LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zpbtrs.f
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1 *> \brief \b ZPBTRS
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
22 *
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 * ..
30 *
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 *
112 *> \author Univ. of Tennessee
113 *> \author Univ. of California Berkeley
114 *> \author Univ. of Colorado Denver
115 *> \author NAG Ltd.
116 *
117 *> \ingroup complex16OTHERcomputational
118 *
119 * =====================================================================
120  SUBROUTINE zpbtrs( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
121 *
122 * -- LAPACK computational routine --
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 *
181 * Solve A*X = B where A = U**H *U.
182 *
183  DO 10 j = 1, nrhs
184 *
185 * Solve U**H *X = B, overwriting B with X.
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 *
197 * Solve A*X = B where A = L*L**H.
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 *
206 * Solve L**H *X = B, overwriting B with X.
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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBSV
Definition: ztbsv.f:189
subroutine zpbtrs(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
ZPBTRS
Definition: zpbtrs.f:121