LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cpbsv.f
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00001 *> \brief <b> CPBSV computes the solution to system of linear equations A * X = B for OTHER matrices</b>
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CPBSV + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cpbsv.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX            AB( LDAB, * ), B( LDB, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> CPBSV computes the solution to a complex system of linear equations
00038 *>    A * X = B,
00039 *> where A is an N-by-N Hermitian positive definite band matrix and X
00040 *> and B are N-by-NRHS matrices.
00041 *>
00042 *> The Cholesky decomposition is used to factor A as
00043 *>    A = U**H * U,  if UPLO = 'U', or
00044 *>    A = L * L**H,  if UPLO = 'L',
00045 *> where U is an upper triangular band matrix, and L is a lower
00046 *> triangular band matrix, with the same number of superdiagonals or
00047 *> subdiagonals as A.  The factored form of A is then used to solve the
00048 *> system of equations A * X = B.
00049 *> \endverbatim
00050 *
00051 *  Arguments:
00052 *  ==========
00053 *
00054 *> \param[in] UPLO
00055 *> \verbatim
00056 *>          UPLO is CHARACTER*1
00057 *>          = 'U':  Upper triangle of A is stored;
00058 *>          = 'L':  Lower triangle of A is stored.
00059 *> \endverbatim
00060 *>
00061 *> \param[in] N
00062 *> \verbatim
00063 *>          N is INTEGER
00064 *>          The number of linear equations, i.e., the order of the
00065 *>          matrix A.  N >= 0.
00066 *> \endverbatim
00067 *>
00068 *> \param[in] KD
00069 *> \verbatim
00070 *>          KD is INTEGER
00071 *>          The number of superdiagonals of the matrix A if UPLO = 'U',
00072 *>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] NRHS
00076 *> \verbatim
00077 *>          NRHS is INTEGER
00078 *>          The number of right hand sides, i.e., the number of columns
00079 *>          of the matrix B.  NRHS >= 0.
00080 *> \endverbatim
00081 *>
00082 *> \param[in,out] AB
00083 *> \verbatim
00084 *>          AB is COMPLEX array, dimension (LDAB,N)
00085 *>          On entry, the upper or lower triangle of the Hermitian band
00086 *>          matrix A, stored in the first KD+1 rows of the array.  The
00087 *>          j-th column of A is stored in the j-th column of the array AB
00088 *>          as follows:
00089 *>          if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
00090 *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).
00091 *>          See below for further details.
00092 *>
00093 *>          On exit, if INFO = 0, the triangular factor U or L from the
00094 *>          Cholesky factorization A = U**H*U or A = L*L**H of the band
00095 *>          matrix A, in the same storage format as A.
00096 *> \endverbatim
00097 *>
00098 *> \param[in] LDAB
00099 *> \verbatim
00100 *>          LDAB is INTEGER
00101 *>          The leading dimension of the array AB.  LDAB >= KD+1.
00102 *> \endverbatim
00103 *>
00104 *> \param[in,out] B
00105 *> \verbatim
00106 *>          B is COMPLEX array, dimension (LDB,NRHS)
00107 *>          On entry, the N-by-NRHS right hand side matrix B.
00108 *>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
00109 *> \endverbatim
00110 *>
00111 *> \param[in] LDB
00112 *> \verbatim
00113 *>          LDB is INTEGER
00114 *>          The leading dimension of the array B.  LDB >= max(1,N).
00115 *> \endverbatim
00116 *>
00117 *> \param[out] INFO
00118 *> \verbatim
00119 *>          INFO is INTEGER
00120 *>          = 0:  successful exit
00121 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00122 *>          > 0:  if INFO = i, the leading minor of order i of A is not
00123 *>                positive definite, so the factorization could not be
00124 *>                completed, and the solution has not been computed.
00125 *> \endverbatim
00126 *
00127 *  Authors:
00128 *  ========
00129 *
00130 *> \author Univ. of Tennessee 
00131 *> \author Univ. of California Berkeley 
00132 *> \author Univ. of Colorado Denver 
00133 *> \author NAG Ltd. 
00134 *
00135 *> \date November 2011
00136 *
00137 *> \ingroup complexOTHERsolve
00138 *
00139 *> \par Further Details:
00140 *  =====================
00141 *>
00142 *> \verbatim
00143 *>
00144 *>  The band storage scheme is illustrated by the following example, when
00145 *>  N = 6, KD = 2, and UPLO = 'U':
00146 *>
00147 *>  On entry:                       On exit:
00148 *>
00149 *>      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
00150 *>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
00151 *>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
00152 *>
00153 *>  Similarly, if UPLO = 'L' the format of A is as follows:
00154 *>
00155 *>  On entry:                       On exit:
00156 *>
00157 *>     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
00158 *>     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
00159 *>     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
00160 *>
00161 *>  Array elements marked * are not used by the routine.
00162 *> \endverbatim
00163 *>
00164 *  =====================================================================
00165       SUBROUTINE CPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
00166 *
00167 *  -- LAPACK driver routine (version 3.4.0) --
00168 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00169 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00170 *     November 2011
00171 *
00172 *     .. Scalar Arguments ..
00173       CHARACTER          UPLO
00174       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
00175 *     ..
00176 *     .. Array Arguments ..
00177       COMPLEX            AB( LDAB, * ), B( LDB, * )
00178 *     ..
00179 *
00180 *  =====================================================================
00181 *
00182 *     .. External Functions ..
00183       LOGICAL            LSAME
00184       EXTERNAL           LSAME
00185 *     ..
00186 *     .. External Subroutines ..
00187       EXTERNAL           CPBTRF, CPBTRS, XERBLA
00188 *     ..
00189 *     .. Intrinsic Functions ..
00190       INTRINSIC          MAX
00191 *     ..
00192 *     .. Executable Statements ..
00193 *
00194 *     Test the input parameters.
00195 *
00196       INFO = 0
00197       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00198          INFO = -1
00199       ELSE IF( N.LT.0 ) THEN
00200          INFO = -2
00201       ELSE IF( KD.LT.0 ) THEN
00202          INFO = -3
00203       ELSE IF( NRHS.LT.0 ) THEN
00204          INFO = -4
00205       ELSE IF( LDAB.LT.KD+1 ) THEN
00206          INFO = -6
00207       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00208          INFO = -8
00209       END IF
00210       IF( INFO.NE.0 ) THEN
00211          CALL XERBLA( 'CPBSV ', -INFO )
00212          RETURN
00213       END IF
00214 *
00215 *     Compute the Cholesky factorization A = U**H*U or A = L*L**H.
00216 *
00217       CALL CPBTRF( UPLO, N, KD, AB, LDAB, INFO )
00218       IF( INFO.EQ.0 ) THEN
00219 *
00220 *        Solve the system A*X = B, overwriting B with X.
00221 *
00222          CALL CPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
00223 *
00224       END IF
00225       RETURN
00226 *
00227 *     End of CPBSV
00228 *
00229       END
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