LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dsptrf.f
Go to the documentation of this file.
00001 *> \brief \b DSPTRF
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DSPTRF + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsptrf.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsptrf.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsptrf.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DSPTRF( UPLO, N, AP, IPIV, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       INTEGER            IPIV( * )
00029 *       DOUBLE PRECISION   AP( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> DSPTRF 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 DOUBLE PRECISION 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 doubleOTHERcomputational
00113 *
00114 *> \par Further Details:
00115 *  =====================
00116 *>
00117 *> \verbatim
00118 *>
00119 *>  If UPLO = 'U', then A = U*D*U**T, where
00120 *>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
00121 *>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
00122 *>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
00123 *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
00124 *>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
00125 *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
00126 *>
00127 *>             (   I    v    0   )   k-s
00128 *>     U(k) =  (   0    I    0   )   s
00129 *>             (   0    0    I   )   n-k
00130 *>                k-s   s   n-k
00131 *>
00132 *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
00133 *>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
00134 *>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
00135 *>
00136 *>  If UPLO = 'L', then A = L*D*L**T, where
00137 *>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
00138 *>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
00139 *>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
00140 *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
00141 *>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
00142 *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
00143 *>
00144 *>             (   I    0     0   )  k-1
00145 *>     L(k) =  (   0    I     0   )  s
00146 *>             (   0    v     I   )  n-k-s+1
00147 *>                k-1   s  n-k-s+1
00148 *>
00149 *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
00150 *>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
00151 *>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
00152 *> \endverbatim
00153 *
00154 *> \par Contributors:
00155 *  ==================
00156 *>
00157 *>  J. Lewis, Boeing Computer Services Company
00158 *>
00159 *  =====================================================================
00160       SUBROUTINE DSPTRF( UPLO, N, AP, IPIV, INFO )
00161 *
00162 *  -- LAPACK computational routine (version 3.4.0) --
00163 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00164 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00165 *     November 2011
00166 *
00167 *     .. Scalar Arguments ..
00168       CHARACTER          UPLO
00169       INTEGER            INFO, N
00170 *     ..
00171 *     .. Array Arguments ..
00172       INTEGER            IPIV( * )
00173       DOUBLE PRECISION   AP( * )
00174 *     ..
00175 *
00176 *  =====================================================================
00177 *
00178 *     .. Parameters ..
00179       DOUBLE PRECISION   ZERO, ONE
00180       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00181       DOUBLE PRECISION   EIGHT, SEVTEN
00182       PARAMETER          ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
00183 *     ..
00184 *     .. Local Scalars ..
00185       LOGICAL            UPPER
00186       INTEGER            I, IMAX, J, JMAX, K, KC, KK, KNC, KP, KPC,
00187      $                   KSTEP, KX, NPP
00188       DOUBLE PRECISION   ABSAKK, ALPHA, COLMAX, D11, D12, D21, D22, R1,
00189      $                   ROWMAX, T, WK, WKM1, WKP1
00190 *     ..
00191 *     .. External Functions ..
00192       LOGICAL            LSAME
00193       INTEGER            IDAMAX
00194       EXTERNAL           LSAME, IDAMAX
00195 *     ..
00196 *     .. External Subroutines ..
00197       EXTERNAL           DSCAL, DSPR, DSWAP, XERBLA
00198 *     ..
00199 *     .. Intrinsic Functions ..
00200       INTRINSIC          ABS, MAX, SQRT
00201 *     ..
00202 *     .. Executable Statements ..
00203 *
00204 *     Test the input parameters.
00205 *
00206       INFO = 0
00207       UPPER = LSAME( UPLO, 'U' )
00208       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00209          INFO = -1
00210       ELSE IF( N.LT.0 ) THEN
00211          INFO = -2
00212       END IF
00213       IF( INFO.NE.0 ) THEN
00214          CALL XERBLA( 'DSPTRF', -INFO )
00215          RETURN
00216       END IF
00217 *
00218 *     Initialize ALPHA for use in choosing pivot block size.
