LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ssptrf.f
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00001 *> \brief \b SSPTRF
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00009 *> Download SSPTRF + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SSPTRF( UPLO, N, AP, IPIV, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       INTEGER            IPIV( * )
00029 *       REAL               AP( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> SSPTRF computes the factorization of a real symmetric matrix A stored
00039 *> in packed format 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, and D is symmetric and block diagonal with
00045 *> 1-by-1 and 2-by-2 diagonal blocks.
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] UPLO
00052 *> \verbatim
00053 *>          UPLO is CHARACTER*1
00054 *>          = 'U':  Upper triangle of A is stored;
00055 *>          = 'L':  Lower triangle of A is stored.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The order of the matrix A.  N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in,out] AP
00065 *> \verbatim
00066 *>          AP is REAL array, dimension (N*(N+1)/2)
00067 *>          On entry, the upper or lower triangle of the symmetric matrix
00068 *>          A, packed columnwise in a linear array.  The j-th column of A
00069 *>          is stored in the array AP as follows:
00070 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00071 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00072 *>
00073 *>          On exit, the block diagonal matrix D and the multipliers used
00074 *>          to obtain the factor U or L, stored as a packed triangular
00075 *>          matrix overwriting A (see below for further details).
00076 *> \endverbatim
00077 *>
00078 *> \param[out] IPIV
00079 *> \verbatim
00080 *>          IPIV is INTEGER array, dimension (N)
00081 *>          Details of the interchanges and the block structure of D.
00082 *>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
00083 *>          interchanged and D(k,k) is a 1-by-1 diagonal block.
00084 *>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
00085 *>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
00086 *>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
00087 *>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
00088 *>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
00089 *> \endverbatim
00090 *>
00091 *> \param[out] INFO
00092 *> \verbatim
00093 *>          INFO is INTEGER
00094 *>          = 0: successful exit
00095 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00096 *>          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
00097 *>               has been completed, but the block diagonal matrix D is
00098 *>               exactly singular, and division by zero will occur if it
00099 *>               is used to solve a system of equations.
00100 *> \endverbatim
00101 *
00102 *  Authors:
00103 *  ========
00104 *
00105 *> \author Univ. of Tennessee 
00106 *> \author Univ. of California Berkeley 
00107 *> \author Univ. of Colorado Denver 
00108 *> \author NAG Ltd. 
00109 *
00110 *> \date November 2011
00111 *
00112 *> \ingroup realOTHERcomputational
00113 *
00114 *> \par Further Details:
00115 *  =====================
00116 *>
00117 *> \verbatim
00118 *>
00119 *>  5-96 - Based on modifications by J. Lewis, Boeing Computer Services
00120 *>         Company
00121 *>
00122 *>  If UPLO = 'U', then A = U*D*U**T, where
00123 *>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
00124 *>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
00125 *>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
00126 *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
00127 *>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
00128 *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
00129 *>
00130 *>             (   I    v    0   )   k-s
00131 *>     U(k) =  (   0    I    0   )   s
00132 *>             (   0    0    I   )   n-k
00133 *>                k-s   s   n-k
00134 *>
00135 *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
00136 *>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
00137 *>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
00138 *>
00139 *>  If UPLO = 'L', then A = L*D*L**T, where
00140 *>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
00141 *>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
00142 *>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
00143 *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
00144 *>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
00145 *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
00146 *>
00147 *>             (   I    0     0   )  k-1
00148 *>     L(k) =  (   0    I     0   )  s
00149 *>             (   0    v     I   )  n-k-s+1
00150 *>                k-1   s  n-k-s+1
00151 *>
00152 *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
00153 *>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
00154 *>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
00155 *> \endverbatim
00156 *>
00157 *  =====================================================================
00158       SUBROUTINE SSPTRF( UPLO, N, AP, IPIV, INFO )
00159 *
00160 *  -- LAPACK computational routine (version 3.4.0) --
00161 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00162 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00163 *     November 2011
00164 *
00165 *     .. Scalar Arguments ..
00166       CHARACTER          UPLO
00167       INTEGER            INFO, N
00168 *     ..
00169 *     .. Array Arguments ..
