LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zpbtrs.f
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00001 *> \brief \b ZPBTRS
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZPBTRS + 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/zpbtrs.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZPBTRS( 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*16         AB( LDAB, * ), B( LDB, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> ZPBTRS solves a system of linear equations A*X = B with a Hermitian
00038 *> positive definite band matrix A using the Cholesky factorization
00039 *> A = U**H *U or A = L*L**H computed by ZPBTRF.
00040 *> \endverbatim
00041 *
00042 *  Arguments:
00043 *  ==========
00044 *
00045 *> \param[in] UPLO
00046 *> \verbatim
00047 *>          UPLO is CHARACTER*1
00048 *>          = 'U':  Upper triangular factor stored in AB;
00049 *>          = 'L':  Lower triangular factor stored in AB.
00050 *> \endverbatim
00051 *>
00052 *> \param[in] N
00053 *> \verbatim
00054 *>          N is INTEGER
00055 *>          The order of the matrix A.  N >= 0.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] KD
00059 *> \verbatim
00060 *>          KD is INTEGER
00061 *>          The number of superdiagonals of the matrix A if UPLO = 'U',
00062 *>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] NRHS
00066 *> \verbatim
00067 *>          NRHS is INTEGER
00068 *>          The number of right hand sides, i.e., the number of columns
00069 *>          of the matrix B.  NRHS >= 0.
00070 *> \endverbatim
00071 *>
00072 *> \param[in] AB
00073 *> \verbatim
00074 *>          AB is COMPLEX*16 array, dimension (LDAB,N)
00075 *>          The triangular factor U or L from the Cholesky factorization
00076 *>          A = U**H *U or A = L*L**H of the band matrix A, stored in the
00077 *>          first KD+1 rows of the array.  The j-th column of U or L is
00078 *>          stored in the j-th column of the array AB as follows:
00079 *>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
00080 *>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
00081 *> \endverbatim
00082 *>
00083 *> \param[in] LDAB
00084 *> \verbatim
00085 *>          LDAB is INTEGER
00086 *>          The leading dimension of the array AB.  LDAB >= KD+1.
00087 *> \endverbatim
00088 *>
00089 *> \param[in,out] B
00090 *> \verbatim
00091 *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
00092 *>          On entry, the right hand side matrix B.
00093 *>          On exit, the solution matrix X.
00094 *> \endverbatim
00095 *>
00096 *> \param[in] LDB
00097 *> \verbatim
00098 *>          LDB is INTEGER
00099 *>          The leading dimension of the array B.  LDB >= max(1,N).
00100 *> \endverbatim
00101 *>
00102 *> \param[out] INFO
00103 *> \verbatim
00104 *>          INFO is INTEGER
00105 *>          = 0:  successful exit
00106 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00107 *> \endverbatim
00108 *
00109 *  Authors:
00110 *  ========
00111 *
00112 *> \author Univ. of Tennessee 
00113 *> \author Univ. of California Berkeley 
00114 *> \author Univ. of Colorado Denver 
00115 *> \author NAG Ltd. 
00116 *
00117 *> \date November 2011
00118 *
00119 *> \ingroup complex16OTHERcomputational
00120 *
00121 *  =====================================================================
00122       SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
00123 *
00124 *  -- LAPACK computational routine (version 3.4.0) --
00125 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00126 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00127 *     November 2011
00128 *
00129 *     .. Scalar Arguments ..
00130       CHARACTER          UPLO
00131       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
00132 *     ..
00133 *     .. Array Arguments ..
00134       COMPLEX*16         AB( LDAB, * ), B( LDB, * )
00135 *     ..
00136 *
00137 *  =====================================================================
00138 *
00139 *     .. Local Scalars ..
00140       LOGICAL            UPPER
00141       INTEGER            J
00142 *     ..
00143 *     .. External Functions ..
00144       LOGICAL            LSAME
00145       EXTERNAL           LSAME
00146 *     ..
00147 *     .. External Subroutines ..
00148       EXTERNAL           XERBLA, ZTBSV
00149 *     ..
00150 *     .. Intrinsic Functions ..
00151       INTRINSIC          MAX
00152 *     ..
00153 *     .. Executable Statements ..
00154 *
00155 *     Test the input parameters.
00156 *
00157       INFO = 0
00158       UPPER = LSAME( UPLO, 'U' )
00159       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00160          INFO = -1
00161       ELSE IF( N.LT.0 ) THEN
00162          INFO = -2
00163       ELSE IF( KD.LT.0 ) THEN
00164          INFO = -3
00165       ELSE IF( NRHS.LT.0 ) THEN
00166          INFO = -4
00167       ELSE IF( LDAB.LT.KD+1 ) THEN
00168          INFO = -6
00169       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00170          INFO = -8
00171       END IF
00172       IF( INFO.NE.0 ) THEN
00173          CALL XERBLA( 'ZPBTRS', -INFO )
00174          RETURN
00175       END IF
00176 *
00177 *     Quick return if possible
00178 *
00179       IF( N.EQ.0 .OR. NRHS.EQ.0 )
00180      $   RETURN
00181 *
00182       IF( UPPER ) THEN
00183 *
00184 *        Solve A*X = B where A = U**H *U.
00185 *
00186          DO 10 J = 1, NRHS
00187 *
00188 *           Solve U**H *X = B, overwriting B with X.
00189 *
00190             CALL ZTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
00191      $                  KD, AB, LDAB, B( 1, J ), 1 )
00192 *
00193 *           Solve U*X = B, overwriting B with X.
00194 *
00195             CALL ZTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
00196      $                  LDAB, B( 1, J ), 1 )
00197    10    CONTINUE
00198       ELSE
00199 *
00200 *        Solve A*X = B where A = L*L**H.
00201 *
00202          DO 20 J = 1, NRHS
00203 *
00204 *           Solve L*X = B, overwriting B with X.
00205 *
00206             CALL ZTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
00207      $                  LDAB, B( 1, J ), 1 )
00208 *
00209 *           Solve L**H *X = B, overwriting B with X.
00210 *
00211             CALL ZTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
00212      $                  KD, AB, LDAB, B( 1, J ), 1 )
00213    20    CONTINUE
00214       END IF
00215 *
00216       RETURN
00217 *
00218 *     End of ZPBTRS
00219 *
00220       END
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