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Annotation of rpl/lapack/lapack/dgttrs.f, revision 1.1.1.1

1.1       bertrand    1:       SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
                      2:      $                   INFO )
                      3: *
                      4: *  -- LAPACK routine (version 3.2) --
                      5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                      7: *     November 2006
                      8: *
                      9: *     .. Scalar Arguments ..
                     10:       CHARACTER          TRANS
                     11:       INTEGER            INFO, LDB, N, NRHS
                     12: *     ..
                     13: *     .. Array Arguments ..
                     14:       INTEGER            IPIV( * )
                     15:       DOUBLE PRECISION   B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
                     16: *     ..
                     17: *
                     18: *  Purpose
                     19: *  =======
                     20: *
                     21: *  DGTTRS solves one of the systems of equations
                     22: *     A*X = B  or  A'*X = B,
                     23: *  with a tridiagonal matrix A using the LU factorization computed
                     24: *  by DGTTRF.
                     25: *
                     26: *  Arguments
                     27: *  =========
                     28: *
                     29: *  TRANS   (input) CHARACTER*1
                     30: *          Specifies the form of the system of equations.
                     31: *          = 'N':  A * X = B  (No transpose)
                     32: *          = 'T':  A'* X = B  (Transpose)
                     33: *          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
                     34: *
                     35: *  N       (input) INTEGER
                     36: *          The order of the matrix A.
                     37: *
                     38: *  NRHS    (input) INTEGER
                     39: *          The number of right hand sides, i.e., the number of columns
                     40: *          of the matrix B.  NRHS >= 0.
                     41: *
                     42: *  DL      (input) DOUBLE PRECISION array, dimension (N-1)
                     43: *          The (n-1) multipliers that define the matrix L from the
                     44: *          LU factorization of A.
                     45: *
                     46: *  D       (input) DOUBLE PRECISION array, dimension (N)
                     47: *          The n diagonal elements of the upper triangular matrix U from
                     48: *          the LU factorization of A.
                     49: *
                     50: *  DU      (input) DOUBLE PRECISION array, dimension (N-1)
                     51: *          The (n-1) elements of the first super-diagonal of U.
                     52: *
                     53: *  DU2     (input) DOUBLE PRECISION array, dimension (N-2)
                     54: *          The (n-2) elements of the second super-diagonal of U.
                     55: *
                     56: *  IPIV    (input) INTEGER array, dimension (N)
                     57: *          The pivot indices; for 1 <= i <= n, row i of the matrix was
                     58: *          interchanged with row IPIV(i).  IPIV(i) will always be either
                     59: *          i or i+1; IPIV(i) = i indicates a row interchange was not
                     60: *          required.
                     61: *
                     62: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
                     63: *          On entry, the matrix of right hand side vectors B.
                     64: *          On exit, B is overwritten by the solution vectors X.
                     65: *
                     66: *  LDB     (input) INTEGER
                     67: *          The leading dimension of the array B.  LDB >= max(1,N).
                     68: *
                     69: *  INFO    (output) INTEGER
                     70: *          = 0:  successful exit
                     71: *          < 0:  if INFO = -i, the i-th argument had an illegal value
                     72: *
                     73: *  =====================================================================
                     74: *
                     75: *     .. Local Scalars ..
                     76:       LOGICAL            NOTRAN
                     77:       INTEGER            ITRANS, J, JB, NB
                     78: *     ..
                     79: *     .. External Functions ..
                     80:       INTEGER            ILAENV
                     81:       EXTERNAL           ILAENV
                     82: *     ..
                     83: *     .. External Subroutines ..
                     84:       EXTERNAL           DGTTS2, XERBLA
                     85: *     ..
                     86: *     .. Intrinsic Functions ..
                     87:       INTRINSIC          MAX, MIN
                     88: *     ..
                     89: *     .. Executable Statements ..
                     90: *
                     91:       INFO = 0
                     92:       NOTRAN = ( TRANS.EQ.'N' .OR. TRANS.EQ.'n' )
                     93:       IF( .NOT.NOTRAN .AND. .NOT.( TRANS.EQ.'T' .OR. TRANS.EQ.
                     94:      $    't' ) .AND. .NOT.( TRANS.EQ.'C' .OR. TRANS.EQ.'c' ) ) THEN
                     95:          INFO = -1
                     96:       ELSE IF( N.LT.0 ) THEN
                     97:          INFO = -2
                     98:       ELSE IF( NRHS.LT.0 ) THEN
                     99:          INFO = -3
                    100:       ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
                    101:          INFO = -10
                    102:       END IF
                    103:       IF( INFO.NE.0 ) THEN
                    104:          CALL XERBLA( 'DGTTRS', -INFO )
                    105:          RETURN
                    106:       END IF
                    107: *
                    108: *     Quick return if possible
                    109: *
                    110:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
                    111:      $   RETURN
                    112: *
                    113: *     Decode TRANS
                    114: *
                    115:       IF( NOTRAN ) THEN
                    116:          ITRANS = 0
                    117:       ELSE
                    118:          ITRANS = 1
                    119:       END IF
                    120: *
                    121: *     Determine the number of right-hand sides to solve at a time.
                    122: *
                    123:       IF( NRHS.EQ.1 ) THEN
                    124:          NB = 1
                    125:       ELSE
                    126:          NB = MAX( 1, ILAENV( 1, 'DGTTRS', TRANS, N, NRHS, -1, -1 ) )
                    127:       END IF
                    128: *
                    129:       IF( NB.GE.NRHS ) THEN
                    130:          CALL DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
                    131:       ELSE
                    132:          DO 10 J = 1, NRHS, NB
                    133:             JB = MIN( NRHS-J+1, NB )
                    134:             CALL DGTTS2( ITRANS, N, JB, DL, D, DU, DU2, IPIV, B( 1, J ),
                    135:      $                   LDB )
                    136:    10    CONTINUE
                    137:       END IF
                    138: *
                    139: *     End of DGTTRS
                    140: *
                    141:       END