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   *> \brief \b ZHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm, calling Level 2 BLAS).
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZHETF2 + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetf2.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetf2.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetf2.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, LDA, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       COMPLEX*16         A( LDA, * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHETF2 computes the factorization of a complex Hermitian matrix A
   *> using the Bunch-Kaufman diagonal pivoting method:
   *>
   *>    A = U*D*U**H  or  A = L*D*L**H
   *>
   *> where U (or L) is a product of permutation and unit upper (lower)
   *> triangular matrices, U**H is the conjugate transpose of U, and D is
   *> Hermitian 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.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          Specifies whether the upper or lower triangular part of the
   *>          Hermitian matrix A is stored:
   *>          = 'U':  Upper triangular
   *>          = 'L':  Lower triangular
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is COMPLEX*16 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, the block diagonal matrix D and the multipliers used
   *>          to obtain the factor U or L (see below for further details).
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N)
   *>          Details of the interchanges and the block structure of D.
   *>
   *>          If UPLO = 'U':
   *>             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 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':
   *>             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 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.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is 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.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup complex16HEcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  If UPLO = 'U', then A = U*D*U**H, 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**H, 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).
   *> \endverbatim
   *
   *> \par Contributors:
   *  ==================
   *>
   *> \verbatim
   *>  09-29-06 - patch from
   *>    Bobby Cheng, MathWorks
   *>
   *>    Replace l.210 and l.393
   *>         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
   *>    by
   *>         IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
   *>
   *>  01-01-96 - Based on modifications by
   *>    J. Lewis, Boeing Computer Services Company
   *>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
   *> \endverbatim
   *
   *  =====================================================================
       SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO )        SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2011                                                      --  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
Line 14 Line 202
       COMPLEX*16         A( LDA, * )        COMPLEX*16         A( LDA, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHETF2 computes the factorization of a complex Hermitian matrix A  
 *  using the Bunch-Kaufman diagonal pivoting method:  
 *  
 *     A = U*D*U**H  or  A = L*D*L**H  
 *  
 *  where U (or L) is a product of permutation and unit upper (lower)  
 *  triangular matrices, U**H is the conjugate transpose of U, and D is  
 *  Hermitian 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  
 *          Hermitian 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 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, 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.210 and l.393  
 *         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN  
 *    by  
 *         IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN  
 *  
 *  01-01-96 - Based on modifications by  
 *    J. Lewis, Boeing Computer Services Company  
 *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA  
 *  
 *  If UPLO = 'U', then A = U*D*U**H, 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**H, 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 ..  *     .. Parameters ..
Line 199 Line 279
          ABSAKK = ABS( DBLE( A( K, K ) ) )           ABSAKK = ABS( DBLE( A( K, K ) ) )
 *  *
 *        IMAX is the row-index of the largest off-diagonal element in  *        IMAX is the row-index of the largest off-diagonal element in
 *        column K, and COLMAX is its absolute value  *        column K, and COLMAX is its absolute value.
   *        Determine both COLMAX and IMAX.
 *  *
          IF( K.GT.1 ) THEN           IF( K.GT.1 ) THEN
             IMAX = IZAMAX( K-1, A( 1, K ), 1 )              IMAX = IZAMAX( K-1, A( 1, K ), 1 )
Line 210 Line 291
 *  *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN           IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
 *  *
 *           Column K is zero or contains a NaN: set INFO and continue  *           Column K is zero or underflow, or contains a NaN:
   *           set INFO and continue
 *  *
             IF( INFO.EQ.0 )              IF( INFO.EQ.0 )
      $         INFO = K       $         INFO = K
             KP = K              KP = K
             A( K, K ) = DBLE( A( K, K ) )              A( K, K ) = DBLE( A( K, K ) )
          ELSE           ELSE
   *
   *           ============================================================
   *
   *           Test for interchange
   *
             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN              IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
 *  *
 *              no interchange, use 1-by-1 pivot block  *              no interchange, use 1-by-1 pivot block
Line 225 Line 312
             ELSE              ELSE
 *  *
 *              JMAX is the column-index of the largest off-diagonal  *              JMAX is the column-index of the largest off-diagonal
 *              element in row IMAX, and ROWMAX is its absolute value  *              element in row IMAX, and ROWMAX is its absolute value.
