LAPACK 3.3.0

zpbtrs.f

Go to the documentation of this file.
00001       SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
00011 *     ..
00012 *     .. Array Arguments ..
00013       COMPLEX*16         AB( LDAB, * ), B( LDB, * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  ZPBTRS solves a system of linear equations A*X = B with a Hermitian
00020 *  positive definite band matrix A using the Cholesky factorization
00021 *  A = U**H*U or A = L*L**H computed by ZPBTRF.
00022 *
00023 *  Arguments
00024 *  =========
00025 *
00026 *  UPLO    (input) CHARACTER*1
00027 *          = 'U':  Upper triangular factor stored in AB;
00028 *          = 'L':  Lower triangular factor stored in AB.
00029 *
00030 *  N       (input) INTEGER
00031 *          The order of the matrix A.  N >= 0.
00032 *
00033 *  KD      (input) INTEGER
00034 *          The number of superdiagonals of the matrix A if UPLO = 'U',
00035 *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
00036 *
00037 *  NRHS    (input) INTEGER
00038 *          The number of right hand sides, i.e., the number of columns
00039 *          of the matrix B.  NRHS >= 0.
00040 *
00041 *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)
00042 *          The triangular factor U or L from the Cholesky factorization
00043 *          A = U**H*U or A = L*L**H of the band matrix A, stored in the
00044 *          first KD+1 rows of the array.  The j-th column of U or L is
00045 *          stored in the j-th column of the array AB as follows:
00046 *          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
00047 *          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
00048 *
00049 *  LDAB    (input) INTEGER
00050 *          The leading dimension of the array AB.  LDAB >= KD+1.
00051 *
00052 *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
00053 *          On entry, the right hand side matrix B.
00054 *          On exit, the solution matrix X.
00055 *
00056 *  LDB     (input) INTEGER
00057 *          The leading dimension of the array B.  LDB >= max(1,N).
00058 *
00059 *  INFO    (output) INTEGER
00060 *          = 0:  successful exit
00061 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00062 *
00063 *  =====================================================================
00064 *
00065 *     .. Local Scalars ..
00066       LOGICAL            UPPER
00067       INTEGER            J
00068 *     ..
00069 *     .. External Functions ..
00070       LOGICAL            LSAME
00071       EXTERNAL           LSAME
00072 *     ..
00073 *     .. External Subroutines ..
00074       EXTERNAL           XERBLA, ZTBSV
00075 *     ..
00076 *     .. Intrinsic Functions ..
00077       INTRINSIC          MAX
00078 *     ..
00079 *     .. Executable Statements ..
00080 *
00081 *     Test the input parameters.
00082 *
00083       INFO = 0
00084       UPPER = LSAME( UPLO, 'U' )
00085       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00086          INFO = -1
00087       ELSE IF( N.LT.0 ) THEN
00088          INFO = -2
00089       ELSE IF( KD.LT.0 ) THEN
00090          INFO = -3
00091       ELSE IF( NRHS.LT.0 ) THEN
00092          INFO = -4
00093       ELSE IF( LDAB.LT.KD+1 ) THEN
00094          INFO = -6
00095       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00096          INFO = -8
00097       END IF
00098       IF( INFO.NE.0 ) THEN
00099          CALL XERBLA( 'ZPBTRS', -INFO )
00100          RETURN
00101       END IF
00102 *
00103 *     Quick return if possible
00104 *
00105       IF( N.EQ.0 .OR. NRHS.EQ.0 )
00106      $   RETURN
00107 *
00108       IF( UPPER ) THEN
00109 *
00110 *        Solve A*X = B where A = U'*U.
00111 *
00112          DO 10 J = 1, NRHS
00113 *
00114 *           Solve U'*X = B, overwriting B with X.
00115 *
00116             CALL ZTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
00117      $                  KD, AB, LDAB, B( 1, J ), 1 )
00118 *
00119 *           Solve U*X = B, overwriting B with X.
00120 *
00121             CALL ZTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
00122      $                  LDAB, B( 1, J ), 1 )
00123    10    CONTINUE
00124       ELSE
00125 *
00126 *        Solve A*X = B where A = L*L'.
00127 *
00128          DO 20 J = 1, NRHS
00129 *
00130 *           Solve L*X = B, overwriting B with X.
00131 *
00132             CALL ZTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
00133      $                  LDAB, B( 1, J ), 1 )
00134 *
00135 *           Solve L'*X = B, overwriting B with X.
00136 *
00137             CALL ZTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
00138      $                  KD, AB, LDAB, B( 1, J ), 1 )
00139    20    CONTINUE
00140       END IF
00141 *
00142       RETURN
00143 *
00144 *     End of ZPBTRS
00145 *
00146       END
 All Files Functions