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

1.1       bertrand    1:       SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
                      2: *
                      3: *  -- LAPACK 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: *  DPBTRS solves a system of linear equations A*X = B with a symmetric
                     20: *  positive definite band matrix A using the Cholesky factorization
                     21: *  A = U**T*U or A = L*L**T computed by DPBTRF.
                     22: *
                     23: *  Arguments
                     24: *  =========
                     25: *
                     26: *  UPLO    (input) CHARACTER*1
                     27: *          = 'U':  Upper triangular factor stored in AB;
                     28: *          = 'L':  Lower triangular factor stored in AB.
                     29: *
                     30: *  N       (input) INTEGER
                     31: *          The order of the matrix A.  N >= 0.
                     32: *
                     33: *  KD      (input) INTEGER
                     34: *          The number of superdiagonals of the matrix A if UPLO = 'U',
                     35: *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
                     36: *
                     37: *  NRHS    (input) INTEGER
                     38: *          The number of right hand sides, i.e., the number of columns
                     39: *          of the matrix B.  NRHS >= 0.
                     40: *
                     41: *  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
                     42: *          The triangular factor U or L from the Cholesky factorization
                     43: *          A = U**T*U or A = L*L**T of the band matrix A, stored in the
                     44: *          first KD+1 rows of the array.  The j-th column of U or L is
                     45: *          stored in the j-th column of the array AB as follows:
                     46: *          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
                     47: *          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
                     48: *
                     49: *  LDAB    (input) INTEGER
                     50: *          The leading dimension of the array AB.  LDAB >= KD+1.
                     51: *
                     52: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
                     53: *          On entry, the right hand side matrix B.
                     54: *          On exit, the solution matrix X.
                     55: *
                     56: *  LDB     (input) INTEGER
                     57: *          The leading dimension of the array B.  LDB >= max(1,N).
                     58: *
                     59: *  INFO    (output) INTEGER
                     60: *          = 0:  successful exit
                     61: *          < 0:  if INFO = -i, the i-th argument had an illegal value
                     62: *
                     63: *  =====================================================================
                     64: *
                     65: *     .. Local Scalars ..
                     66:       LOGICAL            UPPER
                     67:       INTEGER            J
                     68: *     ..
                     69: *     .. External Functions ..
                     70:       LOGICAL            LSAME
                     71:       EXTERNAL           LSAME
                     72: *     ..
                     73: *     .. External Subroutines ..
                     74:       EXTERNAL           DTBSV, XERBLA
                     75: *     ..
                     76: *     .. Intrinsic Functions ..
                     77:       INTRINSIC          MAX
                     78: *     ..
                     79: *     .. Executable Statements ..
                     80: *
                     81: *     Test the input parameters.
                     82: *
                     83:       INFO = 0
                     84:       UPPER = LSAME( UPLO, 'U' )
                     85:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
                     86:          INFO = -1
                     87:       ELSE IF( N.LT.0 ) THEN
                     88:          INFO = -2
                     89:       ELSE IF( KD.LT.0 ) THEN
                     90:          INFO = -3
                     91:       ELSE IF( NRHS.LT.0 ) THEN
                     92:          INFO = -4
                     93:       ELSE IF( LDAB.LT.KD+1 ) THEN
                     94:          INFO = -6
                     95:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
                     96:          INFO = -8
                     97:       END IF
                     98:       IF( INFO.NE.0 ) THEN
                     99:          CALL XERBLA( 'DPBTRS', -INFO )
                    100:          RETURN
                    101:       END IF
                    102: *
                    103: *     Quick return if possible
                    104: *
                    105:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
                    106:      $   RETURN
                    107: *
                    108:       IF( UPPER ) THEN
                    109: *
                    110: *        Solve A*X = B where A = U'*U.
                    111: *
                    112:          DO 10 J = 1, NRHS
                    113: *
                    114: *           Solve U'*X = B, overwriting B with X.
                    115: *
                    116:             CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
                    117:      $                  LDAB, B( 1, J ), 1 )
                    118: *
                    119: *           Solve U*X = B, overwriting B with X.
                    120: *
                    121:             CALL DTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
                    122:      $                  LDAB, B( 1, J ), 1 )
                    123:    10    CONTINUE
                    124:       ELSE
                    125: *
                    126: *        Solve A*X = B where A = L*L'.
                    127: *
                    128:          DO 20 J = 1, NRHS
                    129: *
                    130: *           Solve L*X = B, overwriting B with X.
                    131: *
                    132:             CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
                    133:      $                  LDAB, B( 1, J ), 1 )
                    134: *
                    135: *           Solve L'*X = B, overwriting B with X.
                    136: *
                    137:             CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
                    138:      $                  LDAB, B( 1, J ), 1 )
                    139:    20    CONTINUE
                    140:       END IF
                    141: *
                    142:       RETURN
                    143: *
                    144: *     End of DPBTRS
                    145: *
                    146:       END