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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZSPTRF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZSPTRF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsptrf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsptrf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsptrf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, N 00026 * .. 00027 * .. Array Arguments .. 00028 * INTEGER IPIV( * ) 00029 * COMPLEX*16 AP( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> ZSPTRF computes the factorization of a complex symmetric matrix A 00039 *> stored in packed format using the Bunch-Kaufman diagonal pivoting 00040 *> method: 00041 *> 00042 *> A = U*D*U**T or A = L*D*L**T 00043 *> 00044 *> where U (or L) is a product of permutation and unit upper (lower) 00045 *> triangular matrices, and D is symmetric and block diagonal with 00046 *> 1-by-1 and 2-by-2 diagonal blocks. 00047 *> \endverbatim 00048 * 00049 * Arguments: 00050 * ========== 00051 * 00052 *> \param[in] UPLO 00053 *> \verbatim 00054 *> UPLO is CHARACTER*1 00055 *> = 'U': Upper triangle of A is stored; 00056 *> = 'L': Lower triangle of A is stored. 00057 *> \endverbatim 00058 *> 00059 *> \param[in] N 00060 *> \verbatim 00061 *> N is INTEGER 00062 *> The order of the matrix A. N >= 0. 00063 *> \endverbatim 00064 *> 00065 *> \param[in,out] AP 00066 *> \verbatim 00067 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 00068 *> On entry, the upper or lower triangle of the symmetric matrix 00069 *> A, packed columnwise in a linear array. The j-th column of A 00070 *> is stored in the array AP as follows: 00071 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00072 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00073 *> 00074 *> On exit, the block diagonal matrix D and the multipliers used 00075 *> to obtain the factor U or L, stored as a packed triangular 00076 *> matrix overwriting A (see below for further details). 00077 *> \endverbatim 00078 *> 00079 *> \param[out] IPIV 00080 *> \verbatim 00081 *> IPIV is INTEGER array, dimension (N) 00082 *> Details of the interchanges and the block structure of D. 00083 *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were 00084 *> interchanged and D(k,k) is a 1-by-1 diagonal block. 00085 *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and 00086 *> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) 00087 *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = 00088 *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were 00089 *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 00090 *> \endverbatim 00091 *> 00092 *> \param[out] INFO 00093 *> \verbatim 00094 *> INFO is INTEGER 00095 *> = 0: successful exit 00096 *> < 0: if INFO = -i, the i-th argument had an illegal value 00097 *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization 00098 *> has been completed, but the block diagonal matrix D is 00099 *> exactly singular, and division by zero will occur if it 00100 *> is used to solve a system of equations. 