![]() |
LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
|
00001 *> \brief \b CHPTRF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CHPTRF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chptrf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chptrf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chptrf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CHPTRF( 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 AP( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> CHPTRF computes the factorization of a complex Hermitian packed 00039 *> matrix A using the Bunch-Kaufman diagonal pivoting method: 00040 *> 00041 *> A = U*D*U**H or A = L*D*L**H 00042 *> 00043 *> where U (or L) is a product of permutation and unit upper (lower) 00044 *> triangular matrices, and D is Hermitian 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 COMPLEX array, dimension (N*(N+1)/2) 00067 *> On entry, the upper or lower triangle of the Hermitian 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 complexOTHERcomputational 00113 * 00114 *> \par Further Details: 00115 * ===================== 00116 *> 00117 *> \verbatim 00118 *> 00119 *> If UPLO = 'U', then A = U*D*U**H, 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**H, 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 CHPTRF( 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 COMPLEX AP( * ) 00174 * .. 00175 * 00176 * ===================================================================== 00177 * 00178 * .. Parameters .. 00179 REAL ZERO, ONE 00180 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00181 REAL EIGHT, SEVTEN 00182 PARAMETER ( EIGHT = 8.0E+0, SEVTEN = 17.0E+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 REAL ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, ROWMAX, 00189 $ TT 00190 COMPLEX D12, D21, T, WK, WKM1, WKP1, ZDUM 00191 * .. 00192 * .. External Functions .. 00193 LOGICAL LSAME 00194 INTEGER ICAMAX 00195 REAL SLAPY2 00196 EXTERNAL LSAME, ICAMAX, SLAPY2 00197 * .. 00198 * .. External Subroutines .. 00199 EXTERNAL CHPR, CSSCAL, CSWAP, XERBLA 00200 * .. 00201 * .. Intrinsic Functions .. 00202 INTRINSIC ABS, AIMAG, CMPLX, CONJG, MAX, REAL, SQRT 00203 * .. 00204 * .. Statement Functions .. 00205 REAL CABS1 00206 * .. 00207 * .. Statement Function definitions .. 00208 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00209 * .. 00210 * .. Executable Statements .. 00211 * 00212 * Test the input parameters. 