```      SUBROUTINE ZSYTF2( UPLO, N, A, LDA, IPIV, 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, N
*     ..
*     .. Array Arguments ..
INTEGER            IPIV( * )
COMPLEX*16         A( LDA, * )
*     ..
*
*  Purpose
*  =======
*
*  ZSYTF2 computes the factorization of a complex symmetric matrix A
*  using the Bunch-Kaufman diagonal pivoting method:
*
*     A = U*D*U'  or  A = L*D*L'
*
*  where U (or L) is a product of permutation and unit upper (lower)
*  triangular matrices, U' is the transpose of U, and D is symmetric and
*  block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
*
*  This is the unblocked version of the algorithm, calling Level 2 BLAS.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          symmetric matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  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.
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -k, the k-th argument had an illegal value
*          > 0: if INFO = k, D(k,k) 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
*  ===============
*
*  09-29-06 - patch from
*    Bobby Cheng, MathWorks
*
*    Replace l.209 and l.377
*         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
*    by
*         IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
*
*  1-96 - Based on modifications by J. Lewis, Boeing Computer Services
*         Company
*
*  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).
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO, ONE
PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
DOUBLE PRECISION   EIGHT, SEVTEN
PARAMETER          ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
COMPLEX*16         CONE
PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
LOGICAL            UPPER
INTEGER            I, IMAX, J, JMAX, K, KK, KP, KSTEP
DOUBLE PRECISION   ABSAKK, ALPHA, COLMAX, ROWMAX
COMPLEX*16         D11, D12, D21, D22, R1, T, WK, WKM1, WKP1, Z
*     ..
*     .. External Functions ..
LOGICAL            DISNAN, LSAME
INTEGER            IZAMAX
EXTERNAL           DISNAN, LSAME, IZAMAX
*     ..
*     .. External Subroutines ..
EXTERNAL           XERBLA, ZSCAL, ZSWAP, ZSYR
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, DBLE, DIMAG, MAX, SQRT
*     ..
*     .. Statement Functions ..
DOUBLE PRECISION   CABS1
*     ..
*     .. Statement Function definitions ..
CABS1( Z ) = ABS( DBLE( Z ) ) + ABS( DIMAG( Z ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
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
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZSYTF2', -INFO )
RETURN
END IF
*
*     Initialize ALPHA for use in choosing pivot block size.
*
ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
*
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
*        1 or 2
*
K = N
10    CONTINUE
*
*        If K < 1, exit from loop
*
IF( K.LT.1 )
\$      GO TO 70
KSTEP = 1
*
*        Determine rows and columns to be interchanged and whether
*        a 1-by-1 or 2-by-2 pivot block will be used
*
ABSAKK = CABS1( A( K, K ) )
*
*        IMAX is the row-index of the largest off-diagonal element in
*        column K, and COLMAX is its absolute value
*
IF( K.GT.1 ) THEN
IMAX = IZAMAX( K-1, A( 1, K ), 1 )
COLMAX = CABS1( A( IMAX, K ) )
ELSE
COLMAX = ZERO
END IF
*
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. DISNAN(ABSAKK) ) THEN
*
*           Column K is zero or contains a NaN: set INFO and continue
*
IF( INFO.EQ.0 )
\$         INFO = K
KP = K
ELSE
IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
*
*              no interchange, use 1-by-1 pivot block
*
KP = K
ELSE
*
*              JMAX is the column-index of the largest off-diagonal
*              element in row IMAX, and ROWMAX is its absolute value
*
JMAX = IMAX + IZAMAX( K-IMAX, A( IMAX, IMAX+1 ), LDA )
ROWMAX = CABS1( A( IMAX, JMAX ) )
IF( IMAX.GT.1 ) THEN
JMAX = IZAMAX( IMAX-1, A( 1, IMAX ), 1 )
ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) )
END IF
*
IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
*
*                 no interchange, use 1-by-1 pivot block
*
KP = K
ELSE IF( CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX ) THEN
*
*                 interchange rows and columns K and IMAX, use 1-by-1
*                 pivot block
*
KP = IMAX
ELSE
*
*                 interchange rows and columns K-1 and IMAX, use 2-by-2
*                 pivot block
*
KP = IMAX
KSTEP = 2
END IF
END IF
*
KK = K - KSTEP + 1
IF( KP.NE.KK ) THEN
*
*              Interchange rows and columns KK and KP in the leading
*              submatrix A(1:k,1:k)
*
CALL ZSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
CALL ZSWAP( KK-KP-1, A( KP+1, KK ), 1, A( KP, KP+1 ),
\$                     LDA )
T = A( KK, KK )
A( KK, KK ) = A( KP, KP )
A( KP, KP ) = T
IF( KSTEP.EQ.2 ) THEN
T = A( K-1, K )
A( K-1, K ) = A( KP, K )
A( KP, K ) = T
END IF
END IF
*
*
IF( KSTEP.EQ.1 ) THEN
*
*              1-by-1 pivot block D(k): column k now holds
*
*              W(k) = U(k)*D(k)
*
*              where U(k) is the k-th column of U
*
*              Perform a rank-1 update of A(1:k-1,1:k-1) as