00101 *> \endverbatim 00102 * 00103 * Authors: 00104 * ======== 00105 * 00106 *> \author Univ. of Tennessee 00107 *> \author Univ. of California Berkeley 00108 *> \author Univ. of Colorado Denver 00109 *> \author NAG Ltd. 00110 * 00111 *> \date November 2011 00112 * 00113 *> \ingroup complex16OTHERcomputational 00114 * 00115 *> \par Further Details: 00116 * ===================== 00117 *> 00118 *> \verbatim 00119 *> 00120 *> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services 00121 *> Company 00122 *> 00123 *> If UPLO = 'U', then A = U*D*U**T, where 00124 *> U = P(n)*U(n)* ... *P(k)U(k)* ..., 00125 *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to 00126 *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 00127 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 00128 *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such 00129 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then 00130 *> 00131 *> ( I v 0 ) k-s 00132 *> U(k) = ( 0 I 0 ) s 00133 *> ( 0 0 I ) n-k 00134 *> k-s s n-k 00135 *> 00136 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). 00137 *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), 00138 *> and A(k,k), and v overwrites A(1:k-2,k-1:k). 00139 *> 00140 *> If UPLO = 'L', then A = L*D*L**T, where 00141 *> L = P(1)*L(1)* ... *P(k)*L(k)* ..., 00142 *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to 00143 *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 00144 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 00145 *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such 00146 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then 00147 *> 00148 *> ( I 0 0 ) k-1 00149 *> L(k) = ( 0 I 0 ) s 00150 *> ( 0 v I ) n-k-s+1 00151 *> k-1 s n-k-s+1 00152 *> 00153 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). 00154 *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), 00155 *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). 00156 *> \endverbatim 00157 *> 00158 * ===================================================================== 00159 SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO ) 00160 * 00161 * -- LAPACK computational routine (version 3.4.0) -- 00162 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00163 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00164 * November 2011 00165 * 00166 * .. Scalar Arguments .. 00167 CHARACTER UPLO 00168 INTEGER INFO, N 00169 * .. 00170 * .. Array Arguments .. 00171 INTEGER IPIV( * ) 00172 COMPLEX*16 AP( * ) 00173 * .. 00174 * 00175 * ===================================================================== 00176 * 00177 * .. Parameters .. 00178 DOUBLE PRECISION ZERO, ONE 00179 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00180 DOUBLE PRECISION EIGHT, SEVTEN 00181 PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 ) 00182 COMPLEX*16 CONE 00183 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) 00184 * .. 00185 * .. Local Scalars .. 00186 LOGICAL UPPER 00187 INTEGER I, IMAX, J, JMAX, K, KC, KK, KNC, KP, KPC, 00188 $ KSTEP, KX, NPP 00189 DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, ROWMAX 00190 COMPLEX*16 D11, D12, D21, D22, R1, T, WK, WKM1, WKP1, ZDUM 00191 * .. 00192 * .. External Functions .. 00193 LOGICAL LSAME 00194 INTEGER IZAMAX 00195 EXTERNAL LSAME, IZAMAX 00196 * .. 00197 * .. External Subroutines .. 00198 EXTERNAL XERBLA, ZSCAL, ZSPR, ZSWAP 00199 * .. 00200 * .. Intrinsic Functions .. 00201 INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT 00202 * .. 00203 * .. Statement Functions .. 00204 DOUBLE PRECISION CABS1 00205 * .. 00206 * .. Statement Function definitions .. 00207 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00208 * .. 00209 * .. Executable Statements .. 00210 * 00211 * Test the input parameters. 