00170       INTEGER            IPIV( * )
00171       REAL               AP( * )
00172 *     ..
00173 *
00174 *  =====================================================================
00175 *
00176 *     .. Parameters ..
00177       REAL               ZERO, ONE
00178       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00179       REAL               EIGHT, SEVTEN
00180       PARAMETER          ( EIGHT = 8.0E+0, SEVTEN = 17.0E+0 )
00181 *     ..
00182 *     .. Local Scalars ..
00183       LOGICAL            UPPER
00184       INTEGER            I, IMAX, J, JMAX, K, KC, KK, KNC, KP, KPC,
00185      $                   KSTEP, KX, NPP
00186       REAL               ABSAKK, ALPHA, COLMAX, D11, D12, D21, D22, R1,
00187      $                   ROWMAX, T, WK, WKM1, WKP1
00188 *     ..
00189 *     .. External Functions ..
00190       LOGICAL            LSAME
00191       INTEGER            ISAMAX
00192       EXTERNAL           LSAME, ISAMAX
00193 *     ..
00194 *     .. External Subroutines ..
00195       EXTERNAL           SSCAL, SSPR, SSWAP, XERBLA
00196 *     ..
00197 *     .. Intrinsic Functions ..
00198       INTRINSIC          ABS, MAX, SQRT
00199 *     ..
00200 *     .. Executable Statements ..
00201 *
00202 *     Test the input parameters.
00203 *
00204       INFO = 0
00205       UPPER = LSAME( UPLO, 'U' )
00206       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00207          INFO = -1
00208       ELSE IF( N.LT.0 ) THEN
00209          INFO = -2
00210       END IF
00211       IF( INFO.NE.0 ) THEN
00212          CALL XERBLA( 'SSPTRF', -INFO )
00213          RETURN
00214       END IF
00215 *
00216 *     Initialize ALPHA for use in choosing pivot block size.
00217 *
00218       ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
00219 *
00220       IF( UPPER ) THEN
00221 *
00222 *        Factorize A as U*D*U**T using the upper triangle of A
00223 *
00224 *        K is the main loop index, decreasing from N to 1 in steps of
00225 *        1 or 2
00226 *
00227          K = N
00228          KC = ( N-1 )*N / 2 + 1
00229    10    CONTINUE
00230          KNC = KC
00231 *
00232 *        If K < 1, exit from loop
00233 *
00234          IF( K.LT.1 )
00235      $      GO TO 110
00236          KSTEP = 1
00237 *
00238 *        Determine rows and columns to be interchanged and whether
00239 *        a 1-by-1 or 2-by-2 pivot block will be used
00240 *
00241          ABSAKK = ABS( AP( KC+K-1 ) )
00242 *
00243 *        IMAX is the row-index of the largest off-diagonal element in
00244 *        column K, and COLMAX is its absolute value
00245 *
00246          IF( K.GT.1 ) THEN
00247             IMAX = ISAMAX( K-1, AP( KC ), 1 )
00248             COLMAX = ABS( AP( KC+IMAX-1 ) )
00249          ELSE
00250             COLMAX = ZERO
00251          END IF
00252 *
00253          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
00254 *
00255 *           Column K is zero: set INFO and continue
00256 *
00257             IF( INFO.EQ.0 )
00258      $         INFO = K
00259             KP = K
00260          ELSE
00261             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
00262 *
00263 *              no interchange, use 1-by-1 pivot block
00264 *
00265                KP = K
00266             ELSE
00267 *
00268                ROWMAX = ZERO
00269                JMAX = IMAX
00270                KX = IMAX*( IMAX+1 ) / 2 + IMAX
00271                DO 20 J = IMAX + 1, K
00272                   IF( ABS( AP( KX ) ).GT.ROWMAX ) THEN
00273                      ROWMAX = ABS( AP( KX ) )
00274                      JMAX = J
00275                   END IF
00276                   KX = KX + J
00277    20          CONTINUE
00278                KPC = ( IMAX-1 )*IMAX / 2 + 1
00279                IF( IMAX.GT.1 ) THEN
00280                   JMAX = ISAMAX( IMAX-1, AP( KPC ), 1 )
00281                   ROWMAX = MAX( ROWMAX, ABS( AP( KPC+JMAX-1 ) ) )
00282                END IF
00283 *