00213 * 00214 INFO = 0 00215 UPPER = LSAME( UPLO, 'U' ) 00216 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00217 INFO = -1 00218 ELSE IF( N.LT.0 ) THEN 00219 INFO = -2 00220 END IF 00221 IF( INFO.NE.0 ) THEN 00222 CALL XERBLA( 'CHPTRF', -INFO ) 00223 RETURN 00224 END IF 00225 * 00226 * Initialize ALPHA for use in choosing pivot block size. 00227 * 00228 ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT 00229 * 00230 IF( UPPER ) THEN 00231 * 00232 * Factorize A as U*D*U**H using the upper triangle of A 00233 * 00234 * K is the main loop index, decreasing from N to 1 in steps of 00235 * 1 or 2 00236 * 00237 K = N 00238 KC = ( N-1 )*N / 2 + 1 00239 10 CONTINUE 00240 KNC = KC 00241 * 00242 * If K < 1, exit from loop 00243 * 00244 IF( K.LT.1 ) 00245 $ GO TO 110 00246 KSTEP = 1 00247 * 00248 * Determine rows and columns to be interchanged and whether 00249 * a 1-by-1 or 2-by-2 pivot block will be used 00250 * 00251 ABSAKK = ABS( REAL( AP( KC+K-1 ) ) ) 00252 * 00253 * IMAX is the row-index of the largest off-diagonal element in 00254 * column K, and COLMAX is its absolute value 00255 * 00256 IF( K.GT.1 ) THEN 00257 IMAX = ICAMAX( K-1, AP( KC ), 1 ) 00258 COLMAX = CABS1( AP( KC+IMAX-1 ) ) 00259 ELSE 00260 COLMAX = ZERO 00261 END IF 00262 * 00263 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00264 * 00265 * Column K is zero: set INFO and continue 00266 * 00267 IF( INFO.EQ.0 ) 00268 $ INFO = K 00269 KP = K 00270 AP( KC+K-1 ) = REAL( AP( KC+K-1 ) ) 00271 ELSE 00272 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00273 * 00274 * no interchange, use 1-by-1 pivot block 00275 * 00276 KP = K 00277 ELSE 00278 * 00279 * JMAX is the column-index of the largest off-diagonal 00280 * element in row IMAX, and ROWMAX is its absolute value 00281 * 00282 ROWMAX = ZERO 00283 JMAX = IMAX 00284 KX = IMAX*( IMAX+1 ) / 2 + IMAX 00285 DO 20 J = IMAX + 1, K 00286 IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN 00287 ROWMAX = CABS1( AP( KX ) ) 00288 JMAX = J 00289 END IF 00290 KX = KX + J 00291 20 CONTINUE 00292 KPC = ( IMAX-1 )*IMAX / 2 + 1 00293 IF( IMAX.GT.1 ) THEN 00294 JMAX = ICAMAX( IMAX-1, AP( KPC ), 1 ) 00295 ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-1 ) ) ) 00296 END IF 00297 * 00298 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00299 * 00300 * no interchange, use 1-by-1 pivot block 00301 * 00302 KP = K 00303 ELSE IF( ABS( REAL( AP( KPC+IMAX-1 ) ) ).GE.ALPHA* 00304 $ ROWMAX ) THEN 00305 * 00306 * interchange rows and columns K and IMAX, use 1-by-1 00307 * pivot block 00308 * 00309 KP = IMAX 00310 ELSE 00311 * 00312 * interchange rows and columns K-1 and IMAX, use 2-by-2 00313 * pivot block 00314 * 00315 KP = IMAX 00316 KSTEP = 2 00317 END IF 00318 END IF 00319 * 00320 KK = K - KSTEP + 1 00321 IF( KSTEP.EQ.2 ) 00322 $ KNC = KNC - K + 1 00323 IF( KP.NE.KK ) THEN 00324 * 00325 * Interchange rows and columns KK and KP in the leading 00326 * submatrix A(1:k,1:k) 00327 * 00328 CALL CSWAP( KP-1, AP( KNC ), 1, AP( KPC ), 1 ) 00329 KX = KPC + KP - 1 00330 DO 30 J = KP + 1, KK - 1 00331 KX = KX + J - 1 00332 T = CONJG( AP( KNC+J-1 ) ) 00333 AP( KNC+J-1 ) = CONJG( AP( KX ) ) 00334 AP( KX ) = T 00335 30 CONTINUE 00336 AP( KX+KK-1 ) = CONJG( AP( KX+KK-1 ) ) 00337 R1 = REAL( AP( KNC+KK-1 ) ) 00338 AP( KNC+KK-1 ) = REAL( AP( KPC+KP-1 ) ) 00339 AP( KPC+KP-1 ) = R1 00340 IF( KSTEP.EQ.2 ) THEN 00341 AP( KC+K-1 ) = REAL( AP( KC+K-1 ) ) 00342 T = AP( KC+K-2 ) 00343 AP( KC+K-2 ) = AP( KC+KP-1 ) 00344 AP( KC+KP-1 ) = T 00345 END IF 00346 ELSE 00347 AP( KC+K-1 ) = REAL( AP( KC+K-1 ) ) 00348 IF( KSTEP.EQ.2 ) 00349 $ AP( KC-1 ) = REAL( AP( KC-1 ) ) 00350 END IF 00351 * 00352 * Update the leading submatrix 00353 * 00354 IF( KSTEP.EQ.1 ) THEN 00355 * 00356 * 1-by-1 pivot block D(k): column k now holds 00357 * 00358 * W(k) = U(k)*D(k) 00359 * 00360 * where U(k) is the k-th column of U 00361 * 00362 * Perform a rank-1 update of A(1:k-1,1:k-1) as 00363 * 00364 * A := A - U(k)*D(k)*U(k)**H = A - W(k)*1/D(k)*W(k)**H 00365 * 00366 R1 = ONE / REAL( AP( KC+K-1 ) ) 00367 CALL CHPR( UPLO, K-1, -R1, AP( KC ), 1, AP ) 00368 * 00369 * Store U(k) in column k 00370 * 00371 CALL CSSCAL( K-1, R1, AP( KC ), 1 ) 00372 ELSE 00373 * 00374 * 2-by-2 pivot block D(k): columns k and k-1 now hold 00375 * 00376 * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) 00377 * 00378 * where U(k) and U(k-1) are the k-th and (k-1)-th columns 00379 * of U 00380 * 00381 * Perform a rank-2 update of A(1:k-2,1:k-2) as 00382 * 00383 * A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**H 00384 * = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**H 00385 * 00386 IF( K.GT.2 ) THEN 00387 * 00388 D = SLAPY2( REAL( AP( K-1+( K-1 )*K / 2 ) ), 00389 $ AIMAG( AP( K-1+( K-1 )*K / 2 ) ) ) 00390 D22 = REAL( AP( K-1+( K-2 )*( K-1 ) / 2 ) ) / D 00391 D11 = REAL( AP( K+( K-1 )*K / 2 ) ) / D 00392 TT = ONE / ( D11*D22-ONE ) 00393 D12 = AP( K-1+( K-1 )*K / 2 ) / D 00394 D = TT / D 00395 * 00396 DO 50 J = K - 2, 1, -1 00397 WKM1 = D*( D11*AP( J+( K-2 )*( K-1 ) / 2 )- 00398 $ CONJG( D12 )*AP( J+( K-1 )*K / 2 ) ) 00399 WK = D*( D22*AP( J+( K-1 )*K / 2 )-D12* 00400 $ AP( J+( K-2 )*( K-1 ) / 2 ) ) 00401 DO 40 I = J, 1, -1 00402 AP( I+( J-1 )*J / 2 ) = AP( I+( J-1 )*J / 2 ) - 00403 $ AP( I+( K-1 )*K / 2 )*CONJG( WK ) - 00404 $ AP( I+( K-2 )*( K-1 ) / 2 )*CONJG( WKM1 ) 00405 40 CONTINUE 00406 AP( J+( K-1 )*K / 2 ) = WK 00407 AP( J+( K-2 )*( K-1 ) / 2 ) = WKM1 00408 AP( J+( J-1 )*J / 2 ) = CMPLX( REAL( AP( J+( J-1 )* $ J / 2 ) ), 0.0E+0 ) 00409 50 CONTINUE 00410 * 00411 END IF 00412 * 00413 END IF 00414 END IF 00415 * 00416 * Store details of the interchanges in IPIV 00417 * 00418 IF( KSTEP.EQ.1 ) THEN 00419 IPIV( K ) = KP 00420 ELSE 00421 IPIV( K ) = -KP 00422 IPIV( K-1 ) = -KP 00423 END IF 00424 * 00425 * Decrease K and return to the start of the main loop 00426 * 00427 K = K - KSTEP 00428 KC = KNC - K 00429 GO TO 10 00430 * 00431 ELSE 00432 * 00433 * Factorize A as L*D*L**H using the lower triangle of A 00434 * 00435 * K is the main loop index, increasing from 1 to N in steps of 00436 * 1 