00219 *
00220       ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
00221 *
00222       IF( UPPER ) THEN
00223 *
00224 *        Factorize A as U*D*U**T using the upper triangle of A
00225 *
00226 *        K is the main loop index, decreasing from N to 1 in steps of
00227 *        1 or 2
00228 *
00229          K = N
00230          KC = ( N-1 )*N / 2 + 1
00231    10    CONTINUE
00232          KNC = KC
00233 *
00234 *        If K < 1, exit from loop
00235 *
00236          IF( K.LT.1 )
00237      $      GO TO 110
00238          KSTEP = 1
00239 *
00240 *        Determine rows and columns to be interchanged and whether
00241 *        a 1-by-1 or 2-by-2 pivot block will be used
00242 *
00243          ABSAKK = ABS( AP( KC+K-1 ) )
00244 *
00245 *        IMAX is the row-index of the largest off-diagonal element in
00246 *        column K, and COLMAX is its absolute value
00247 *
00248          IF( K.GT.1 ) THEN
00249             IMAX = IDAMAX( K-1, AP( KC ), 1 )
00250             COLMAX = ABS( AP( KC+IMAX-1 ) )
00251          ELSE
00252             COLMAX = ZERO
00253          END IF
00254 *
00255          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
00256 *
00257 *           Column K is zero: set INFO and continue
00258 *
00259             IF( INFO.EQ.0 )
00260      $         INFO = K
00261             KP = K
00262          ELSE
00263             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
00264 *
00265 *              no interchange, use 1-by-1 pivot block
00266 *
00267                KP = K
00268             ELSE
00269 *
00270                ROWMAX = ZERO
00271                JMAX = IMAX
00272                KX = IMAX*( IMAX+1 ) / 2 + IMAX
00273                DO 20 J = IMAX + 1, K
00274                   IF( ABS( AP( KX ) ).GT.ROWMAX ) THEN
00275                      ROWMAX = ABS( AP( KX ) )
00276                      JMAX = J
00277                   END IF
00278                   KX = KX + J
00279    20          CONTINUE
00280                KPC = ( IMAX-1 )*IMAX / 2 + 1
00281                IF( IMAX.GT.1 ) THEN
00282                   JMAX = IDAMAX( IMAX-1, AP( KPC ), 1 )
00283                   ROWMAX = MAX( ROWMAX, ABS( AP( KPC+JMAX-1 ) ) )
00284                END IF
00285 *
00286                IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
00287 *
00288 *                 no interchange, use 1-by-1 pivot block
00289 *
00290                   KP = K
00291                ELSE IF( ABS( AP( KPC+IMAX-1 ) ).GE.ALPHA*ROWMAX ) THEN
00292 *
00293 *                 interchange rows and columns K and IMAX, use 1-by-1
00294 *                 pivot block
00295 *
00296                   KP = IMAX
00297                ELSE
00298 *
00299 *                 interchange rows and columns K-1 and IMAX, use 2-by-2
00300 *                 pivot block
00301 *
00302                   KP = IMAX
00303                   KSTEP = 2
00304                END IF
00305             END IF
00306 *
00307             KK = K - KSTEP + 1
00308             IF( KSTEP.EQ.2 )
00309      $         KNC = KNC - K + 1
00310             IF( KP.NE.KK ) THEN
00311 *
00312 *              Interchange rows and columns KK and KP in the leading
00313 *              submatrix A(1:k,1:k)
00314 *
00315                CALL DSWAP( KP-1, AP( KNC ), 1, AP( KPC ), 1 )
00316                KX = KPC + KP - 1
00317                DO 30 J = KP + 1, KK - 1
00318                   KX = KX + J - 1
00319                   T = AP( KNC+J-1 )
00320                   AP( KNC+J-1 ) = AP( KX )
00321                   AP( KX ) = T
00322    30          CONTINUE
00323                T = AP( KNC+KK-1 )
00324                AP( KNC+KK-1 ) = AP( KPC+KP-1 )
00325                AP( KPC+KP-1 ) = T
00326                IF( KSTEP.EQ.2 ) THEN
00327                   T = AP( KC+K-2 )
00328                   AP( KC+K-2 ) = AP( KC+KP-1 )
00329                   AP( KC+KP-1 ) = T
00330                END IF
00331             END IF
00332 *
00333 *           Update the leading submatrix
00334 *
00335             IF( KSTEP.EQ.1 ) THEN
00336 *
00337 *              1-by-1 pivot block D(k): column k now holds
00338 *
00339 *              W(k) = U(k)*D(k)
00340 *
00341 *              where U(k) is the k-th column of U
00342 *
00343 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
00344 *
00345 *              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
00346 *
00347                R1 = ONE / AP( KC+K-1 )
00348                CALL DSPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
00349 *
00350 *              Store U(k) in column k
00351 *
00352                CALL DSCAL( K-1, R1, AP( KC ), 1 )
