LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zsytf2.f
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00001 *> \brief \b ZSYTF2
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZSYTF2 + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytf2.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZSYTF2( UPLO, N, A, LDA, IPIV, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, LDA, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       INTEGER            IPIV( * )
00029 *       COMPLEX*16         A( LDA, * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> ZSYTF2 computes the factorization of a complex symmetric matrix A
00039 *> using the Bunch-Kaufman diagonal pivoting method:
00040 *>
00041 *>    A = U*D*U**T  or  A = L*D*L**T
00042 *>
00043 *> where U (or L) is a product of permutation and unit upper (lower)
00044 *> triangular matrices, U**T is the transpose of U, and D is symmetric and
00045 *> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
00046 *>
00047 *> This is the unblocked version of the algorithm, calling Level 2 BLAS.
00048 *> \endverbatim
00049 *
00050 *  Arguments:
00051 *  ==========
00052 *
00053 *> \param[in] UPLO
00054 *> \verbatim
00055 *>          UPLO is CHARACTER*1
00056 *>          Specifies whether the upper or lower triangular part of the
00057 *>          symmetric matrix A is stored:
00058 *>          = 'U':  Upper triangular
00059 *>          = 'L':  Lower triangular
00060 *> \endverbatim
00061 *>
00062 *> \param[in] N
00063 *> \verbatim
00064 *>          N is INTEGER
00065 *>          The order of the matrix A.  N >= 0.
00066 *> \endverbatim
00067 *>
00068 *> \param[in,out] A
00069 *> \verbatim
00070 *>          A is COMPLEX*16 array, dimension (LDA,N)
00071 *>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
00072 *>          n-by-n upper triangular part of A contains the upper
00073 *>          triangular part of the matrix A, and the strictly lower
00074 *>          triangular part of A is not referenced.  If UPLO = 'L', the
00075 *>          leading n-by-n lower triangular part of A contains the lower
00076 *>          triangular part of the matrix A, and the strictly upper
00077 *>          triangular part of A is not referenced.
00078 *>
00079 *>          On exit, the block diagonal matrix D and the multipliers used
00080 *>          to obtain the factor U or L (see below for further details).
00081 *> \endverbatim
00082 *>
00083 *> \param[in] LDA
00084 *> \verbatim
00085 *>          LDA is INTEGER
00086 *>          The leading dimension of the array A.  LDA >= max(1,N).
00087 *> \endverbatim
00088 *>
00089 *> \param[out] IPIV
00090 *> \verbatim
00091 *>          IPIV is INTEGER array, dimension (N)
00092 *>          Details of the interchanges and the block structure of D.
00093 *>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
00094 *>          interchanged and D(k,k) is a 1-by-1 diagonal block.
00095 *>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
00096 *>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
00097 *>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
00098 *>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
00099 *>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
00100 *> \endverbatim
00101 *>
00102 *> \param[out] INFO
00103 *> \verbatim
00104 *>          INFO is INTEGER
00105 *>          = 0: successful exit
00106 *>          < 0: if INFO = -k, the k-th argument had an illegal value
00107 *>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
00108 *>               has been completed, but the block diagonal matrix D is
00109 *>               exactly singular, and division by zero will occur if it
00110 *>               is used to solve a system of equations.
00111 *> \endverbatim
00112 *
00113 *  Authors:
00114 *  ========
00115 *
00116 *> \author Univ. of Tennessee 
00117 *> \author Univ. of California Berkeley 
00118 *> \author Univ. of Colorado Denver 
00119 *> \author NAG Ltd. 
