Annotation of rpl/lapack/lapack/dpbtrs.f, revision 1.15
1.9 bertrand 1: *> \brief \b DPBTRS
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 DPBTRS + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbtrs.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbtrs.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbtrs.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 ! bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPBTRS( 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: * DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
29: * ..
1.15 ! bertrand 30: *
1.9 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPBTRS solves a system of linear equations A*X = B with a symmetric
38: *> positive definite band matrix A using the Cholesky factorization
39: *> A = U**T*U or A = L*L**T computed by DPBTRF.
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 DOUBLE PRECISION array, dimension (LDAB,N)
75: *> The triangular factor U or L from the Cholesky factorization
76: *> A = U**T*U or A = L*L**T 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 DOUBLE PRECISION 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: *
1.15 ! bertrand 117: *> \date December 2016
1.9 bertrand 118: *
119: *> \ingroup doubleOTHERcomputational
120: *
121: * =====================================================================
1.1 bertrand 122: SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
123: *
1.15 ! bertrand 124: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 ! bertrand 127: * December 2016
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: CHARACTER UPLO
131: INTEGER INFO, KD, LDAB, LDB, N, NRHS
132: * ..
133: * .. Array Arguments ..
134: DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
135: * ..
136: *
137: * =====================================================================
138: *
139: * .. Local Scalars ..
140: LOGICAL UPPER
141: INTEGER J
142: * ..
143: * .. External Functions ..
144: LOGICAL LSAME
145: EXTERNAL LSAME
146: * ..
147: * .. External Subroutines ..
148: EXTERNAL DTBSV, XERBLA
149: * ..
150: * .. Intrinsic Functions ..
151: INTRINSIC MAX
152: * ..
153: * .. Executable Statements ..
154: *
155: * Test the input parameters.
156: *
157: INFO = 0
158: UPPER = LSAME( UPLO, 'U' )
159: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
160: INFO = -1
161: ELSE IF( N.LT.0 ) THEN
162: INFO = -2
163: ELSE IF( KD.LT.0 ) THEN
164: INFO = -3
165: ELSE IF( NRHS.LT.0 ) THEN
166: INFO = -4
167: ELSE IF( LDAB.LT.KD+1 ) THEN
168: INFO = -6
169: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
170: INFO = -8
171: END IF
172: IF( INFO.NE.0 ) THEN
173: CALL XERBLA( 'DPBTRS', -INFO )
174: RETURN
175: END IF
176: *
177: * Quick return if possible
178: *
179: IF( N.EQ.0 .OR. NRHS.EQ.0 )
180: $ RETURN
181: *
182: IF( UPPER ) THEN
183: *
1.8 bertrand 184: * Solve A*X = B where A = U**T *U.
1.1 bertrand 185: *
186: DO 10 J = 1, NRHS
187: *
1.8 bertrand 188: * Solve U**T *X = B, overwriting B with X.
1.1 bertrand 189: *
190: CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
191: $ LDAB, B( 1, J ), 1 )
192: *
193: * Solve U*X = B, overwriting B with X.
194: *
195: CALL DTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
196: $ LDAB, B( 1, J ), 1 )
197: 10 CONTINUE
198: ELSE
199: *
1.8 bertrand 200: * Solve A*X = B where A = L*L**T.
1.1 bertrand 201: *
202: DO 20 J = 1, NRHS
203: *
204: * Solve L*X = B, overwriting B with X.
205: *
206: CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
207: $ LDAB, B( 1, J ), 1 )
208: *
1.8 bertrand 209: * Solve L**T *X = B, overwriting B with X.
1.1 bertrand 210: *
211: CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
212: $ LDAB, B( 1, J ), 1 )
213: 20 CONTINUE
214: END IF
215: *
216: RETURN
217: *
218: * End of DPBTRS
219: *
220: END
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