Annotation of rpl/lapack/lapack/ztbtrs.f, revision 1.14
1.8 bertrand 1: *> \brief \b ZTBTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 ! bertrand 9: *> Download ZTBTRS + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztbtrs.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztbtrs.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztbtrs.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 ! bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
22: * LDB, INFO )
1.14 ! bertrand 23: *
1.8 bertrand 24: * .. Scalar Arguments ..
25: * CHARACTER DIAG, TRANS, UPLO
26: * INTEGER INFO, KD, LDAB, LDB, N, NRHS
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 AB( LDAB, * ), B( LDB, * )
30: * ..
1.14 ! bertrand 31: *
1.8 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZTBTRS solves a triangular system of the form
39: *>
40: *> A * X = B, A**T * X = B, or A**H * 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 of 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)
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 COMPLEX*16 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 COMPLEX*16 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: *
1.14 ! bertrand 136: *> \author Univ. of Tennessee
! 137: *> \author Univ. of California Berkeley
! 138: *> \author Univ. of Colorado Denver
! 139: *> \author NAG Ltd.
1.8 bertrand 140: *
1.14 ! bertrand 141: *> \date December 2016
1.8 bertrand 142: *
143: *> \ingroup complex16OTHERcomputational
144: *
145: * =====================================================================
1.1 bertrand 146: SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
147: $ LDB, INFO )
148: *
1.14 ! bertrand 149: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 150: * -- LAPACK is a software package provided by Univ. of Tennessee, --
151: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 ! bertrand 152: * December 2016
1.1 bertrand 153: *
154: * .. Scalar Arguments ..
155: CHARACTER DIAG, TRANS, UPLO
156: INTEGER INFO, KD, LDAB, LDB, N, NRHS
157: * ..
158: * .. Array Arguments ..
159: COMPLEX*16 AB( LDAB, * ), B( LDB, * )
160: * ..
161: *
162: * =====================================================================
163: *
164: * .. Parameters ..
165: COMPLEX*16 ZERO
166: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
167: * ..
168: * .. Local Scalars ..
169: LOGICAL NOUNIT, UPPER
170: INTEGER J
171: * ..
172: * .. External Functions ..
173: LOGICAL LSAME
174: EXTERNAL LSAME
175: * ..
176: * .. External Subroutines ..
177: EXTERNAL XERBLA, ZTBSV
178: * ..
179: * .. Intrinsic Functions ..
180: INTRINSIC MAX
181: * ..
182: * .. Executable Statements ..
183: *
184: * Test the input parameters.
185: *
186: INFO = 0
187: NOUNIT = LSAME( DIAG, 'N' )
188: UPPER = LSAME( UPLO, 'U' )
189: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
190: INFO = -1
191: ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
192: $ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
193: INFO = -2
194: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
195: INFO = -3
196: ELSE IF( N.LT.0 ) THEN
197: INFO = -4
198: ELSE IF( KD.LT.0 ) THEN
199: INFO = -5
200: ELSE IF( NRHS.LT.0 ) THEN
201: INFO = -6
202: ELSE IF( LDAB.LT.KD+1 ) THEN
203: INFO = -8
204: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
205: INFO = -10
206: END IF
207: IF( INFO.NE.0 ) THEN
208: CALL XERBLA( 'ZTBTRS', -INFO )
209: RETURN
210: END IF
211: *
212: * Quick return if possible
213: *
214: IF( N.EQ.0 )
215: $ RETURN
216: *
217: * Check for singularity.
218: *
219: IF( NOUNIT ) THEN
220: IF( UPPER ) THEN
221: DO 10 INFO = 1, N
222: IF( AB( KD+1, INFO ).EQ.ZERO )
223: $ RETURN
224: 10 CONTINUE
225: ELSE
226: DO 20 INFO = 1, N
227: IF( AB( 1, INFO ).EQ.ZERO )
228: $ RETURN
229: 20 CONTINUE
230: END IF
231: END IF
232: INFO = 0
233: *
234: * Solve A * X = B, A**T * X = B, or A**H * X = B.
235: *
236: DO 30 J = 1, NRHS
237: CALL ZTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, B( 1, J ), 1 )
238: 30 CONTINUE
239: *
240: RETURN
241: *
242: * End of ZTBTRS
243: *
244: END
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