00120 *
00121 *> \date November 2011
00122 *
00123 *> \ingroup complex16SYcomputational
00124 *
00125 *> \par Further Details:
00126 *  =====================
00127 *>
00128 *> \verbatim
00129 *>
00130 *>  If UPLO = 'U', then A = U*D*U**T, where
00131 *>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
00132 *>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
00133 *>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
00134 *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
00135 *>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
00136 *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
00137 *>
00138 *>             (   I    v    0   )   k-s
00139 *>     U(k) =  (   0    I    0   )   s
00140 *>             (   0    0    I   )   n-k
00141 *>                k-s   s   n-k
00142 *>
00143 *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
00144 *>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
00145 *>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
00146 *>
00147 *>  If UPLO = 'L', then A = L*D*L**T, where
00148 *>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
00149 *>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
00150 *>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
00151 *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
00152 *>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
00153 *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
00154 *>
00155 *>             (   I    0     0   )  k-1
00156 *>     L(k) =  (   0    I     0   )  s
00157 *>             (   0    v     I   )  n-k-s+1
00158 *>                k-1   s  n-k-s+1
00159 *>
00160 *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
00161 *>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
00162 *>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
00163 *> \endverbatim
00164 *
00165 *> \par Contributors:
00166 *  ==================
00167 *>
00168 *> \verbatim
00169 *>
00170 *>  09-29-06 - patch from
00171 *>    Bobby Cheng, MathWorks
00172 *>
00173 *>    Replace l.209 and l.377
00174 *>         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
00175 *>    by
00176 *>         IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
00177 *>
00178 *>  1-96 - Based on modifications by J. Lewis, Boeing Computer Services
00179 *>         Company
00180 *> \endverbatim
00181 *
00182 *  =====================================================================
00183       SUBROUTINE ZSYTF2( UPLO, N, A, LDA, IPIV, INFO )
00184 *
00185 *  -- LAPACK computational routine (version 3.4.0) --
00186 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00187 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00188 *     November 2011
00189 *
00190 *     .. Scalar Arguments ..
00191       CHARACTER          UPLO
00192       INTEGER            INFO, LDA, N
00193 *     ..
00194 *     .. Array Arguments ..
00195       INTEGER            IPIV( * )
00196       COMPLEX*16         A( LDA, * )
00197 *     ..
00198 *
00199 *  =====================================================================
00200 *
00201 *     .. Parameters ..
00202       DOUBLE PRECISION   ZERO, ONE
00203       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00204       DOUBLE PRECISION   EIGHT, SEVTEN
00205       PARAMETER          ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
00206       COMPLEX*16         CONE
00207       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
00208 *     ..
00209 *     .. Local Scalars ..
00210       LOGICAL            UPPER
00211       INTEGER            I, IMAX, J, JMAX, K, KK, KP, KSTEP
00212       DOUBLE PRECISION   ABSAKK, ALPHA, COLMAX, ROWMAX
00213       COMPLEX*16         D11, D12, D21, D22, R1, T, WK, WKM1, WKP1, Z
00214 *     ..
00215 *     .. External Functions ..
00216       LOGICAL            DISNAN, LSAME
00217       INTEGER            IZAMAX
00218       EXTERNAL           DISNAN, LSAME, IZAMAX
00219 *     ..
00220 *     .. External Subroutines ..
00221       EXTERNAL           XERBLA, ZSCAL, ZSWAP, ZSYR
00222 *     ..
00223 *     .. Intrinsic Functions ..
00224       INTRINSIC          ABS, DBLE, DIMAG, MAX, SQRT
00225 *     ..
00226 *     .. Statement Functions ..
00227       DOUBLE PRECISION   CABS1
00228 *     ..
00229 *     .. Statement Function definitions ..
00230       CABS1( Z ) = ABS( DBLE( Z ) ) + ABS( DIMAG( Z ) )
00231 *     ..
00232 *     .. Executable Statements ..
00233 *
00234 *     Test the input parameters.
00235 *
00236       INFO = 0
00237       UPPER = LSAME( UPLO, 'U' )
00238       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00239          INFO = -1
00240       ELSE IF( N.LT.0 ) THEN
00241          INFO = -2
00242       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00243          INFO = -4
00244       END IF
00245       IF( INFO.NE.0 ) THEN
00246          CALL XERBLA( 'ZSYTF2', -INFO )
00247          RETURN
00248       END IF
00249 *
00250 *     Initialize ALPHA for use in choosing pivot block size.