00353             ELSE
00354 *
00355 *              2-by-2 pivot block D(k): columns k and k-1 now hold
00356 *
00357 *              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
00358 *
00359 *              where U(k) and U(k-1) are the k-th and (k-1)-th columns
00360 *              of U
00361 *
00362 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
00363 *
00364 *              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
00365 *                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
00366 *
00367                IF( K.GT.2 ) THEN
00368 *
00369                   D12 = AP( K-1+( K-1 )*K / 2 )
00370                   D22 = AP( K-1+( K-2 )*( K-1 ) / 2 ) / D12
00371                   D11 = AP( K+( K-1 )*K / 2 ) / D12
00372                   T = ONE / ( D11*D22-ONE )
00373                   D12 = T / D12
00374 *
00375                   DO 50 J = K - 2, 1, -1
00376                      WKM1 = D12*( D11*AP( J+( K-2 )*( K-1 ) / 2 )-
00377      $                      AP( J+( K-1 )*K / 2 ) )
00378                      WK = D12*( D22*AP( J+( K-1 )*K / 2 )-
00379      $                    AP( J+( K-2 )*( K-1 ) / 2 ) )
00380                      DO 40 I = J, 1, -1
00381                         AP( I+( J-1 )*J / 2 ) = AP( I+( J-1 )*J / 2 ) -
00382      $                     AP( I+( K-1 )*K / 2 )*WK -
00383      $                     AP( I+( K-2 )*( K-1 ) / 2 )*WKM1
00384    40                CONTINUE
00385                      AP( J+( K-1 )*K / 2 ) = WK
00386                      AP( J+( K-2 )*( K-1 ) / 2 ) = WKM1
00387    50             CONTINUE
00388 *
00389                END IF
00390 *
00391             END IF
00392          END IF
00393 *
00394 *        Store details of the interchanges in IPIV
00395 *
00396          IF( KSTEP.EQ.1 ) THEN
00397             IPIV( K ) = KP
00398          ELSE
00399             IPIV( K ) = -KP
00400             IPIV( K-1 ) = -KP
00401          END IF
00402 *
00403 *        Decrease K and return to the start of the main loop
00404 *
00405          K = K - KSTEP
00406          KC = KNC - K
00407          GO TO 10
00408 *
00409       ELSE
00410 *
00411 *        Factorize A as L*D*L**T using the lower triangle of A
00412 *
00413 *        K is the main loop index, increasing from 1 to N in steps of
00414 *        1 or 2
00415 *
00416          K = 1
00417          KC = 1
00418          NPP = N*( N+1 ) / 2
00419    60    CONTINUE
00420          KNC = KC
00421 *
00422 *        If K > N, exit from loop
00423 *
00424          IF( K.GT.N )
00425      $      GO TO 110
00426          KSTEP = 1
00427 *
00428 *        Determine rows and columns to be interchanged and whether
00429 *        a 1-by-1 or 2-by-2 pivot block will be used
00430 *
00431          ABSAKK = ABS( AP( KC ) )
00432 *
00433 *        IMAX is the row-index of the largest off-diagonal element in
00434 *        column K, and COLMAX is its absolute value
00435 *
00436          IF( K.LT.N ) THEN
00437             IMAX = K + IDAMAX( N-K, AP( KC+1 ), 1 )
00438             COLMAX = ABS( AP( KC+IMAX-K ) )
00439          ELSE
00440             COLMAX = ZERO
00441          END IF
00442 *
00443          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
00444 *
00445 *           Column K is zero: set INFO and continue
00446 *
00447             IF( INFO.EQ.0 )
00448      $         INFO = K
00449             KP = K
00450          ELSE
00451             IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
00452 *
00453 *              no interchange, use 1-by-1 pivot block
00454 *
00455                KP = K
00456             ELSE
00457 *
00458 *              JMAX is the column-index of the largest off-diagonal
00459 *              element in row IMAX, and ROWMAX is its absolute value
00460 *
00461                ROWMAX = ZERO
00462                KX = KC + IMAX - K
00463                DO 70 J = K, IMAX - 1
00464                   IF( ABS( AP( KX ) ).GT.ROWMAX ) THEN
00465                      ROWMAX = ABS( AP( KX ) )
00466                      JMAX = J
00467                   END IF
00468                   KX = KX + N - J
00469    70          CONTINUE
00470                KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1
00471                IF( IMAX.LT.N ) THEN
00472                   JMAX = IMAX + IDAMAX( N-IMAX, AP( KPC+1 ), 1 )
00473                   ROWMAX = MAX( ROWMAX, ABS( AP( KPC+JMAX-IMAX ) ) )
00474                END IF
00475 *
00476                IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
00477 *
00478 *                 no interchange, use 1-by-1 pivot block
00479 *
00480                   KP = K
00481                ELSE IF( ABS( AP( KPC ) ).GE.ALPHA*ROWMAX ) THEN
