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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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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