00284                IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
00285 *
00286 *                 no interchange, use 1-by-1 pivot block
00287 *
00288                   KP = K
00289                ELSE IF( ABS( AP( KPC+IMAX-1 ) ).GE.ALPHA*ROWMAX ) THEN
00290 *
00291 *                 interchange rows and columns K and IMAX, use 1-by-1
00292 *                 pivot block
00293 *
00294                   KP = IMAX
00295                ELSE
00296 *
00297 *                 interchange rows and columns K-1 and IMAX, use 2-by-2
00298 *                 pivot block
00299 *
00300                   KP = IMAX
00301                   KSTEP = 2
00302                END IF
00303             END IF
00304 *
00305             KK = K - KSTEP + 1
00306             IF( KSTEP.EQ.2 )
00307      $         KNC = KNC - K + 1
00308             IF( KP.NE.KK ) THEN
00309 *
00310 *              Interchange rows and columns KK and KP in the leading
00311 *              submatrix A(1:k,1:k)
00312 *
00313                CALL SSWAP( KP-1, AP( KNC ), 1, AP( KPC ), 1 )
00314                KX = KPC + KP - 1
00315                DO 30 J = KP + 1, KK - 1
00316                   KX = KX + J - 1
00317                   T = AP( KNC+J-1 )
00318                   AP( KNC+J-1 ) = AP( KX )
00319                   AP( KX ) = T
00320    30          CONTINUE
00321                T = AP( KNC+KK-1 )
00322                AP( KNC+KK-1 ) = AP( KPC+KP-1 )
00323                AP( KPC+KP-1 ) = T
00324                IF( KSTEP.EQ.2 ) THEN
00325                   T = AP( KC+K-2 )
00326                   AP( KC+K-2 ) = AP( KC+KP-1 )
00327                   AP( KC+KP-1 ) = T
00328                END IF
00329             END IF
00330 *
00331 *           Update the leading submatrix
00332 *
00333             IF( KSTEP.EQ.1 ) THEN
00334 *
00335 *              1-by-1 pivot block D(k): column k now holds
00336 *
00337 *              W(k) = U(k)*D(k)
00338 *
00339 *              where U(k) is the k-th column of U
00340 *
00341 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
00342 *
00343 *              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
00344 *
00345                R1 = ONE / AP( KC+K-1 )
00346                CALL SSPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
00347 *
00348 *              Store U(k) in column k
00349 *
00350                CALL SSCAL( K-1, R1, AP( KC ), 1 )
00351             ELSE
00352 *
00353 *              2-by-2 pivot block D(k): columns k and k-1 now hold
00354 *
00355 *              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
00356 *
00357 *              where U(k) and U(k-1) are the k-th and (k-1)-th columns
00358 *              of U
00359 *
00360 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
00361 *
00362 *              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
00363 *                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
00364 *
00365                IF( K.GT.2 ) THEN
00366 *
00367                   D12 = AP( K-1+( K-1 )*K / 2 )
00368                   D22 = AP( K-1+( K-2 )*( K-1 ) / 2 ) / D12
00369                   D11 = AP( K+( K-1 )*K / 2 ) / D12
00370                   T = ONE / ( D11*D22-ONE )
00371                   D12 = T / D12
00372 *
00373                   DO 50 J = K - 2, 1, -1
00374                      WKM1 = D12*( D11*AP( J+( K-2 )*( K-1 ) / 2 )-
00375      $                      AP( J+( K-1 )*K / 2 ) )
00376                      WK = D12*( D22*AP( J+( K-1 )*K / 2 )-
00377      $                    AP( J+( K-2 )*( K-1 ) / 2 ) )
00378                      DO 40 I = J, 1, -1
00379                         AP( I+( J-1 )*J / 2 ) = AP( I+( J-1 )*J / 2 ) -
00380      $                     AP( I+( K-1 )*K / 2 )*WK -
00381      $                     AP( I+( K-2 )*( K-1 ) / 2 )*WKM1
00382    40                CONTINUE
00383                      AP( J+( K-1 )*K / 2 ) = WK
00384                      AP( J+( K-2 )*( K-1 ) / 2 ) = WKM1
00385    50             CONTINUE