00482 *
00483 *                 interchange rows and columns K and IMAX, use 1-by-1
00484 *                 pivot block
00485 *
00486                   KP = IMAX
00487                ELSE
00488 *
00489 *                 interchange rows and columns K+1 and IMAX, use 2-by-2
00490 *                 pivot block
00491 *
00492                   KP = IMAX
00493                   KSTEP = 2
00494                END IF
00495             END IF
00496 *
00497             KK = K + KSTEP - 1
00498             IF( KSTEP.EQ.2 )
00499      $         KNC = KNC + N - K + 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 DSWAP( N-KP, AP( KNC+KP-KK+1 ), 1, AP( KPC+1 ),
00507      $                        1 )
00508                KX = KNC + KP - KK
00509                DO 80 J = KK + 1, KP - 1
00510                   KX = KX + N - J + 1
00511                   T = AP( KNC+J-KK )
00512                   AP( KNC+J-KK ) = AP( KX )
00513                   AP( KX ) = T
00514    80          CONTINUE
00515                T = AP( KNC )
00516                AP( KNC ) = AP( KPC )
00517                AP( KPC ) = T
00518                IF( KSTEP.EQ.2 ) THEN
00519                   T = AP( KC+1 )
00520                   AP( KC+1 ) = AP( KC+KP-K )
00521                   AP( KC+KP-K ) = T
00522                END IF
00523             END IF
00524 *
00525 *           Update the trailing submatrix
00526 *
00527             IF( KSTEP.EQ.1 ) THEN
00528 *
00529 *              1-by-1 pivot block D(k): column k now holds
00530 *
00531 *              W(k) = L(k)*D(k)
00532 *
00533 *              where L(k) is the k-th column of L
00534 *
00535                IF( K.LT.N ) THEN
00536 *
00537 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
00538 *
00539 *                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
00540 *
00541                   R1 = ONE / AP( KC )
00542                   CALL DSPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
00543      $                       AP( KC+N-K+1 ) )
00544 *
00545 *                 Store L(k) in column K
00546 *
00547                   CALL DSCAL( N-K, R1, AP( KC+1 ), 1 )
00548                END IF
00549             ELSE
00550 *
00551 *              2-by-2 pivot block D(k): columns K and K+1 now hold
00552 *
00553 *              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
00554 *
00555 *              where L(k) and L(k+1) are the k-th and (k+1)-th columns
00556 *              of L
00557 *
00558                IF( K.LT.N-1 ) THEN
00559 *
00560 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
00561 *
00562 *                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
00563 *                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
00564 *
00565 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
00566 *                 columns of L
00567 *
00568                   D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 )
00569                   D11 = AP( K+1+K*( 2*N-K-1 ) / 2 ) / D21
00570                   D22 = AP( K+( K-1 )*( 2*N-K ) / 2 ) / D21
00571                   T = ONE / ( D11*D22-ONE )
00572                   D21 = T / D21
00573 *
00574                   DO 100 J = K + 2, N
00575                      WK = D21*( D11*AP( J+( K-1 )*( 2*N-K ) / 2 )-
00576      $                    AP( J+K*( 2*N-K-1 ) / 2 ) )
00577                      WKP1 = D21*( D22*AP( J+K*( 2*N-K-1 ) / 2 )-
00578      $                      AP( J+( K-1 )*( 2*N-K ) / 2 ) )
00579 *
00580                      DO 90 I = J, N
00581                         AP( I+( J-1 )*( 2*N-J ) / 2 ) = AP( I+( J-1 )*
00582      $                     ( 2*N-J ) / 2 ) - AP( I+( K-1 )*( 2*N-K ) /
00583      $                     2 )*WK - AP( I+K*( 2*N-K-1 ) / 2 )*WKP1
00584    90                CONTINUE
00585 *
00586                      AP( J+( K-1 )*( 2*N-K ) / 2 ) = WK
00587                      AP( J+K*( 2*N-K-1 ) / 2 ) = WKP1
00588 *
00589   100             CONTINUE
00590                END IF
00591             END IF
00592          END IF
00593 *
00594 *        Store details of the interchanges in IPIV
00595 *
00596          IF( KSTEP.EQ.1 ) THEN
00597             IPIV( K ) = KP
00598          ELSE
00599             IPIV( K ) = -KP
00600             IPIV( K+1 ) = -KP
00601          END IF
00602 *
00603 *        Increase K and return to the start of the main loop
00604 *
00605          K = K + KSTEP
00606          KC = KNC + N - K + 2
00607          GO TO 60
00608 *
00609       END IF
00610 *
00611   110 CONTINUE
00612       RETURN
00613 *
00614 *     End of DSPTRF
00615 *
00616       END
 All Files Functions