
121: *
1.18 ! bertrand 122: * -- LAPACK computational routine --
1.1 bertrand 123: * -- LAPACK is a software package provided by Univ. of Tennessee, --
124: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125: *
126: * .. Scalar Arguments ..
127: CHARACTER UPLO
128: INTEGER INFO, KD, LDAB, LDB, N, NRHS
129: * ..
130: * .. Array Arguments ..
131: COMPLEX*16 AB( LDAB, * ), B( LDB, * )
132: * ..
133: *
134: * =====================================================================
135: *
136: * .. Local Scalars ..
137: LOGICAL UPPER
138: INTEGER J
139: * ..
140: * .. External Functions ..
141: LOGICAL LSAME
142: EXTERNAL LSAME
143: * ..
144: * .. External Subroutines ..
145: EXTERNAL XERBLA, ZTBSV
146: * ..
147: * .. Intrinsic Functions ..
148: INTRINSIC MAX
149: * ..
150: * .. Executable Statements ..
151: *
152: * Test the input parameters.
153: *
154: INFO = 0
155: UPPER = LSAME( UPLO, 'U' )
156: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
157: INFO = -1
158: ELSE IF( N.LT.0 ) THEN
159: INFO = -2
160: ELSE IF( KD.LT.0 ) THEN
161: INFO = -3
162: ELSE IF( NRHS.LT.0 ) THEN
163: INFO = -4
164: ELSE IF( LDAB.LT.KD+1 ) THEN
165: INFO = -6
166: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
167: INFO = -8
168: END IF
169: IF( INFO.NE.0 ) THEN
170: CALL XERBLA( 'ZPBTRS', -INFO )
171: RETURN
172: END IF
173: *
174: * Quick return if possible
175: *
176: IF( N.EQ.0 .OR. NRHS.EQ.0 )
177: $ RETURN
178: *
179: IF( UPPER ) THEN
180: *
1.8 bertrand 181: * Solve A*X = B where A = U**H *U.
1.1 bertrand 182: *
183: DO 10 J = 1, NRHS
184: *
1.8 bertrand 185: * Solve U**H *X = B, overwriting B with X.
1.1 bertrand 186: *
187: CALL ZTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
188: $ KD, AB, LDAB, B( 1, J ), 1 )
189: *
190: * Solve U*X = B, overwriting B with X.
191: *
192: CALL ZTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
193: $ LDAB, B( 1, J ), 1 )
194: 10 CONTINUE
195: ELSE
196: *
1.8 bertrand 197: * Solve A*X = B where A = L*L**H.
1.1 bertrand 198: *
199: DO 20 J = 1, NRHS
200: *
201: * Solve L*X = B, overwriting B with X.
202: *
203: CALL ZTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
204: $ LDAB, B( 1, J ), 1 )
205: *
1.8 bertrand 206: * Solve L**H *X = B, overwriting B with X.
1.1 bertrand 207: *
208: CALL ZTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
209: $ KD, AB, LDAB, B( 1, J ), 1 )
210: 20 CONTINUE
211: END IF
212: *
213: RETURN
214: *
215: * End of ZPBTRS
216: *
217: END
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