00386 *
00387                END IF
00388 *
00389             END IF
00390          END IF
00391 *
00392 *        Store details of the interchanges in IPIV
00393 *
00394          IF( KSTEP.EQ.1 ) THEN
00395             IPIV( K ) = KP
00396          ELSE
00397             IPIV( K ) = -KP
00398             IPIV( K-1 ) = -KP
00399          END IF
00400 *
00401 *        Decrease K and return to the start of the main loop
00402 *
00403          K = K - KSTEP
00404          KC = KNC - K
00405          GO TO 10
00406 *
00407       ELSE
00408 *
00409 *        Factorize A as L*D*L**T using the lower triangle of A
00410 *
00411 *        K is the main loop index, increasing from 1 to N in steps of
00412 *        1 or 2
00413 *
00414          K = 1
00415          KC = 1
00416          NPP = N*( N+1 ) / 2
00417    60    CONTINUE
00418          KNC = KC
00419 *
00420 *        If K > N, exit from loop
00421 *
00422          IF( K.GT.N )
00423      $      GO TO 110
00424          KSTEP = 1
00425 *
00426 *        Determine rows and columns to be interchanged and whether
00427 *        a 1-by-1 or 2-by-2 pivot block will be used
00428 *
00429          ABSAKK = ABS( AP( KC ) )
00430 *
00431 *        IMAX is the row-index of the largest off-diagonal element in
00432 *        column K, and COLMAX is its absolute value
00433 *
00434          IF( K.LT.N ) THEN
00435             IMAX = K + ISAMAX( N-K, AP( KC+1 ), 1 )
00436             COLMAX = ABS( AP( KC+IMAX-K ) )
00437          ELSE
00438             COLMAX = ZERO
00439          END IF
00440 *
00441          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
00442 *
00443 *           Column K is zero: set INFO and continue
00444 *
00445             IF( INFO.EQ.0 )
00446      $         INFO = K
00447             KP = K
00448          ELSE
00449             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
00450 *
00451 *              no interchange, use 1-by-1 pivot block
00452 *
00453                KP = K
00454             ELSE
00455 *
00456 *              JMAX is the column-index of the largest off-diagonal
00457 *              element in row IMAX, and ROWMAX is its absolute value
00458 *
00459                ROWMAX = ZERO
00460                KX = KC + IMAX - K
00461                DO 70 J = K, IMAX - 1
00462                   IF( ABS( AP( KX ) ).GT.ROWMAX ) THEN
00463                      ROWMAX = ABS( AP( KX ) )
00464                      JMAX = J
00465                   END IF
00466                   KX = KX + N - J
00467    70          CONTINUE
00468                KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1
00469                IF( IMAX.LT.N ) THEN
00470                   JMAX = IMAX + ISAMAX( N-IMAX, AP( KPC+1 ), 1 )
00471                   ROWMAX = MAX( ROWMAX, ABS( AP( KPC+JMAX-IMAX ) ) )
00472                END IF
00473 *
00474                IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
00475 *
00476 *                 no interchange, use 1-by-1 pivot block
00477 *
00478                   KP = K
00479                ELSE IF( ABS( AP( KPC ) ).GE.ALPHA*ROWMAX ) THEN
00480 *
00481 *                 interchange rows and columns K and IMAX, use 1-by-1
00482 *                 pivot block
00483 *
00484                   KP = IMAX
00485                ELSE
00486 *
00487 *                 interchange rows and columns K+1 and IMAX, use 2-by-2
00488 *                 pivot block
00489 *
00490                   KP = IMAX
00491                   KSTEP = 2
00492                END IF
00493             END IF
00494 *
00495             KK = K + KSTEP - 1
00496             IF( KSTEP.EQ.2 )
00497      $         KNC = KNC + N - K + 1
00498             IF( KP.NE.KK ) THEN
00499 *
00500 *              Interchange rows and columns KK and KP in the trailing
00501 *              submatrix A(k:n,k:n)
00502 *
00503                IF( KP.LT.N )
00504      $            CALL SSWAP( N-KP, AP( KNC+KP-KK+1 ), 1, AP( KPC+1 ),
00505      $                        1 )