00251 *
00252       ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
00253 *
00254       IF( UPPER ) THEN
00255 *
00256 *        Factorize A as U*D*U**T using the upper triangle of A
00257 *
00258 *        K is the main loop index, decreasing from N to 1 in steps of
00259 *        1 or 2
00260 *
00261          K = N
00262    10    CONTINUE
00263 *
00264 *        If K < 1, exit from loop
00265 *
00266          IF( K.LT.1 )
00267      $      GO TO 70
00268          KSTEP = 1
00269 *
00270 *        Determine rows and columns to be interchanged and whether
00271 *        a 1-by-1 or 2-by-2 pivot block will be used
00272 *
00273          ABSAKK = CABS1( A( K, K ) )
00274 *
00275 *        IMAX is the row-index of the largest off-diagonal element in
00276 *        column K, and COLMAX is its absolute value
00277 *
00278          IF( K.GT.1 ) THEN
00279             IMAX = IZAMAX( K-1, A( 1, K ), 1 )
00280             COLMAX = CABS1( A( IMAX, K ) )
00281          ELSE
00282             COLMAX = ZERO
00283          END IF
00284 *
00285          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. DISNAN(ABSAKK) ) THEN
00286 *
00287 *           Column K is zero or NaN: set INFO and continue
00288 *
00289             IF( INFO.EQ.0 )
00290      $         INFO = K
00291             KP = K
00292          ELSE
00293             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
00294 *
00295 *              no interchange, use 1-by-1 pivot block
00296 *
00297                KP = K
00298             ELSE
00299 *
00300 *              JMAX is the column-index of the largest off-diagonal
00301 *              element in row IMAX, and ROWMAX is its absolute value
00302 *
00303                JMAX = IMAX + IZAMAX( K-IMAX, A( IMAX, IMAX+1 ), LDA )
00304                ROWMAX = CABS1( A( IMAX, JMAX ) )
00305                IF( IMAX.GT.1 ) THEN
00306                   JMAX = IZAMAX( IMAX-1, A( 1, IMAX ), 1 )
00307                   ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) )
00308                END IF
00309 *
00310                IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
00311 *
00312 *                 no interchange, use 1-by-1 pivot block
00313 *
00314                   KP = K
00315                ELSE IF( CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX ) THEN
00316 *
00317 *                 interchange rows and columns K and IMAX, use 1-by-1
00318 *                 pivot block
00319 *
00320                   KP = IMAX
00321                ELSE
00322 *
00323 *                 interchange rows and columns K-1 and IMAX, use 2-by-2
00324 *                 pivot block
00325 *
00326                   KP = IMAX
00327                   KSTEP = 2
00328                END IF
00329             END IF
00330 *
00331             KK = K - KSTEP + 1
00332             IF( KP.NE.KK ) THEN
00333 *
00334 *              Interchange rows and columns KK and KP in the leading
00335 *              submatrix A(1:k,1:k)
00336 *
00337                CALL ZSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
00338                CALL ZSWAP( KK-KP-1, A( KP+1, KK ), 1, A( KP, KP+1 ),
00339      $                     LDA )
00340                T = A( KK, KK )
00341                A( KK, KK ) = A( KP, KP )
00342                A( KP, KP ) = T
00343                IF( KSTEP.EQ.2 ) THEN
00344                   T = A( K-1, K )
00345                   A( K-1, K ) = A( KP, K )
00346                   A( KP, K ) = T
00347                END IF
00348             END IF
00349 *
00350 *           Update the leading submatrix
00351 *
00352             IF( KSTEP.EQ.1 ) THEN
00353 *
00354 *              1-by-1 pivot block D(k): column k now holds
00355 *
00356 *              W(k) = U(k)*D(k)
00357 *
00358 *              where U(k) is the k-th column of U
00359 *
00360 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
00361 *
00362 *              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
00363 *
00364                R1 = CONE / A( K, K )
00365                CALL ZSYR( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
