dsytrf.f

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      SUBROUTINE DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DSYTRF computes the factorization of a real 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
*  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) DOUBLE PRECISION 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) DOUBLE PRECISION 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           DLASYF, DSYTF2, XERBLA
*     ..
*     .. 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, 'DSYTRF', UPLO, N, -1, -1, -1 )
         LWKOPT = N*NB
         WORK( 1 ) = LWKOPT
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DSYTRF', -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, 'DSYTRF', 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 DLASYF;
*        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 DLASYF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, LDWORK,
     $                   IINFO )
         ELSE
*
*           Use unblocked code to factorize columns 1:k of A
*
            CALL DSYTF2( 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 DLASYF;
*        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 DLASYF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ),
     $                   WORK, LDWORK, IINFO )
         ELSE
*
*           Use unblocked code to factorize columns k:n of A
*
            CALL DSYTF2( 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 DSYTRF
*
      END