cppsv.f

          SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          COMPLEX            AP( * ), B( LDB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CPPSV computes the solution to a complex system of linear equations
    *     A * X = B,
    *  where A is an N-by-N Hermitian positive definite matrix stored in
    *  packed format and X and B are N-by-NRHS matrices.
    *
    *  The Cholesky decomposition is used to factor A as
    *     A = U**H* U,  if UPLO = 'U', or
    *     A = L * L**H,  if UPLO = 'L',
    *  where U is an upper triangular matrix and L is a lower triangular
    *  matrix.  The factored form of A is then used to solve the system of
    *  equations A * X = B.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangle of A is stored;
    *          = 'L':  Lower triangle of A is stored.
    *
    *  N       (input) INTEGER
    *          The number of linear equations, i.e., the order of the
    *          matrix A.  N >= 0.
    *
    *  NRHS    (input) INTEGER
    *          The number of right hand sides, i.e., the number of columns
    *          of the matrix B.  NRHS >= 0.
    *
    *  AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
    *          On entry, the upper or lower triangle of the Hermitian matrix
    *          A, packed columnwise in a linear array.  The j-th column of A
    *          is stored in the array AP as follows:
    *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    *          See below for further details.
    *
    *          On exit, if INFO = 0, the factor U or L from the Cholesky
    *          factorization A = U**H*U or A = L*L**H, in the same storage
    *          format as A.
    *
    *  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
    *          On entry, the N-by-NRHS right hand side matrix B.
    *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the array B.  LDB >= max(1,N).
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *          > 0:  if INFO = i, the leading minor of order i of A is not
    *                positive definite, so the factorization could not be
    *                completed, and the solution has not been computed.
    *
    *  Further Details
    *  ===============
    *
    *  The packed storage scheme is illustrated by the following example
    *  when N = 4, UPLO = 'U':
    *
    *  Two-dimensional storage of the Hermitian matrix A:
    *
    *     a11 a12 a13 a14
    *         a22 a23 a24
    *             a33 a34     (aij = conjg(aji))
    *                 a44
    *
    *  Packed storage of the upper triangle of A:
    *
    *  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
    *
    *  =====================================================================
    *
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CPPTRF, CPPTRS, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( NRHS.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -6
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CPPSV ', -INFO )
             RETURN
          END IF
    *
    *     Compute the Cholesky factorization A = U'*U or A = L*L'.
    *
          CALL CPPTRF( UPLO, N, AP, INFO )
          IF( INFO.EQ.0 ) THEN
    *
    *        Solve the system A*X = B, overwriting B with X.
    *
             CALL CPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
    *
          END IF
          RETURN
    *
    *     End of CPPSV
    *
          END