LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
stbtrs.f
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1 *> \brief \b STBTRS
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE STBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
22 * LDB, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER DIAG, TRANS, UPLO
26 * INTEGER INFO, KD, LDAB, LDB, N, NRHS
27 * ..
28 * .. Array Arguments ..
29 * REAL AB( LDAB, * ), B( LDB, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> STBTRS solves a triangular system of the form
39 *>
40 *> A * X = B or A**T * X = B,
41 *>
42 *> where A is a triangular band matrix of order N, and B is an
43 *> N-by NRHS matrix. A check is made to verify that A is nonsingular.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] UPLO
50 *> \verbatim
51 *> UPLO is CHARACTER*1
52 *> = 'U': A is upper triangular;
53 *> = 'L': A is lower triangular.
54 *> \endverbatim
55 *>
56 *> \param[in] TRANS
57 *> \verbatim
58 *> TRANS is CHARACTER*1
59 *> Specifies the form the system of equations:
60 *> = 'N': A * X = B (No transpose)
61 *> = 'T': A**T * X = B (Transpose)
62 *> = 'C': A**H * X = B (Conjugate transpose = Transpose)
63 *> \endverbatim
64 *>
65 *> \param[in] DIAG
66 *> \verbatim
67 *> DIAG is CHARACTER*1
68 *> = 'N': A is non-unit triangular;
69 *> = 'U': A is unit triangular.
70 *> \endverbatim
71 *>
72 *> \param[in] N
73 *> \verbatim
74 *> N is INTEGER
75 *> The order of the matrix A. N >= 0.
76 *> \endverbatim
77 *>
78 *> \param[in] KD
79 *> \verbatim
80 *> KD is INTEGER
81 *> The number of superdiagonals or subdiagonals of the
82 *> triangular band matrix A. KD >= 0.
83 *> \endverbatim
84 *>
85 *> \param[in] NRHS
86 *> \verbatim
87 *> NRHS is INTEGER
88 *> The number of right hand sides, i.e., the number of columns
89 *> of the matrix B. NRHS >= 0.
90 *> \endverbatim
91 *>
92 *> \param[in] AB
93 *> \verbatim
94 *> AB is REAL array, dimension (LDAB,N)
95 *> The upper or lower triangular band matrix A, stored in the
96 *> first kd+1 rows of AB. The j-th column of A is stored
97 *> in the j-th column of the array AB as follows:
98 *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
99 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
100 *> If DIAG = 'U', the diagonal elements of A are not referenced
101 *> and are assumed to be 1.
102 *> \endverbatim
103 *>
104 *> \param[in] LDAB
105 *> \verbatim
106 *> LDAB is INTEGER
107 *> The leading dimension of the array AB. LDAB >= KD+1.
108 *> \endverbatim
109 *>
110 *> \param[in,out] B
111 *> \verbatim
112 *> B is REAL array, dimension (LDB,NRHS)
113 *> On entry, the right hand side matrix B.
114 *> On exit, if INFO = 0, the solution matrix X.
115 *> \endverbatim
116 *>
117 *> \param[in] LDB
118 *> \verbatim
119 *> LDB is INTEGER
120 *> The leading dimension of the array B. LDB >= max(1,N).
121 *> \endverbatim
122 *>
123 *> \param[out] INFO
124 *> \verbatim
125 *> INFO is INTEGER
126 *> = 0: successful exit
127 *> < 0: if INFO = -i, the i-th argument had an illegal value
128 *> > 0: if INFO = i, the i-th diagonal element of A is zero,
129 *> indicating that the matrix is singular and the
130 *> solutions X have not been computed.
131 *> \endverbatim
132 *
133 * Authors:
134 * ========
135 *
136 *> \author Univ. of Tennessee
137 *> \author Univ. of California Berkeley
138 *> \author Univ. of Colorado Denver
139 *> \author NAG Ltd.
140 *
141 *> \ingroup realOTHERcomputational
142 *
143 * =====================================================================
144  SUBROUTINE stbtrs( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
145  \$ LDB, INFO )
146 *
147 * -- LAPACK computational routine --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 *
151 * .. Scalar Arguments ..
152  CHARACTER DIAG, TRANS, UPLO
153  INTEGER INFO, KD, LDAB, LDB, N, NRHS
154 * ..
155 * .. Array Arguments ..
156  REAL AB( LDAB, * ), B( LDB, * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  REAL ZERO
163  parameter( zero = 0.0e+0 )
164 * ..
165 * .. Local Scalars ..
166  LOGICAL NOUNIT, UPPER
167  INTEGER J
168 * ..
169 * .. External Functions ..
170  LOGICAL LSAME
171  EXTERNAL lsame
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL stbsv, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC max
178 * ..
179 * .. Executable Statements ..
180 *
181 * Test the input parameters.
182 *
183  info = 0
184  nounit = lsame( diag, 'N' )
185  upper = lsame( uplo, 'U' )
186  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
187  info = -1
188  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
189  \$ lsame( trans, 'T' ) .AND. .NOT.lsame( trans, 'C' ) ) THEN
190  info = -2
191  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
192  info = -3
193  ELSE IF( n.LT.0 ) THEN
194  info = -4
195  ELSE IF( kd.LT.0 ) THEN
196  info = -5
197  ELSE IF( nrhs.LT.0 ) THEN
198  info = -6
199  ELSE IF( ldab.LT.kd+1 ) THEN
200  info = -8
201  ELSE IF( ldb.LT.max( 1, n ) ) THEN
202  info = -10
203  END IF
204  IF( info.NE.0 ) THEN
205  CALL xerbla( 'STBTRS', -info )
206  RETURN
207  END IF
208 *
209 * Quick return if possible
210 *
211  IF( n.EQ.0 )
212  \$ RETURN
213 *
214 * Check for singularity.
215 *
216  IF( nounit ) THEN
217  IF( upper ) THEN
218  DO 10 info = 1, n
219  IF( ab( kd+1, info ).EQ.zero )
220  \$ RETURN
221  10 CONTINUE
222  ELSE
223  DO 20 info = 1, n
224  IF( ab( 1, info ).EQ.zero )
225  \$ RETURN
226  20 CONTINUE
227  END IF
228  END IF
229  info = 0
230 *
231 * Solve A * X = B or A**T * X = B.
232 *
233  DO 30 j = 1, nrhs
234  CALL stbsv( uplo, trans, diag, n, kd, ab, ldab, b( 1, j ), 1 )
235  30 CONTINUE
236 *
237  RETURN
238 *
239 * End of STBTRS
240 *
241  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine stbtrs(UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
STBTRS
Definition: stbtrs.f:146
subroutine stbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBSV
Definition: stbsv.f:189