00366 *
00367 *              Store U(k) in column k
00368 *
00369                CALL ZSCAL( K-1, R1, A( 1, K ), 1 )
00370             ELSE
00371 *
00372 *              2-by-2 pivot block D(k): columns k and k-1 now hold
00373 *
00374 *              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
00375 *
00376 *              where U(k) and U(k-1) are the k-th and (k-1)-th columns
00377 *              of U
00378 *
00379 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
00380 *
00381 *              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
00382 *                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
00383 *
00384                IF( K.GT.2 ) THEN
00385 *
00386                   D12 = A( K-1, K )
00387                   D22 = A( K-1, K-1 ) / D12
00388                   D11 = A( K, K ) / D12
00389                   T = CONE / ( D11*D22-CONE )
00390                   D12 = T / D12
00391 *
00392                   DO 30 J = K - 2, 1, -1
00393                      WKM1 = D12*( D11*A( J, K-1 )-A( J, K ) )
00394                      WK = D12*( D22*A( J, K )-A( J, K-1 ) )
00395                      DO 20 I = J, 1, -1
00396                         A( I, J ) = A( I, J ) - A( I, K )*WK -
00397      $                              A( I, K-1 )*WKM1
00398    20                CONTINUE
00399                      A( J, K ) = WK
00400                      A( J, K-1 ) = WKM1
00401    30             CONTINUE
00402 *
00403                END IF
00404 *
00405             END IF
00406          END IF
00407 *
00408 *        Store details of the interchanges in IPIV
00409 *
00410          IF( KSTEP.EQ.1 ) THEN
00411             IPIV( K ) = KP
00412          ELSE
00413             IPIV( K ) = -KP
00414             IPIV( K-1 ) = -KP
00415          END IF
00416 *
00417 *        Decrease K and return to the start of the main loop
00418 *
00419          K = K - KSTEP
00420          GO TO 10
00421 *
00422       ELSE
00423 *
00424 *        Factorize A as L*D*L**T using the lower triangle of A
00425 *
00426 *        K is the main loop index, increasing from 1 to N in steps of
00427 *        1 or 2
00428 *
00429          K = 1
00430    40    CONTINUE
00431 *
00432 *        If K > N, exit from loop
00433 *
00434          IF( K.GT.N )
00435      $      GO TO 70
00436          KSTEP = 1
00437 *
00438 *        Determine rows and columns to be interchanged and whether
00439 *        a 1-by-1 or 2-by-2 pivot block will be used
00440 *
00441          ABSAKK = CABS1( A( K, K ) )
00442 *
00443 *        IMAX is the row-index of the largest off-diagonal element in
00444 *        column K, and COLMAX is its absolute value
00445 *
00446          IF( K.LT.N ) THEN
00447             IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )
00448             COLMAX = CABS1( A( IMAX, K ) )
00449          ELSE
00450             COLMAX = ZERO
00451          END IF
00452 *
00453          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. DISNAN(ABSAKK) ) THEN
00454 *
00455 *           Column K is zero or NaN: set INFO and continue
00456 *
00457             IF( INFO.EQ.0 )
00458      $         INFO = K
00459             KP = K
00460          ELSE
00461             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
00462 *
00463 *              no interchange, use 1-by-1 pivot block
00464 *
00465                KP = K
00466             ELSE
00467 *
00468 *              JMAX is the column-index of the largest off-diagonal
00469 *              element in row IMAX, and ROWMAX is its absolute value
00470 *
00471                JMAX = K - 1 + IZAMAX( IMAX-K, A( IMAX, K ), LDA )
00472                ROWMAX = CABS1( A( IMAX, JMAX ) )
00473                IF( IMAX.LT.N ) THEN
00474                   JMAX = IMAX + IZAMAX( N-IMAX, A( IMAX+1, IMAX ), 1 )
00475                   ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) )
00476                END IF
00477 *
00478                IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
00479 *
00480 *                 no interchange, use 1-by-1 pivot block