00212 * 00213 INFO = 0 00214 UPPER = LSAME( UPLO, 'U' ) 00215 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00216 INFO = -1 00217 ELSE IF( N.LT.0 ) THEN 00218 INFO = -2 00219 END IF 00220 IF( INFO.NE.0 ) THEN 00221 CALL XERBLA( 'ZSPTRF', -INFO ) 00222 RETURN 00223 END IF 00224 * 00225 * Initialize ALPHA for use in choosing pivot block size. 00226 * 00227 ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT 00228 * 00229 IF( UPPER ) THEN 00230 * 00231 * Factorize A as U*D*U**T using the upper triangle of A 00232 * 00233 * K is the main loop index, decreasing from N to 1 in steps of 00234 * 1 or 2 00235 * 00236 K = N 00237 KC = ( N-1 )*N / 2 + 1 00238 10 CONTINUE 00239 KNC = KC 00240 * 00241 * If K < 1, exit from loop 00242 * 00243 IF( K.LT.1 ) 00244 $ GO TO 110 00245 KSTEP = 1 00246 * 00247 * Determine rows and columns to be interchanged and whether 00248 * a 1-by-1 or 2-by-2 pivot block will be used 00249 * 00250 ABSAKK = CABS1( AP( KC+K-1 ) ) 00251 * 00252 * IMAX is the row-index of the largest off-diagonal element in 00253 * column K, and COLMAX is its absolute value 00254 * 00255 IF( K.GT.1 ) THEN 00256 IMAX = IZAMAX( K-1, AP( KC ), 1 ) 00257 COLMAX = CABS1( AP( KC+IMAX-1 ) ) 00258 ELSE 00259 COLMAX = ZERO 00260 END IF 00261 * 00262 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00263 * 00264 * Column K is zero: set INFO and continue 00265 * 00266 IF( INFO.EQ.0 ) 00267 $ INFO = K 00268 KP = K 00269 ELSE 00270 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00271 * 00272 * no interchange, use 1-by-1 pivot block 00273 * 00274 KP = K 00275 ELSE 00276 * 00277 ROWMAX = ZERO 00278 JMAX = IMAX 00279 KX = IMAX*( IMAX+1 ) / 2 + IMAX 00280 DO 20 J = IMAX + 1, K 00281 IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN 00282 ROWMAX = CABS1( AP( KX ) ) 00283 JMAX = J 00284 END IF 00285 KX = KX + J 00286 20 CONTINUE 00287 KPC = ( IMAX-1 )*IMAX / 2 + 1 00288 IF( IMAX.GT.1 ) THEN 00289 JMAX = IZAMAX( IMAX-1, AP( KPC ), 1 ) 00290 ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-1 ) ) ) 00291 END IF 00292 * 00293 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00294 * 00295 * no interchange, use 1-by-1 pivot block 00296 * 00297 KP = K 00298 ELSE IF( CABS1( AP( KPC+IMAX-1 ) ).GE.ALPHA*ROWMAX ) THEN 00299 * 00300 * interchange rows and columns K and IMAX, use 1-by-1 00301 * pivot block 00302 * 00303 KP = IMAX 00304 ELSE 00305 * 00306 * interchange rows and columns K-1 and IMAX, use 2-by-2 00307 * pivot block 00308 * 00309 KP = IMAX 00310 KSTEP = 2 00311 END IF 00312 END IF 00313 * 00314 KK = K - KSTEP + 1 00315 IF( KSTEP.EQ.2 ) 00316 $ KNC = KNC - K + 1 00317 IF( KP.NE.KK ) THEN 00318 * 00319 * Interchange rows and columns KK and KP in the leading 00320 * submatrix A(1:k,1:k) 00321 * 00322 CALL ZSWAP( KP-1, AP( KNC ), 1, AP( KPC ), 1 ) 00323 KX = KPC + KP - 1 00324 DO 30 J = KP + 1, KK - 1 00325 KX = KX + J - 1 00326 T = AP( KNC+J-1 ) 00327 AP( KNC+J-1 ) = AP( KX ) 00328 AP( KX ) = T 00329 30 CONTINUE 00330 T = AP( KNC+KK-1 ) 00331 AP( KNC+KK-1 ) = AP( KPC+KP-1 ) 00332 AP( KPC+KP-1 ) = T 00333 IF( KSTEP.EQ.2 ) THEN 00334 T = AP( KC+K-2 ) 00335 AP( KC+K-2 ) = AP( KC+KP-1 ) 00336 AP( KC+KP-1 ) = T 00337 END IF 00338 END IF 00339 * 00340 * Update the leading submatrix 00341 * 00342 IF( KSTEP.EQ.1 ) THEN 00343 * 00344 * 1-by-1 pivot block D(k): column k now holds 00345 * 00346 * W(k) = U(k)*D(k) 00347 * 00348 * where U(k) is the k-th column of U 00349 * 00350 * Perform a rank-1 update of A(1:k-1,1:k-1) as 00351 * 00352 * A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T 00353 * 00354 R1 = CONE / AP( KC+K-1 ) 00355 CALL ZSPR( UPLO, K-1, -R1, AP( KC ), 1, AP ) 00356 * 00357 * Store U(k) in column k 00358 * 00359 CALL ZSCAL( K-1, R1, AP( KC ), 1 ) 00360 ELSE 00361 * 00362 * 2-by-2 pivot block D(k): columns k and k-1 now hold 00363 * 00364 * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) 00365 * 00366 * where U(k) and U(k-1) are the k-th and (k-1)-th columns 00367 * of U 00368 * 00369 * Perform a rank-2 update of A(1:k-2,1:k-2) as 00370 * 00371 * A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T 00372 * = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T 00373 * 00374 IF( K.GT.2 ) THEN 00375 * 00376 D12 = AP( K-1+( K-1 )*K / 2 ) 00377 D22 = AP( K-1+( K-2 )*( K-1 ) / 2 ) / D12 00378 D11 = AP( K+( K-1 )*K / 2 ) / D12 00379 T = CONE / ( D11*D22-CONE ) 00380 D12 = T / D12 00381 * 00382 DO 50 J = K - 2, 1, -1 00383 WKM1 = D12*( D11*AP( J+( K-2 )*( K-1 ) / 2 )- 00384 $ AP( J+( K-1 )*K / 2 ) ) 00385 WK = D12*( D22*AP( J+( K-1 )*K / 2 )- 00386 $ AP( J+( K-2 )*( K-1 ) / 2 ) ) 00387 DO 40 I = J, 1, -1 00388 AP( I+( J-1 )*J / 2 ) = AP( I+( J-1 )*J / 2 ) - 00389 $ AP( I+( K-1 )*K / 2 )*WK - 00390 $ AP( I+( K-2 )*( K-1 ) / 2 )*WKM1 00391 40 CONTINUE 00392 AP( J+( K-1 )*K / 2 ) = WK 00393 AP( J+( K-2 )*( K-1 ) / 2 ) = WKM1 00394 50 CONTINUE 00395 * 00396 END IF 00397 END IF 00398 END IF 00399 * 00400 * Store details of the interchanges in IPIV 00401 * 00402 IF( KSTEP.EQ.1 ) THEN 00403 IPIV( K ) = KP 00404 ELSE 00405 IPIV( K ) = -KP 00406 IPIV( K-1 ) = -KP 00407 END IF 00408 * 00409 * Decrease K and return to the start of the main loop 00410 * 00411 K = K - KSTEP 00412 KC = KNC - K 00413 GO TO 10 00414 * 00415 ELSE 00416 * 00417 * Factorize A as L*D*L**T using the lower triangle of A 00418 * 00419 * K is the main loop index, increasing from 1 to N in steps of 00420 * 1 or 2 00421 * 00422 K = 1 00423 KC = 1 00424 NPP = N*( N+1 ) / 2 00425 60 CONTINUE 00426 KNC = KC 00427 * 00428 * If K > N, exit from loop 00429 * 00430 IF( K.GT.N ) 00431 $ GO TO 110 00432 KSTEP = 1 00433 * 00434 * Determine rows and columns to be interchanged and whether 00435 * a 1-by-1 or 2-by-2 pivot block will be used 00436 * 00437 ABSAKK = CABS1( AP( KC ) ) 00438 * 00439 * IMAX is the row-index of the largest off-diagonal element in 00440 * column K, and COLMAX is its absolute value 00441 * 00442 IF( K.LT.N ) THEN 00443 IMAX = K + IZAMAX( N-K, AP( KC+1 ), 1 ) 00444 COLMAX = CABS1( AP( KC+IMAX-K ) ) 00445 ELSE 00446 COLMAX = ZERO 00447 END IF 00448 * 00449 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00450 * 00451 * Column K is zero: set INFO and continue 00452 * 00453 IF( INFO.EQ.0 ) 00454 $ INFO = K 00455 KP = K 00456 ELSE 00457 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00458 * 00459 * no interchange, use 1-by-1 pivot block 00460 * 00461 KP = K 00462 ELSE 00463 * 00464 * JMAX is the column-index of the largest off-diagonal 00465 * element in row IMAX, and ROWMAX is its absolute value 00466 * 00467 ROWMAX = ZERO 00468 KX = KC + IMAX - K 00469 DO 70 J = K, IMAX - 1 00470 IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN 00471 ROWMAX = CABS1( AP( KX ) ) 00472 JMAX = J 00473 END IF 00474 KX = KX + N - J 00475 70 CONTINUE 00476 KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1 00477 IF( IMAX.LT.N ) THEN 00478 JMAX = IMAX + IZAMAX( N-IMAX, AP( KPC+1 ), 1 ) 00479 ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-IMAX ) ) ) 00480 END IF 00481 * 00482 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00483 * 00484 * no interchange, use 1-by-1 pivot block 00485 * 00486 KP = K 00487 ELSE IF( CABS1( AP( KPC ) ).GE.ALPHA*ROWMAX ) THEN 00488 * 00489 * interchange rows and columns K and IMAX, use 1-by-1 00490 * pivot block 00491 * 00492 KP = IMAX 00493 ELSE 00494 * 00495 * interchange rows and columns K+1 and IMAX, use 2-by-2 00496 * pivot block 00497 * 00498 KP = IMAX 00499 KSTEP = 2 00500 END IF 00501 END IF 00502 * 00503 KK = K + KSTEP - 1 00504 IF( KSTEP.EQ.2 ) 00505 $ KNC = KNC + N - K + 1 00506 IF( KP.NE.KK ) THEN 00507 * 00508 * Interchange rows and columns KK and KP in the trailing 00509 * submatrix A(k:n,k:n) 00510 * 00511 IF( KP.LT.N ) 00512 $ CALL ZSWAP( N-KP, AP( KNC+KP-KK+1 ), 1, AP( KPC+1 ), 00513 $ 1 ) 00514 KX = KNC + KP - KK 00515 DO 80 J = KK + 1, KP - 1 00516 KX = KX + N - J + 1 00517 T = AP( KNC+J-KK ) 00518 AP( KNC+J-KK ) = AP( KX ) 00519 AP( KX ) = T 00520 80 CONTINUE 00521 T = AP( KNC ) 00522 AP( KNC ) = AP( KPC ) 00523 AP( KPC ) = T 00524 IF( KSTEP.EQ.2 ) THEN 00525 T = AP( KC+1 ) 00526 AP( KC+1 ) = AP( KC+KP-K ) 00527 AP( KC+KP-K ) = T 00528 END IF 00529 END IF 00530 * 00531 * Update the trailing submatrix 00532 * 00533 IF( KSTEP.EQ.1 ) THEN 00534 * 00535 * 1-by-1 pivot block D(k): column k now holds 00536 * 00537 * W(k) = L(k)*D(k) 00538 * 00539 * where L(k) is the k-th column of L 00540 * 00541 IF( K.LT.N ) THEN 00542 * 00543 * Perform a rank-1 update of A(k+1:n,k+1:n) as 00544 * 00545 * A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T 00546 * 00547 R1 = CONE / AP( KC ) 00548 CALL ZSPR( UPLO, N-K, -R1, AP( KC+1 ), 1, 00549 $ AP( KC+N-K+1 ) ) 00550 * 00551 * Store L(k) in column K 00552 * 00553 CALL ZSCAL( N-K, R1, AP( KC+1 ), 1 ) 00554 END IF 00555 ELSE 00556 * 00557 * 2-by-2 pivot block D(k): columns K and K+1 now hold 00558 * 00559 * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) 00560 * 00561 * where L(k) and L(k+1) are the k-th and (k+1)-th columns 00562 * of L 00563 * 00564 IF( K.LT.N-1 ) THEN 00565 * 00566 * Perform a rank-2 update of A(k+2:n,k+2:n) as 00567 * 00568 * A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T 00569 * = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T 00570 * 00571 * where L(k) and L(k+1) are the k-th and (k+1)-th 00572 * columns of L 00573 * 00574 D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 ) 00575 D11 = AP( K+1+K*( 2*N-K-1 ) / 2 ) / D21 00576 D22 = AP( K+( K-1 )*( 2*N-K ) / 2 ) / D21 00577 T = CONE / ( D11*D22-CONE ) 00578 D21 = T / D21 00579 * 00580 DO 100 J = K + 2, N 00581 WK = D21*( D11*AP( J+( K-1 )*( 2*N-K ) / 2 )- 00582 $ AP( J+K*( 2*N-K-1 ) / 2 ) ) 00583 WKP1 = D21*( D22*AP( J+K*( 2*N-K-1 ) / 2 )- 00584 $ AP( J+( K-1 )*( 2*N-K ) / 2 ) ) 00585 DO 90 I = J, N 00586 AP( I+( J-1 )*( 2*N-J ) / 2 ) = AP( I+( J-1 )* 00587 $ ( 2*N-J ) / 2 ) - AP( I+( K-1 )*( 2*N-K ) / 00588 $ 2 )*WK - AP( I+K*( 2*N-K-1 ) / 2 )*WKP1 00589 90 CONTINUE 00590 AP( J+( K-1 )*( 2*N-K ) / 2 ) = WK 00591 AP( J+K*( 2*N-K-1 ) / 2 ) = WKP1 00592 100 CONTINUE 00593 END IF 00594 END IF 00595 END IF 00596 * 00597 * Store details of the interchanges in IPIV 00598 * 00599 IF( KSTEP.EQ.1 ) THEN 00600 IPIV( K ) = KP 00601 ELSE 00602 IPIV( K ) = -KP 00603 IPIV( K+1 ) = -KP 00604 END IF 00605 * 00606 * Increase K and return to the start of the main loop 00607 * 00608 K = K + KSTEP 00609 KC = KNC + N - K + 2 00610 GO TO 60 00611 * 00612 END IF 00613 * 00614 110 CONTINUE 00615 RETURN 00616 * 00617 * End of ZSPTRF 00618 * 00619 END