Annotation of rpl/lapack/lapack/dpbtrs.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DPBTRS
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 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">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DPBTRS( 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: * DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
! 29: * ..
! 30: *
! 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: *
! 112: *> \author Univ. of Tennessee
! 113: *> \author Univ. of California Berkeley
! 114: *> \author Univ. of Colorado Denver
! 115: *> \author NAG Ltd.
! 116: *
! 117: *> \date November 2011
! 118: *
! 119: *> \ingroup doubleOTHERcomputational
! 120: *
! 121: * =====================================================================
1.1 bertrand 122: SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
123: *
1.9 ! bertrand 124: * -- LAPACK computational routine (version 3.4.0) --
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..--
1.9 ! bertrand 127: * November 2011
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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