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Annotation of rpl/lapack/lapack/zpbsv.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE ZPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
        !             2: *
        !             3: *  -- LAPACK driver routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       CHARACTER          UPLO
        !            10:       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
        !            11: *     ..
        !            12: *     .. Array Arguments ..
        !            13:       COMPLEX*16         AB( LDAB, * ), B( LDB, * )
        !            14: *     ..
        !            15: *
        !            16: *  Purpose
        !            17: *  =======
        !            18: *
        !            19: *  ZPBSV computes the solution to a complex system of linear equations
        !            20: *     A * X = B,
        !            21: *  where A is an N-by-N Hermitian positive definite band matrix and X
        !            22: *  and B are N-by-NRHS matrices.
        !            23: *
        !            24: *  The Cholesky decomposition is used to factor A as
        !            25: *     A = U**H * U,  if UPLO = 'U', or
        !            26: *     A = L * L**H,  if UPLO = 'L',
        !            27: *  where U is an upper triangular band matrix, and L is a lower
        !            28: *  triangular band matrix, with the same number of superdiagonals or
        !            29: *  subdiagonals as A.  The factored form of A is then used to solve the
        !            30: *  system of equations A * X = B.
        !            31: *
        !            32: *  Arguments
        !            33: *  =========
        !            34: *
        !            35: *  UPLO    (input) CHARACTER*1
        !            36: *          = 'U':  Upper triangle of A is stored;
        !            37: *          = 'L':  Lower triangle of A is stored.
        !            38: *
        !            39: *  N       (input) INTEGER
        !            40: *          The number of linear equations, i.e., the order of the
        !            41: *          matrix A.  N >= 0.
        !            42: *
        !            43: *  KD      (input) INTEGER
        !            44: *          The number of superdiagonals of the matrix A if UPLO = 'U',
        !            45: *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
        !            46: *
        !            47: *  NRHS    (input) INTEGER
        !            48: *          The number of right hand sides, i.e., the number of columns
        !            49: *          of the matrix B.  NRHS >= 0.
        !            50: *
        !            51: *  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
        !            52: *          On entry, the upper or lower triangle of the Hermitian band
        !            53: *          matrix A, stored in the first KD+1 rows of the array.  The
        !            54: *          j-th column of A is stored in the j-th column of the array AB
        !            55: *          as follows:
        !            56: *          if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
        !            57: *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).
        !            58: *          See below for further details.
        !            59: *
        !            60: *          On exit, if INFO = 0, the triangular factor U or L from the
        !            61: *          Cholesky factorization A = U**H*U or A = L*L**H of the band
        !            62: *          matrix A, in the same storage format as A.
        !            63: *
        !            64: *  LDAB    (input) INTEGER
        !            65: *          The leading dimension of the array AB.  LDAB >= KD+1.
        !            66: *
        !            67: *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
        !            68: *          On entry, the N-by-NRHS right hand side matrix B.
        !            69: *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
        !            70: *
        !            71: *  LDB     (input) INTEGER
        !            72: *          The leading dimension of the array B.  LDB >= max(1,N).
        !            73: *
        !            74: *  INFO    (output) INTEGER
        !            75: *          = 0:  successful exit
        !            76: *          < 0:  if INFO = -i, the i-th argument had an illegal value
        !            77: *          > 0:  if INFO = i, the leading minor of order i of A is not
        !            78: *                positive definite, so the factorization could not be
        !            79: *                completed, and the solution has not been computed.
        !            80: *
        !            81: *  Further Details
        !            82: *  ===============
        !            83: *
        !            84: *  The band storage scheme is illustrated by the following example, when
        !            85: *  N = 6, KD = 2, and UPLO = 'U':
        !            86: *
        !            87: *  On entry:                       On exit:
        !            88: *
        !            89: *      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
        !            90: *      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
        !            91: *     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
        !            92: *
        !            93: *  Similarly, if UPLO = 'L' the format of A is as follows:
        !            94: *
        !            95: *  On entry:                       On exit:
        !            96: *
        !            97: *     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
        !            98: *     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
        !            99: *     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
        !           100: *
        !           101: *  Array elements marked * are not used by the routine.
        !           102: *
        !           103: *  =====================================================================
        !           104: *
        !           105: *     .. External Functions ..
        !           106:       LOGICAL            LSAME
        !           107:       EXTERNAL           LSAME
        !           108: *     ..
        !           109: *     .. External Subroutines ..
        !           110:       EXTERNAL           XERBLA, ZPBTRF, ZPBTRS
        !           111: *     ..
        !           112: *     .. Intrinsic Functions ..
        !           113:       INTRINSIC          MAX
        !           114: *     ..
        !           115: *     .. Executable Statements ..
        !           116: *
        !           117: *     Test the input parameters.
        !           118: *
        !           119:       INFO = 0
        !           120:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
        !           121:          INFO = -1
        !           122:       ELSE IF( N.LT.0 ) THEN
        !           123:          INFO = -2
        !           124:       ELSE IF( KD.LT.0 ) THEN
        !           125:          INFO = -3
        !           126:       ELSE IF( NRHS.LT.0 ) THEN
        !           127:          INFO = -4
        !           128:       ELSE IF( LDAB.LT.KD+1 ) THEN
        !           129:          INFO = -6
        !           130:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
        !           131:          INFO = -8
        !           132:       END IF
        !           133:       IF( INFO.NE.0 ) THEN
        !           134:          CALL XERBLA( 'ZPBSV ', -INFO )
        !           135:          RETURN
        !           136:       END IF
        !           137: *
        !           138: *     Compute the Cholesky factorization A = U'*U or A = L*L'.
        !           139: *
        !           140:       CALL ZPBTRF( UPLO, N, KD, AB, LDAB, INFO )
        !           141:       IF( INFO.EQ.0 ) THEN
        !           142: *
        !           143: *        Solve the system A*X = B, overwriting B with X.
        !           144: *
        !           145:          CALL ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
        !           146: *
        !           147:       END IF
        !           148:       RETURN
        !           149: *
        !           150: *     End of ZPBSV
        !           151: *
        !           152:       END