chesv.f

          SUBROUTINE CHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
         $                  LWORK, 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, LDA, LDB, LWORK, N, NRHS
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CHESV computes the solution to a complex system of linear equations
    *     A * X = B,
    *  where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
    *  matrices.
    *
    *  The diagonal pivoting method is used to factor A as
    *     A = U * D * U**H,  if UPLO = 'U', or
    *     A = L * D * L**H,  if UPLO = 'L',
    *  where U (or L) is a product of permutation and unit upper (lower)
    *  triangular matrices, and D is Hermitian and block diagonal with
    *  1-by-1 and 2-by-2 diagonal blocks.  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.
    *
    *  A       (input/output) COMPLEX array, dimension (LDA,N)
    *          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
    *          N-by-N upper triangular part of A contains the upper
    *          triangular part of the matrix A, and the strictly lower
    *          triangular part of A is not referenced.  If UPLO = 'L', the
    *          leading N-by-N lower triangular part of A contains the lower
    *          triangular part of the matrix A, and the strictly upper
    *          triangular part of A is not referenced.
    *
    *          On exit, if INFO = 0, the block diagonal matrix D and the
    *          multipliers used to obtain the factor U or L from the
    *          factorization A = U*D*U**H or A = L*D*L**H as computed by
    *          CHETRF.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  IPIV    (output) INTEGER array, dimension (N)
    *          Details of the interchanges and the block structure of D, as
    *          determined by CHETRF.  If IPIV(k) > 0, then rows and columns
    *          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
    *          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
    *          then rows and columns k-1 and -IPIV(k) were interchanged and
    *          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
    *          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
    *          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
    *          diagonal block.
    *
    *  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).
    *
    *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The length of WORK.  LWORK >= 1, and for best performance
    *          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
    *          CHETRF.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal size of the WORK array, returns
    *          this value as the first entry of the WORK array, and no error
    *          message related to LWORK is issued by XERBLA.
    *
    *  INFO    (output) INTEGER
    *          = 0: successful exit
    *          < 0: if INFO = -i, the i-th argument had an illegal value
    *          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
    *               has been completed, but the block diagonal matrix D is
    *               exactly singular, so the solution could not be computed.
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          LOGICAL            LQUERY
          INTEGER            LWKOPT, NB
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           ILAENV, LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CHETRF, CHETRS, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          LQUERY = ( LWORK.EQ.-1 )
          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( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -5
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -8
          ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
             INFO = -10
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             IF( N.EQ.0 ) THEN
                LWKOPT = 1
             ELSE
                NB = ILAENV( 1, 'CHETRF', UPLO, N, -1, -1, -1 )
                LWKOPT = N*NB
             END IF
             WORK( 1 ) = LWKOPT
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CHESV ', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Compute the factorization A = U*D*U' or A = L*D*L'.
    *
          CALL CHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
          IF( INFO.EQ.0 ) THEN
    *
    *        Solve the system A*X = B, overwriting B with X.
    *
             CALL CHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
    *
          END IF
    *
          WORK( 1 ) = LWKOPT
    *
          RETURN
    *
    *     End of CHESV
    *
          END