zsytrf.f

          SUBROUTINE ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, LDA, LWORK, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX*16         A( LDA, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZSYTRF computes the factorization of a complex symmetric matrix A
    *  using the Bunch-Kaufman diagonal pivoting method.  The form of the
    *  factorization is
    *
    *     A = U*D*U**T  or  A = L*D*L**T
    *
    *  where U (or L) is a product of permutation and unit upper (lower)
    *  triangular matrices, and D is symmetric and block diagonal with
    *  with 1-by-1 and 2-by-2 diagonal blocks.
    *
    *  This is the blocked version of the algorithm, calling Level 3 BLAS.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangle of A is stored;
    *          = 'L':  Lower triangle of A is stored.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
    *          On entry, the symmetric 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, the block diagonal matrix D and the multipliers used
    *          to obtain the factor U or L (see below for further details).
    *
    *  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.
    *          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.
    *
    *  WORK    (workspace/output) COMPLEX*16 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.  For best performance
    *          LWORK >= N*NB, where NB is the block size returned by ILAENV.
    *
    *          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, and division by zero will occur if it
    *                is used to solve a system of equations.
    *
    *  Further Details
    *  ===============
    *
    *  If UPLO = 'U', then A = U*D*U', where
    *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
    *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
    *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    *  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
    *  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    *
    *             (   I    v    0   )   k-s
    *     U(k) =  (   0    I    0   )   s
    *             (   0    0    I   )   n-k
    *                k-s   s   n-k
    *
    *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
    *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
    *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
    *
    *  If UPLO = 'L', then A = L*D*L', where
    *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
    *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
    *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    *  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
    *  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    *
    *             (   I    0     0   )  k-1
    *     L(k) =  (   0    I     0   )  s
    *             (   0    v     I   )  n-k-s+1
    *                k-1   s  n-k-s+1
    *
    *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
    *  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
    *  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          LOGICAL            LQUERY, UPPER
          INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           LSAME, ILAENV
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZLASYF, ZSYTF2
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          UPPER = LSAME( UPLO, 'U' )
          LQUERY = ( LWORK.EQ.-1 )
          IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -4
          ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
             INFO = -7
          END IF
    *
          IF( INFO.EQ.0 ) THEN
    *
    *        Determine the block size
    *
             NB = ILAENV( 1, 'ZSYTRF', UPLO, N, -1, -1, -1 )
             LWKOPT = N*NB
             WORK( 1 ) = LWKOPT
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZSYTRF', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
          NBMIN = 2
          LDWORK = N
          IF( NB.GT.1 .AND. NB.LT.N ) THEN
             IWS = LDWORK*NB
             IF( LWORK.LT.IWS ) THEN
                NB = MAX( LWORK / LDWORK, 1 )
                NBMIN = MAX( 2, ILAENV( 2, 'ZSYTRF', UPLO, N, -1, -1, -1 ) )
             END IF
          ELSE
             IWS = 1
          END IF
          IF( NB.LT.NBMIN )
         $   NB = N
    *
          IF( UPPER ) THEN
    *
    *        Factorize A as U*D*U' using the upper triangle of A
    *
    *        K is the main loop index, decreasing from N to 1 in steps of
    *        KB, where KB is the number of columns factorized by ZLASYF;
    *        KB is either NB or NB-1, or K for the last block
    *
             K = N
       10    CONTINUE
    *
    *        If K < 1, exit from loop
    *
             IF( K.LT.1 )
         $      GO TO 40
    *
             IF( K.GT.NB ) THEN
    *
    *           Factorize columns k-kb+1:k of A and use blocked code to
    *           update columns 1:k-kb
    *
                CALL ZLASYF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, N, IINFO )
             ELSE
    *
    *           Use unblocked code to factorize columns 1:k of A
    *
                CALL ZSYTF2( UPLO, K, A, LDA, IPIV, IINFO )
                KB = K
             END IF
    *
    *        Set INFO on the first occurrence of a zero pivot
    *
             IF( INFO.EQ.0 .AND. IINFO.GT.0 )
         $      INFO = IINFO
    *
    *        Decrease K and return to the start of the main loop
    *
             K = K - KB
             GO TO 10
    *
          ELSE
    *
    *        Factorize A as L*D*L' using the lower triangle of A
    *
    *        K is the main loop index, increasing from 1 to N in steps of
    *        KB, where KB is the number of columns factorized by ZLASYF;
    *        KB is either NB or NB-1, or N-K+1 for the last block
    *
             K = 1
       20    CONTINUE
    *
    *        If K > N, exit from loop
    *
             IF( K.GT.N )
         $      GO TO 40
    *
             IF( K.LE.N-NB ) THEN
    *
    *           Factorize columns k:k+kb-1 of A and use blocked code to
    *           update columns k+kb:n
    *
                CALL ZLASYF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ),
         $                   WORK, N, IINFO )
             ELSE
    *
    *           Use unblocked code to factorize columns k:n of A
    *
                CALL ZSYTF2( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ), IINFO )
                KB = N - K + 1
             END IF
    *
    *        Set INFO on the first occurrence of a zero pivot
    *
             IF( INFO.EQ.0 .AND. IINFO.GT.0 )
         $      INFO = IINFO + K - 1
    *
    *        Adjust IPIV
    *
             DO 30 J = K, K + KB - 1
                IF( IPIV( J ).GT.0 ) THEN
                   IPIV( J ) = IPIV( J ) + K - 1
                ELSE
                   IPIV( J ) = IPIV( J ) - K + 1
                END IF
       30    CONTINUE
    *
    *        Increase K and return to the start of the main loop
    *
             K = K + KB
             GO TO 20
    *
          END IF
    *
       40 CONTINUE
          WORK( 1 ) = LWKOPT
          RETURN
    *
    *     End of ZSYTRF
    *
          END