00506                KX = KNC + KP - KK
00507                DO 80 J = KK + 1, KP - 1
00508                   KX = KX + N - J + 1
00509                   T = AP( KNC+J-KK )
00510                   AP( KNC+J-KK ) = AP( KX )
00511                   AP( KX ) = T
00512    80          CONTINUE
00513                T = AP( KNC )
00514                AP( KNC ) = AP( KPC )
00515                AP( KPC ) = T
00516                IF( KSTEP.EQ.2 ) THEN
00517                   T = AP( KC+1 )
00518                   AP( KC+1 ) = AP( KC+KP-K )
00519                   AP( KC+KP-K ) = T
00520                END IF
00521             END IF
00522 *
00523 *           Update the trailing submatrix
00524 *
00525             IF( KSTEP.EQ.1 ) THEN
00526 *
00527 *              1-by-1 pivot block D(k): column k now holds
00528 *
00529 *              W(k) = L(k)*D(k)
00530 *
00531 *              where L(k) is the k-th column of L
00532 *
00533                IF( K.LT.N ) THEN
00534 *
00535 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
00536 *
00537 *                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
00538 *
00539                   R1 = ONE / AP( KC )
00540                   CALL SSPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
00541      $                       AP( KC+N-K+1 ) )
00542 *
00543 *                 Store L(k) in column K
00544 *
00545                   CALL SSCAL( N-K, R1, AP( KC+1 ), 1 )
00546                END IF
00547             ELSE
00548 *
00549 *              2-by-2 pivot block D(k): columns K and K+1 now hold
00550 *
00551 *              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
00552 *
00553 *              where L(k) and L(k+1) are the k-th and (k+1)-th columns
00554 *              of L
00555 *
00556                IF( K.LT.N-1 ) THEN
00557 *
00558 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
00559 *
00560 *                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
00561 *                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
00562 *
00563 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
00564 *                 columns of L
00565 *
00566                   D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 )
00567                   D11 = AP( K+1+K*( 2*N-K-1 ) / 2 ) / D21
00568                   D22 = AP( K+( K-1 )*( 2*N-K ) / 2 ) / D21
00569                   T = ONE / ( D11*D22-ONE )
00570                   D21 = T / D21
00571 *
00572                   DO 100 J = K + 2, N
00573                      WK = D21*( D11*AP( J+( K-1 )*( 2*N-K ) / 2 )-
00574      $                    AP( J+K*( 2*N-K-1 ) / 2 ) )
00575                      WKP1 = D21*( D22*AP( J+K*( 2*N-K-1 ) / 2 )-
00576      $                      AP( J+( K-1 )*( 2*N-K ) / 2 ) )
00577 *
00578                      DO 90 I = J, N
00579                         AP( I+( J-1 )*( 2*N-J ) / 2 ) = AP( I+( J-1 )*
00580      $                     ( 2*N-J ) / 2 ) - AP( I+( K-1 )*( 2*N-K ) /
00581      $                     2 )*WK - AP( I+K*( 2*N-K-1 ) / 2 )*WKP1
00582    90                CONTINUE
00583 *
00584                      AP( J+( K-1 )*( 2*N-K ) / 2 ) = WK
00585                      AP( J+K*( 2*N-K-1 ) / 2 ) = WKP1
00586 *
00587   100             CONTINUE
00588                END IF
00589             END IF
00590          END IF
00591 *
00592 *        Store details of the interchanges in IPIV
00593 *
00594          IF( KSTEP.EQ.1 ) THEN
00595             IPIV( K ) = KP
00596          ELSE
00597             IPIV( K ) = -KP
00598             IPIV( K+1 ) = -KP
00599          END IF
00600 *
00601 *        Increase K and return to the start of the main loop
00602 *
00603          K = K + KSTEP
00604          KC = KNC + N - K + 2
00605          GO TO 60
00606 *
00607       END IF
00608 *
00609   110 CONTINUE
00610       RETURN
00611 *
00612 *     End of SSPTRF
00613 *
00614       END
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