*
*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
*
R1 = CONE / A( K, K )
CALL ZSYR( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
*
*              Store U(k) in column k
*
CALL ZSCAL( K-1, R1, A( 1, K ), 1 )
ELSE
*
*              2-by-2 pivot block D(k): columns k and k-1 now hold
*
*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
*
*              where U(k) and U(k-1) are the k-th and (k-1)-th columns
*              of U
*
*              Perform a rank-2 update of A(1:k-2,1:k-2) as
*
*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
*
IF( K.GT.2 ) THEN
*
D12 = A( K-1, K )
D22 = A( K-1, K-1 ) / D12
D11 = A( K, K ) / D12
T = CONE / ( D11*D22-CONE )
D12 = T / D12
*
DO 30 J = K - 2, 1, -1
WKM1 = D12*( D11*A( J, K-1 )-A( J, K ) )
WK = D12*( D22*A( J, K )-A( J, K-1 ) )
DO 20 I = J, 1, -1
A( I, J ) = A( I, J ) - A( I, K )*WK -
\$                              A( I, K-1 )*WKM1
20                CONTINUE
A( J, K ) = WK
A( J, K-1 ) = WKM1
30             CONTINUE
*
END IF
*
END IF
END IF
*
*        Store details of the interchanges in IPIV
*
IF( KSTEP.EQ.1 ) THEN
IPIV( K ) = KP
ELSE
IPIV( K ) = -KP
IPIV( K-1 ) = -KP
END IF
*
*        Decrease K and return to the start of the main loop
*
K = K - KSTEP
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
*        1 or 2
*
K = 1
40    CONTINUE
*
*        If K > N, exit from loop
*
IF( K.GT.N )
\$      GO TO 70
KSTEP = 1
*
*        Determine rows and columns to be interchanged and whether
*        a 1-by-1 or 2-by-2 pivot block will be used
*
ABSAKK = CABS1( A( K, K ) )
*
*        IMAX is the row-index of the largest off-diagonal element in
*        column K, and COLMAX is its absolute value
*
IF( K.LT.N ) THEN
IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )
COLMAX = CABS1( A( IMAX, K ) )
ELSE
COLMAX = ZERO
END IF
*
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. DISNAN(ABSAKK) ) THEN
*
*           Column K is zero or contains a NaN: set INFO and continue
*
IF( INFO.EQ.0 )
\$         INFO = K
KP = K
ELSE
IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
*
*              no interchange, use 1-by-1 pivot block
*
KP = K
ELSE
*
*              JMAX is the column-index of the largest off-diagonal
*              element in row IMAX, and ROWMAX is its absolute value
*
JMAX = K - 1 + IZAMAX( IMAX-K, A( IMAX, K ), LDA )
ROWMAX = CABS1( A( IMAX, JMAX ) )
IF( IMAX.LT.N ) THEN
JMAX = IMAX + IZAMAX( N-IMAX, A( IMAX+1, IMAX ), 1 )
ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) )
END IF
*
IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
*
*                 no interchange, use 1-by-1 pivot block
*
KP = K
ELSE IF( CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX ) THEN
*
*                 interchange rows and columns K and IMAX, use 1-by-1
*                 pivot block
*
KP = IMAX
ELSE
*
*                 interchange rows and columns K+1 and IMAX, use 2-by-2
*                 pivot block
*
KP = IMAX
KSTEP = 2
END IF
END IF
*
KK = K + KSTEP - 1
IF( KP.NE.KK ) THEN
*
*              Interchange rows and columns KK and KP in the trailing
*              submatrix A(k:n,k:n)
*
IF( KP.LT.N )
\$            CALL ZSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
CALL ZSWAP( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
\$                     LDA )
T = A( KK, KK )
A( KK, KK ) = A( KP, KP )
A( KP, KP ) = T
IF( KSTEP.EQ.2 ) THEN
T = A( K+1, K )
A( K+1, K ) = A( KP, K )
A( KP, K ) = T
END IF
END IF
*
*           Update the trailing submatrix
*
IF( KSTEP.EQ.1 ) THEN
*
*              1-by-1 pivot block D(k): column k now holds
*
*              W(k) = L(k)*D(k)
*
*              where L(k) is the k-th column of L
*
IF( K.LT.N ) THEN
*
*                 Perform a rank-1 update of A(k+1:n,k+1:n) as
*
*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
*
R1 = CONE / A( K, K )
CALL ZSYR( UPLO, N-K, -R1, A( K+1, K ), 1,
\$                       A( K+1, K+1 ), LDA )
*
*                 Store L(k) in column K
*
CALL ZSCAL( N-K, R1, A( K+1, K ), 1 )
END IF
ELSE
*
*              2-by-2 pivot block D(k)
*
IF( K.LT.N-1 ) THEN
*
*                 Perform a rank-2 update of A(k+2:n,k+2:n) as
*
*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
*
*                 where L(k) and L(k+1) are the k-th and (k+1)-th
*                 columns of L
*
D21 = A( K+1, K )
D11 = A( K+1, K+1 ) / D21
D22 = A( K, K ) / D21
T = CONE / ( D11*D22-CONE )
D21 = T / D21
*
DO 60 J = K + 2, N
WK = D21*( D11*A( J, K )-A( J, K+1 ) )
WKP1 = D21*( D22*A( J, K+1 )-A( J, K ) )
DO 50 I = J, N
A( I, J ) = A( I, J ) - A( I, K )*WK -
\$                              A( I, K+1 )*WKP1
50                CONTINUE
A( J, K ) = WK
A( J, K+1 ) = WKP1
60             CONTINUE
END IF
END IF
END IF
*
*        Store details of the interchanges in IPIV
*
IF( KSTEP.EQ.1 ) THEN
IPIV( K ) = KP
ELSE
IPIV( K ) = -KP
IPIV( K+1 ) = -KP
END IF
*
*        Increase K and return to the start of the main loop
*
K = K + KSTEP
GO TO 40
*
END IF
*
70 CONTINUE
RETURN
*
*     End of ZSYTF2
*
END

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