or 2 00437 * 00438 K = 1 00439 KC = 1 00440 NPP = N*( N+1 ) / 2 00441 60 CONTINUE 00442 KNC = KC 00443 * 00444 * If K > N, exit from loop 00445 * 00446 IF( K.GT.N ) 00447 $ GO TO 110 00448 KSTEP = 1 00449 * 00450 * Determine rows and columns to be interchanged and whether 00451 * a 1-by-1 or 2-by-2 pivot block will be used 00452 * 00453 ABSAKK = ABS( REAL( AP( KC ) ) ) 00454 * 00455 * IMAX is the row-index of the largest off-diagonal element in 00456 * column K, and COLMAX is its absolute value 00457 * 00458 IF( K.LT.N ) THEN 00459 IMAX = K + ICAMAX( N-K, AP( KC+1 ), 1 ) 00460 COLMAX = CABS1( AP( KC+IMAX-K ) ) 00461 ELSE 00462 COLMAX = ZERO 00463 END IF 00464 * 00465 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00466 * 00467 * Column K is zero: set INFO and continue 00468 * 00469 IF( INFO.EQ.0 ) 00470 $ INFO = K 00471 KP = K 00472 AP( KC ) = REAL( AP( KC ) ) 00473 ELSE 00474 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00475 * 00476 * no interchange, use 1-by-1 pivot block 00477 * 00478 KP = K 00479 ELSE 00480 * 00481 * JMAX is the column-index of the largest off-diagonal 00482 * element in row IMAX, and ROWMAX is its absolute value 00483 * 00484 ROWMAX = ZERO 00485 KX = KC + IMAX - K 00486 DO 70 J = K, IMAX - 1 00487 IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN 00488 ROWMAX = CABS1( AP( KX ) ) 00489 JMAX = J 00490 END IF 00491 KX = KX + N - J 00492 70 CONTINUE 00493 KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1 00494 IF( IMAX.LT.N ) THEN 00495 JMAX = IMAX + ICAMAX( N-IMAX, AP( KPC+1 ), 1 ) 00496 ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-IMAX ) ) ) 00497 END IF 00498 * 00499 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00500 * 00501 * no interchange, use 1-by-1 pivot block 00502 * 00503 KP = K 00504 ELSE IF( ABS( REAL( AP( KPC ) ) ).GE.ALPHA*ROWMAX ) THEN 00505 * 00506 * interchange rows and columns K and IMAX, use 1-by-1 00507 * pivot block 00508 * 00509 KP = IMAX 00510 ELSE 00511 * 00512 * interchange rows and columns K+1 and IMAX, use 2-by-2 00513 * pivot block 00514 * 00515 KP = IMAX 00516 KSTEP = 2 00517 END IF 00518 END IF 00519 * 00520 KK = K + KSTEP - 1 00521 IF( KSTEP.EQ.2 ) 00522 $ KNC = KNC + N - K + 1 00523 IF( KP.NE.KK ) THEN 00524 * 00525 * Interchange rows and columns KK and KP in the trailing 00526 * submatrix A(k:n,k:n) 00527 * 00528 IF( KP.LT.N ) 00529 $ CALL CSWAP( N-KP, AP( KNC+KP-KK+1 ), 1, AP( KPC+1 ), 00530 $ 1 ) 00531 KX = KNC + KP - KK 00532 DO 80 J = KK + 1, KP - 1 00533 KX = KX + N - J + 1 00534 T = CONJG( AP( KNC+J-KK ) ) 00535 AP( KNC+J-KK ) = CONJG( AP( KX ) ) 00536 AP( KX ) = T 00537 80 CONTINUE 00538 AP( KNC+KP-KK ) = CONJG( AP( KNC+KP-KK ) ) 00539 R1 = REAL( AP( KNC ) ) 00540 AP( KNC ) = REAL( AP( KPC ) ) 00541 AP( KPC ) = R1 00542 IF( KSTEP.EQ.2 ) THEN 00543 AP( KC ) = REAL( AP( KC ) ) 00544 T = AP( KC+1 ) 00545 AP( KC+1 ) = AP( KC+KP-K ) 00546 AP( KC+KP-K ) = T 00547 END IF 00548 ELSE 00549 AP( KC ) = REAL( AP( KC ) ) 00550 IF( KSTEP.EQ.2 ) 00551 $ AP( KNC ) = REAL( AP( KNC ) ) 00552 END IF 00553 * 00554 * Update the trailing submatrix 00555 * 00556 IF( KSTEP.EQ.1 ) THEN 00557 * 00558 * 1-by-1 pivot block D(k): column k now holds 00559 * 00560 * W(k) = L(k)*D(k) 00561 * 00562 * where L(k) is the k-th column of L 00563 * 00564 IF( K.LT.N ) THEN 00565 * 00566 * Perform a rank-1 update of A(k+1:n,k+1:n) as 00567 * 00568 * A := A - L(k)*D(k)*L(k)**H = A - W(k)*(1/D(k))*W(k)**H 00569 * 00570 R1 = ONE / REAL( AP( KC ) ) 00571 CALL CHPR( UPLO, N-K, -R1, AP( KC+1 ), 1, 00572 $ AP( KC+N-K+1 ) ) 00573 * 00574 * Store L(k) in column K 00575 * 00576 CALL CSSCAL( N-K, R1, AP( KC+1 ), 1 ) 00577 END IF 00578 ELSE 00579 * 00580 * 2-by-2 pivot block D(k): columns K and K+1 now hold 00581 * 00582 * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) 00583 * 00584 * where L(k) and L(k+1) are the k-th and (k+1)-th columns 00585 * of L 00586 * 00587 IF( K.LT.N-1 ) THEN 00588 * 00589 * Perform a rank-2 update of A(k+2:n,k+2:n) as 00590 * 00591 * A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**H 00592 * = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**H 00593 * 00594 * where L(k) and L(k+1) are the k-th and (k+1)-th 00595 * columns of L 00596 * 00597 D = SLAPY2( REAL( AP( K+1+( K-1 )*( 2*N-K ) / 2 ) ), 00598 $ AIMAG( AP( K+1+( K-1 )*( 2*N-K ) / 2 ) ) ) 00599 D11 = REAL( AP( K+1+K*( 2*N-K-1 ) / 2 ) ) / D 00600 D22 = REAL( AP( K+( K-1 )*( 2*N-K ) / 2 ) ) / D 00601 TT = ONE / ( D11*D22-ONE ) 00602 D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 ) / D 00603 D = TT / D 00604 * 00605 DO 100 J = K + 2, N 00606 WK = D*( D11*AP( J+( K-1 )*( 2*N-K ) / 2 )-D21* 00607 $ AP( J+K*( 2*N-K-1 ) / 2 ) ) 00608 WKP1 = D*( D22*AP( J+K*( 2*N-K-1 ) / 2 )- 00609 $ CONJG( D21 )*AP( J+( K-1 )*( 2*N-K ) / 2 ) ) 00610 DO 90 I = J, N 00611 AP( I+( J-1 )*( 2*N-J ) / 2 ) = AP( I+( J-1 )* 00612 $ ( 2*N-J ) / 2 ) - AP( I+( K-1 )*( 2*N-K ) / 00613 $ 2 )*CONJG( WK ) - AP( I+K*( 2*N-K-1 ) / 2 )* 00614 $ CONJG( WKP1 ) 00615 90 CONTINUE 00616 AP( J+( K-1 )*( 2*N-K ) / 2 ) = WK 00617 AP( J+K*( 2*N-K-1 ) / 2 ) = WKP1 00618 AP( J+( J-1 )*( 2*N-J ) / 2 ) 00619 $ = CMPLX( REAL( AP( J+( J-1 )*( 2*N-J ) / 2 ) ), 00620 $ 0.0E+0 ) 00621 100 CONTINUE 00622 END IF 00623 END IF 00624 END IF 00625 * 00626 * Store details of the interchanges in IPIV 00627 * 00628 IF( KSTEP.EQ.1 ) THEN 00629 IPIV( K ) = KP 00630 ELSE 00631 IPIV( K ) = -KP 00632 IPIV( K+1 ) = -KP 00633 END IF 00634 * 00635 * Increase K and return to the start of the main loop 00636 * 00637 K = K + KSTEP 00638 KC = KNC + N - K + 2 00639 GO TO 60 00640 * 00641 END IF 00642 * 00643 110 CONTINUE 00644 RETURN 00645 * 00646 * End of CHPTRF 00647 * 00648 END 00649