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Annotation of rpl/lapack/lapack/zpttrs.f, revision 1.7

1.1       bertrand    1:       SUBROUTINE ZPTTRS( UPLO, N, NRHS, D, E, 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, LDB, N, NRHS
                     11: *     ..
                     12: *     .. Array Arguments ..
                     13:       DOUBLE PRECISION   D( * )
                     14:       COMPLEX*16         B( LDB, * ), E( * )
                     15: *     ..
                     16: *
                     17: *  Purpose
                     18: *  =======
                     19: *
                     20: *  ZPTTRS solves a tridiagonal system of the form
                     21: *     A * X = B
                     22: *  using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF.
                     23: *  D is a diagonal matrix specified in the vector D, U (or L) is a unit
                     24: *  bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
                     25: *  the vector E, and X and B are N by NRHS matrices.
                     26: *
                     27: *  Arguments
                     28: *  =========
                     29: *
                     30: *  UPLO    (input) CHARACTER*1
                     31: *          Specifies the form of the factorization and whether the
                     32: *          vector E is the superdiagonal of the upper bidiagonal factor
                     33: *          U or the subdiagonal of the lower bidiagonal factor L.
                     34: *          = 'U':  A = U'*D*U, E is the superdiagonal of U
                     35: *          = 'L':  A = L*D*L', E is the subdiagonal of L
                     36: *
                     37: *  N       (input) INTEGER
                     38: *          The order of the tridiagonal matrix A.  N >= 0.
                     39: *
                     40: *  NRHS    (input) INTEGER
                     41: *          The number of right hand sides, i.e., the number of columns
                     42: *          of the matrix B.  NRHS >= 0.
                     43: *
                     44: *  D       (input) DOUBLE PRECISION array, dimension (N)
                     45: *          The n diagonal elements of the diagonal matrix D from the
                     46: *          factorization A = U'*D*U or A = L*D*L'.
                     47: *
                     48: *  E       (input) COMPLEX*16 array, dimension (N-1)
                     49: *          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
                     50: *          bidiagonal factor U from the factorization A = U'*D*U.
                     51: *          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
                     52: *          bidiagonal factor L from the factorization A = L*D*L'.
                     53: *
                     54: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
                     55: *          On entry, the right hand side vectors B for the system of
                     56: *          linear equations.
                     57: *          On exit, the solution vectors, X.
                     58: *
                     59: *  LDB     (input) INTEGER
                     60: *          The leading dimension of the array B.  LDB >= max(1,N).
                     61: *
                     62: *  INFO    (output) INTEGER
                     63: *          = 0: successful exit
                     64: *          < 0: if INFO = -k, the k-th argument had an illegal value
                     65: *
                     66: *  =====================================================================
                     67: *
                     68: *     .. Local Scalars ..
                     69:       LOGICAL            UPPER
                     70:       INTEGER            IUPLO, J, JB, NB
                     71: *     ..
                     72: *     .. External Functions ..
                     73:       INTEGER            ILAENV
                     74:       EXTERNAL           ILAENV
                     75: *     ..
                     76: *     .. External Subroutines ..
                     77:       EXTERNAL           XERBLA, ZPTTS2
                     78: *     ..
                     79: *     .. Intrinsic Functions ..
                     80:       INTRINSIC          MAX, MIN
                     81: *     ..
                     82: *     .. Executable Statements ..
                     83: *
                     84: *     Test the input arguments.
                     85: *
                     86:       INFO = 0
                     87:       UPPER = ( UPLO.EQ.'U' .OR. UPLO.EQ.'u' )
                     88:       IF( .NOT.UPPER .AND. .NOT.( UPLO.EQ.'L' .OR. UPLO.EQ.'l' ) ) THEN
                     89:          INFO = -1
                     90:       ELSE IF( N.LT.0 ) THEN
                     91:          INFO = -2
                     92:       ELSE IF( NRHS.LT.0 ) THEN
                     93:          INFO = -3
                     94:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
                     95:          INFO = -7
                     96:       END IF
                     97:       IF( INFO.NE.0 ) THEN
                     98:          CALL XERBLA( 'ZPTTRS', -INFO )
                     99:          RETURN
                    100:       END IF
                    101: *
                    102: *     Quick return if possible
                    103: *
                    104:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
                    105:      $   RETURN
                    106: *
                    107: *     Determine the number of right-hand sides to solve at a time.
                    108: *
                    109:       IF( NRHS.EQ.1 ) THEN
                    110:          NB = 1
                    111:       ELSE
                    112:          NB = MAX( 1, ILAENV( 1, 'ZPTTRS', UPLO, N, NRHS, -1, -1 ) )
                    113:       END IF
                    114: *
                    115: *     Decode UPLO
                    116: *
                    117:       IF( UPPER ) THEN
                    118:          IUPLO = 1
                    119:       ELSE
                    120:          IUPLO = 0
                    121:       END IF
                    122: *
                    123:       IF( NB.GE.NRHS ) THEN
                    124:          CALL ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
                    125:       ELSE
                    126:          DO 10 J = 1, NRHS, NB
                    127:             JB = MIN( NRHS-J+1, NB )
                    128:             CALL ZPTTS2( IUPLO, N, JB, D, E, B( 1, J ), LDB )
                    129:    10    CONTINUE
                    130:       END IF
                    131: *
                    132:       RETURN
                    133: *
                    134: *     End of ZPTTRS
                    135: *
                    136:       END