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Annotation of rpl/lapack/lapack/dgbsv.f, revision 1.3

1.1       bertrand    1:       SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, 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:       INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
                     10: *     ..
                     11: *     .. Array Arguments ..
                     12:       INTEGER            IPIV( * )
                     13:       DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
                     14: *     ..
                     15: *
                     16: *  Purpose
                     17: *  =======
                     18: *
                     19: *  DGBSV computes the solution to a real system of linear equations
                     20: *  A * X = B, where A is a band matrix of order N with KL subdiagonals
                     21: *  and KU superdiagonals, and X and B are N-by-NRHS matrices.
                     22: *
                     23: *  The LU decomposition with partial pivoting and row interchanges is
                     24: *  used to factor A as A = L * U, where L is a product of permutation
                     25: *  and unit lower triangular matrices with KL subdiagonals, and U is
                     26: *  upper triangular with KL+KU superdiagonals.  The factored form of A
                     27: *  is then used to solve the system of equations A * X = B.
                     28: *
                     29: *  Arguments
                     30: *  =========
                     31: *
                     32: *  N       (input) INTEGER
                     33: *          The number of linear equations, i.e., the order of the
                     34: *          matrix A.  N >= 0.
                     35: *
                     36: *  KL      (input) INTEGER
                     37: *          The number of subdiagonals within the band of A.  KL >= 0.
                     38: *
                     39: *  KU      (input) INTEGER
                     40: *          The number of superdiagonals within the band of A.  KU >= 0.
                     41: *
                     42: *  NRHS    (input) INTEGER
                     43: *          The number of right hand sides, i.e., the number of columns
                     44: *          of the matrix B.  NRHS >= 0.
                     45: *
                     46: *  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
                     47: *          On entry, the matrix A in band storage, in rows KL+1 to
                     48: *          2*KL+KU+1; rows 1 to KL of the array need not be set.
                     49: *          The j-th column of A is stored in the j-th column of the
                     50: *          array AB as follows:
                     51: *          AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
                     52: *          On exit, details of the factorization: U is stored as an
                     53: *          upper triangular band matrix with KL+KU superdiagonals in
                     54: *          rows 1 to KL+KU+1, and the multipliers used during the
                     55: *          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
                     56: *          See below for further details.
                     57: *
                     58: *  LDAB    (input) INTEGER
                     59: *          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
                     60: *
                     61: *  IPIV    (output) INTEGER array, dimension (N)
                     62: *          The pivot indices that define the permutation matrix P;
                     63: *          row i of the matrix was interchanged with row IPIV(i).
                     64: *
                     65: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
                     66: *          On entry, the N-by-NRHS right hand side matrix B.
                     67: *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
                     68: *
                     69: *  LDB     (input) INTEGER
                     70: *          The leading dimension of the array B.  LDB >= max(1,N).
                     71: *
                     72: *  INFO    (output) INTEGER
                     73: *          = 0:  successful exit
                     74: *          < 0:  if INFO = -i, the i-th argument had an illegal value
                     75: *          > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization
                     76: *                has been completed, but the factor U is exactly
                     77: *                singular, and the solution has not been computed.
                     78: *
                     79: *  Further Details
                     80: *  ===============
                     81: *
                     82: *  The band storage scheme is illustrated by the following example, when
                     83: *  M = N = 6, KL = 2, KU = 1:
                     84: *
                     85: *  On entry:                       On exit:
                     86: *
                     87: *      *    *    *    +    +    +       *    *    *   u14  u25  u36
                     88: *      *    *    +    +    +    +       *    *   u13  u24  u35  u46
                     89: *      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
                     90: *     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
                     91: *     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
                     92: *     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
                     93: *
                     94: *  Array elements marked * are not used by the routine; elements marked
                     95: *  + need not be set on entry, but are required by the routine to store
                     96: *  elements of U because of fill-in resulting from the row interchanges.
                     97: *
                     98: *  =====================================================================
                     99: *
                    100: *     .. External Subroutines ..
                    101:       EXTERNAL           DGBTRF, DGBTRS, XERBLA
                    102: *     ..
                    103: *     .. Intrinsic Functions ..
                    104:       INTRINSIC          MAX
                    105: *     ..
                    106: *     .. Executable Statements ..
                    107: *
                    108: *     Test the input parameters.
                    109: *
                    110:       INFO = 0
                    111:       IF( N.LT.0 ) THEN
                    112:          INFO = -1
                    113:       ELSE IF( KL.LT.0 ) THEN
                    114:          INFO = -2
                    115:       ELSE IF( KU.LT.0 ) THEN
                    116:          INFO = -3
                    117:       ELSE IF( NRHS.LT.0 ) THEN
                    118:          INFO = -4
                    119:       ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
                    120:          INFO = -6
                    121:       ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
                    122:          INFO = -9
                    123:       END IF
                    124:       IF( INFO.NE.0 ) THEN
                    125:          CALL XERBLA( 'DGBSV ', -INFO )
                    126:          RETURN
                    127:       END IF
                    128: *
                    129: *     Compute the LU factorization of the band matrix A.
                    130: *
                    131:       CALL DGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
                    132:       IF( INFO.EQ.0 ) THEN
                    133: *
                    134: *        Solve the system A*X = B, overwriting B with X.
                    135: *
                    136:          CALL DGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
                    137:      $                B, LDB, INFO )
                    138:       END IF
                    139:       RETURN
                    140: *
                    141: *     End of DGBSV
                    142: *
                    143:       END