dc/d33/cptsv_8f_source.html

00001       SUBROUTINE CPTSV( N, NRHS, D, E, B, LDB, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       INTEGER            INFO, LDB, N, NRHS
00010 *     ..
00011 *     .. Array Arguments ..
00012       REAL               D( * )
00013       COMPLEX            B( LDB, * ), E( * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  CPTSV computes the solution to a complex system of linear equations
00020 *  A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
00021 *  matrix, and X and B are N-by-NRHS matrices.
00022 *
00023 *  A is factored as A = L*D*L**H, and the factored form of A is then
00024 *  used to solve the system of equations.
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  N       (input) INTEGER
00030 *          The order of the matrix A.  N >= 0.
00031 *
00032 *  NRHS    (input) INTEGER
00033 *          The number of right hand sides, i.e., the number of columns
00034 *          of the matrix B.  NRHS >= 0.
00035 *
00036 *  D       (input/output) REAL array, dimension (N)
00037 *          On entry, the n diagonal elements of the tridiagonal matrix
00038 *          A.  On exit, the n diagonal elements of the diagonal matrix
00039 *          D from the factorization A = L*D*L**H.
00040 *
00041 *  E       (input/output) COMPLEX array, dimension (N-1)
00042 *          On entry, the (n-1) subdiagonal elements of the tridiagonal
00043 *          matrix A.  On exit, the (n-1) subdiagonal elements of the
00044 *          unit bidiagonal factor L from the L*D*L**H factorization of
00045 *          A.  E can also be regarded as the superdiagonal of the unit
00046 *          bidiagonal factor U from the U**H*D*U factorization of A.
00047 *
00048 *  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
00049 *          On entry, the N-by-NRHS right hand side matrix B.
00050 *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
00051 *
00052 *  LDB     (input) INTEGER
00053 *          The leading dimension of the array B.  LDB >= max(1,N).
00054 *
00055 *  INFO    (output) INTEGER
00056 *          = 0:  successful exit
00057 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00058 *          > 0:  if INFO = i, the leading minor of order i is not
00059 *                positive definite, and the solution has not been
00060 *                computed.  The factorization has not been completed
00061 *                unless i = N.
00062 *
00063 *  =====================================================================
00064 *
00065 *     .. External Subroutines ..
00066       EXTERNAL           CPTTRF, CPTTRS, XERBLA
00067 *     ..
00068 *     .. Intrinsic Functions ..
00069       INTRINSIC          MAX
00070 *     ..
00071 *     .. Executable Statements ..
00072 *
00073 *     Test the input parameters.
00074 *
00075       INFO = 0
00076       IF( N.LT.0 ) THEN
00077          INFO = -1
00078       ELSE IF( NRHS.LT.0 ) THEN
00079          INFO = -2
00080       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00081          INFO = -6
00082       END IF
00083       IF( INFO.NE.0 ) THEN
00084          CALL XERBLA( 'CPTSV ', -INFO )
00085          RETURN
00086       END IF
00087 *
00088 *     Compute the L*D*L' (or U'*D*U) factorization of A.
00089 *
00090       CALL CPTTRF( N, D, E, INFO )
00091       IF( INFO.EQ.0 ) THEN
00092 *
00093 *        Solve the system A*X = B, overwriting B with X.
00094 *
00095          CALL CPTTRS( 'Lower', N, NRHS, D, E, B, LDB, INFO )
00096       END IF
00097       RETURN
00098 *
00099 *     End of CPTSV
00100 *
00101       END