LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dgbsv.f
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00001 *> \brief <b> DGBSV computes the solution to system of linear equations A * X = B for GB matrices</b> (simple driver)
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DGBSV + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgbsv.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgbsv.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
00025 *       ..
00026 *       .. Array Arguments ..
00027 *       INTEGER            IPIV( * )
00028 *       DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> DGBSV computes the solution to a real system of linear equations
00038 *> A * X = B, where A is a band matrix of order N with KL subdiagonals
00039 *> and KU superdiagonals, and X and B are N-by-NRHS matrices.
00040 *>
00041 *> The LU decomposition with partial pivoting and row interchanges is
00042 *> used to factor A as A = L * U, where L is a product of permutation
00043 *> and unit lower triangular matrices with KL subdiagonals, and U is
00044 *> upper triangular with KL+KU superdiagonals.  The factored form of A
00045 *> is then used to solve the system of equations A * X = B.
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] N
00052 *> \verbatim
00053 *>          N is INTEGER
00054 *>          The number of linear equations, i.e., the order of the
00055 *>          matrix A.  N >= 0.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] KL
00059 *> \verbatim
00060 *>          KL is INTEGER
00061 *>          The number of subdiagonals within the band of A.  KL >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] KU
00065 *> \verbatim
00066 *>          KU is INTEGER
00067 *>          The number of superdiagonals within the band of A.  KU >= 0.
00068 *> \endverbatim
00069 *>
00070 *> \param[in] NRHS
00071 *> \verbatim
00072 *>          NRHS is INTEGER
00073 *>          The number of right hand sides, i.e., the number of columns
00074 *>          of the matrix B.  NRHS >= 0.
00075 *> \endverbatim
00076 *>
00077 *> \param[in,out] AB
00078 *> \verbatim
00079 *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
00080 *>          On entry, the matrix A in band storage, in rows KL+1 to
00081 *>          2*KL+KU+1; rows 1 to KL of the array need not be set.
00082 *>          The j-th column of A is stored in the j-th column of the
00083 *>          array AB as follows:
00084 *>          AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
00085 *>          On exit, details of the factorization: U is stored as an
00086 *>          upper triangular band matrix with KL+KU superdiagonals in
00087 *>          rows 1 to KL+KU+1, and the multipliers used during the
00088 *>          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
00089 *>          See below for further details.
00090 *> \endverbatim
00091 *>
00092 *> \param[in] LDAB
00093 *> \verbatim
00094 *>          LDAB is INTEGER
00095 *>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
00096 *> \endverbatim
00097 *>
00098 *> \param[out] IPIV
00099 *> \verbatim
00100 *>          IPIV is INTEGER array, dimension (N)
00101 *>          The pivot indices that define the permutation matrix P;
00102 *>          row i of the matrix was interchanged with row IPIV(i).
00103 *> \endverbatim
00104 *>
00105 *> \param[in,out] B
00106 *> \verbatim
00107 *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
00108 *>          On entry, the N-by-NRHS right hand side matrix B.
00109 *>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
00110 *> \endverbatim
00111 *>
00112 *> \param[in] LDB
00113 *> \verbatim
00114 *>          LDB is INTEGER
00115 *>          The leading dimension of the array B.  LDB >= max(1,N).
00116 *> \endverbatim
00117 *>
00118 *> \param[out] INFO
00119 *> \verbatim
00120 *>          INFO is INTEGER
00121 *>          = 0:  successful exit
00122 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00123 *>          > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization
00124 *>                has been completed, but the factor U is exactly
00125 *>                singular, and the solution has not been computed.
00126 *> \endverbatim
00127 *
00128 *  Authors:
00129 *  ========
00130 *
00131 *> \author Univ. of Tennessee 
00132 *> \author Univ. of California Berkeley 
00133 *> \author Univ. of Colorado Denver 
00134 *> \author NAG Ltd. 
00135 *
00136 *> \date November 2011
00137 *
00138 *> \ingroup doubleGBsolve
00139 *
00140 *> \par Further Details:
00141 *  =====================
00142 *>
00143 *> \verbatim
00144 *>
00145 *>  The band storage scheme is illustrated by the following example, when
00146 *>  M = N = 6, KL = 2, KU = 1:
00147 *>
00148 *>  On entry:                       On exit:
00149 *>
00150 *>      *    *    *    +    +    +       *    *    *   u14  u25  u36
00151 *>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
00152 *>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
00153 *>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
00154 *>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
00155 *>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
00156 *>
00157 *>  Array elements marked * are not used by the routine; elements marked
00158 *>  + need not be set on entry, but are required by the routine to store
00159 *>  elements of U because of fill-in resulting from the row interchanges.
00160 *> \endverbatim
00161 *>
00162 *  =====================================================================
00163       SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
00164 *
00165 *  -- LAPACK driver routine (version 3.4.0) --
00166 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00167 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00168 *     November 2011
00169 *
00170 *     .. Scalar Arguments ..
00171       INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
00172 *     ..
00173 *     .. Array Arguments ..
00174       INTEGER            IPIV( * )
00175       DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
00176 *     ..
00177 *
00178 *  =====================================================================
00179 *
00180 *     .. External Subroutines ..
00181       EXTERNAL           DGBTRF, DGBTRS, XERBLA
00182 *     ..
00183 *     .. Intrinsic Functions ..
00184       INTRINSIC          MAX
00185 *     ..
00186 *     .. Executable Statements ..
00187 *
00188 *     Test the input parameters.
00189 *
00190       INFO = 0
00191       IF( N.LT.0 ) THEN
00192          INFO = -1
00193       ELSE IF( KL.LT.0 ) THEN
00194          INFO = -2
00195       ELSE IF( KU.LT.0 ) THEN
00196          INFO = -3
00197       ELSE IF( NRHS.LT.0 ) THEN
00198          INFO = -4
00199       ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
00200          INFO = -6
00201       ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
00202          INFO = -9
00203       END IF
00204       IF( INFO.NE.0 ) THEN
00205          CALL XERBLA( 'DGBSV ', -INFO )
00206          RETURN
00207       END IF
00208 *
00209 *     Compute the LU factorization of the band matrix A.
00210 *
00211       CALL DGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
00212       IF( INFO.EQ.0 ) THEN
00213 *
00214 *        Solve the system A*X = B, overwriting B with X.
00215 *
00216          CALL DGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
00217      $                B, LDB, INFO )
00218       END IF
00219       RETURN
00220 *
00221 *     End of DGBSV
00222 *
00223       END
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