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Annotation of rpl/lapack/lapack/dpbsv.f, revision 1.2

1.1       bertrand    1:       SUBROUTINE DPBSV( 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:       DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
                     14: *     ..
                     15: *
                     16: *  Purpose
                     17: *  =======
                     18: *
                     19: *  DPBSV computes the solution to a real system of linear equations
                     20: *     A * X = B,
                     21: *  where A is an N-by-N symmetric 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**T * U,  if UPLO = 'U', or
                     26: *     A = L * L**T,  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) DOUBLE PRECISION array, dimension (LDAB,N)
                     52: *          On entry, the upper or lower triangle of the symmetric 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**T*U or A = L*L**T 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) DOUBLE PRECISION 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           DPBTRF, DPBTRS, XERBLA
                    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( 'DPBSV ', -INFO )
                    135:          RETURN
                    136:       END IF
                    137: *
                    138: *     Compute the Cholesky factorization A = U'*U or A = L*L'.
                    139: *
                    140:       CALL DPBTRF( 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 DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
                    146: *
                    147:       END IF
                    148:       RETURN
                    149: *
                    150: *     End of DPBSV
                    151: *
                    152:       END