   *              Determine only ROWMAX.
 *  *
                JMAX = IMAX + IZAMAX( K-IMAX, A( IMAX, IMAX+1 ), LDA )                 JMAX = IMAX + IZAMAX( K-IMAX, A( IMAX, IMAX+1 ), LDA )
                ROWMAX = CABS1( A( IMAX, JMAX ) )                 ROWMAX = CABS1( A( IMAX, JMAX ) )
Line 239 Line 327
 *                 no interchange, use 1-by-1 pivot block  *                 no interchange, use 1-by-1 pivot block
 *  *
                   KP = K                    KP = K
   *
                ELSE IF( ABS( DBLE( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX )                 ELSE IF( ABS( DBLE( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX )
      $                   THEN       $                   THEN
 *  *
Line 254 Line 343
                   KP = IMAX                    KP = IMAX
                   KSTEP = 2                    KSTEP = 2
                END IF                 END IF
   *
             END IF              END IF
 *  *
   *           ============================================================
   *
             KK = K - KSTEP + 1              KK = K - KSTEP + 1
             IF( KP.NE.KK ) THEN              IF( KP.NE.KK ) THEN
 *  *
Line 382 Line 474
          ABSAKK = ABS( DBLE( A( K, K ) ) )           ABSAKK = ABS( DBLE( A( K, K ) ) )
 *  *
 *        IMAX is the row-index of the largest off-diagonal element in  *        IMAX is the row-index of the largest off-diagonal element in
 *        column K, and COLMAX is its absolute value  *        column K, and COLMAX is its absolute value.
   *        Determine both COLMAX and IMAX.
 *  *
          IF( K.LT.N ) THEN           IF( K.LT.N ) THEN
             IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )              IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )
Line 393 Line 486
 *  *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN           IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
 *  *
 *           Column K is zero or contains a NaN: set INFO and continue  *           Column K is zero or underflow, or contains a NaN:
   *           set INFO and continue
 *  *
             IF( INFO.EQ.0 )              IF( INFO.EQ.0 )
      $         INFO = K       $         INFO = K
             KP = K              KP = K
             A( K, K ) = DBLE( A( K, K ) )              A( K, K ) = DBLE( A( K, K ) )
          ELSE           ELSE
   *
   *           ============================================================
   *
   *           Test for interchange
   *
             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN              IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
 *  *
 *              no interchange, use 1-by-1 pivot block  *              no interchange, use 1-by-1 pivot block
Line 408 Line 507
             ELSE              ELSE
 *  *
 *              JMAX is the column-index of the largest off-diagonal  *              JMAX is the column-index of the largest off-diagonal
 *              element in row IMAX, and ROWMAX is its absolute value  *              element in row IMAX, and ROWMAX is its absolute value.
   *              Determine only ROWMAX.
 *  *
                JMAX = K - 1 + IZAMAX( IMAX-K, A( IMAX, K ), LDA )                 JMAX = K - 1 + IZAMAX( IMAX-K, A( IMAX, K ), LDA )
                ROWMAX = CABS1( A( IMAX, JMAX ) )                 ROWMAX = CABS1( A( IMAX, JMAX ) )
Line 422 Line 522
 *                 no interchange, use 1-by-1 pivot block  *                 no interchange, use 1-by-1 pivot block
 *  *
                   KP = K                    KP = K
   *
                ELSE IF( ABS( DBLE( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX )                 ELSE IF( ABS( DBLE( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX )
      $                   THEN       $                   THEN
 *  *
Line 437 Line 538
                   KP = IMAX                    KP = IMAX
                   KSTEP = 2                    KSTEP = 2
                END IF                 END IF
   *
             END IF              END IF
 *  *
   *           ============================================================
   *
             KK = K + KSTEP - 1              KK = K + KSTEP - 1
             IF( KP.NE.KK ) THEN              IF( KP.NE.KK ) THEN
 *  *
Removed from v.1.8  
changed lines
  Added in v.1.19

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