00481 *
00482                   KP = K
00483                ELSE IF( CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX ) THEN
00484 *
00485 *                 interchange rows and columns K and IMAX, use 1-by-1
00486 *                 pivot block
00487 *
00488                   KP = IMAX
00489                ELSE
00490 *
00491 *                 interchange rows and columns K+1 and IMAX, use 2-by-2
00492 *                 pivot block
00493 *
00494                   KP = IMAX
00495                   KSTEP = 2
00496                END IF
00497             END IF
00498 *
00499             KK = K + KSTEP - 1
00500             IF( KP.NE.KK ) THEN
00501 *
00502 *              Interchange rows and columns KK and KP in the trailing
00503 *              submatrix A(k:n,k:n)
00504 *
00505                IF( KP.LT.N )
00506      $            CALL ZSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
00507                CALL ZSWAP( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
00508      $                     LDA )
00509                T = A( KK, KK )
00510                A( KK, KK ) = A( KP, KP )
00511                A( KP, KP ) = T
00512                IF( KSTEP.EQ.2 ) THEN
00513                   T = A( K+1, K )
00514                   A( K+1, K ) = A( KP, K )
00515                   A( KP, K ) = T
00516                END IF
00517             END IF
00518 *
00519 *           Update the trailing submatrix
00520 *
00521             IF( KSTEP.EQ.1 ) THEN
00522 *
00523 *              1-by-1 pivot block D(k): column k now holds
00524 *
00525 *              W(k) = L(k)*D(k)
00526 *
00527 *              where L(k) is the k-th column of L
00528 *
00529                IF( K.LT.N ) THEN
00530 *
00531 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
00532 *
00533 *                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
00534 *
00535                   R1 = CONE / A( K, K )
00536                   CALL ZSYR( UPLO, N-K, -R1, A( K+1, K ), 1,
00537      $                       A( K+1, K+1 ), LDA )
00538 *
00539 *                 Store L(k) in column K
00540 *
00541                   CALL ZSCAL( N-K, R1, A( K+1, K ), 1 )
00542                END IF
00543             ELSE
00544 *
00545 *              2-by-2 pivot block D(k)
00546 *
00547                IF( K.LT.N-1 ) THEN
00548 *
00549 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
00550 *
00551 *                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
00552 *                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
00553 *
00554 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
00555 *                 columns of L
00556 *
00557                   D21 = A( K+1, K )
00558                   D11 = A( K+1, K+1 ) / D21
00559                   D22 = A( K, K ) / D21
00560                   T = CONE / ( D11*D22-CONE )
00561                   D21 = T / D21
00562 *
00563                   DO 60 J = K + 2, N
00564                      WK = D21*( D11*A( J, K )-A( J, K+1 ) )
00565                      WKP1 = D21*( D22*A( J, K+1 )-A( J, K ) )
00566                      DO 50 I = J, N
00567                         A( I, J ) = A( I, J ) - A( I, K )*WK -
00568      $                              A( I, K+1 )*WKP1
00569    50                CONTINUE
00570                      A( J, K ) = WK
00571                      A( J, K+1 ) = WKP1
00572    60             CONTINUE
00573                END IF
00574             END IF
00575          END IF
00576 *
00577 *        Store details of the interchanges in IPIV
00578 *
00579          IF( KSTEP.EQ.1 ) THEN
00580             IPIV( K ) = KP
00581          ELSE
00582             IPIV( K ) = -KP
00583             IPIV( K+1 ) = -KP
00584          END IF
00585 *
00586 *        Increase K and return to the start of the main loop
00587 *
00588          K = K + KSTEP
00589          GO TO 40
00590 *
00591       END IF
00592 *
00593    70 CONTINUE
00594       RETURN
00595 *
00596 *     End of ZSYTF2
00597 *
00598       END
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