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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHETF2 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHETF2 + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetf2.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetf2.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetf2.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDA, N 00026 * .. 00027 * .. Array Arguments .. 00028 * INTEGER IPIV( * ) 00029 * COMPLEX*16 A( LDA, * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> ZHETF2 computes the factorization of a complex Hermitian matrix A 00039 *> 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, U**H is the conjugate transpose of U, and D is 00045 *> Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 00046 *> 00047 *> This is the unblocked version of the algorithm, calling Level 2 BLAS. 00048 *> \endverbatim 00049 * 00050 * Arguments: 00051 * ========== 00052 * 00053 *> \param[in] UPLO 00054 *> \verbatim 00055 *> UPLO is CHARACTER*1 00056 *> Specifies whether the upper or lower triangular part of the 00057 *> Hermitian matrix A is stored: 00058 *> = 'U': Upper triangular 00059 *> = 'L': Lower triangular 00060 *> \endverbatim 00061 *> 00062 *> \param[in] N 00063 *> \verbatim 00064 *> N is INTEGER 00065 *> The order of the matrix A. N >= 0. 00066 *> \endverbatim 00067 *> 00068 *> \param[in,out] A 00069 *> \verbatim 00070 *> A is COMPLEX*16 array, dimension (LDA,N) 00071 *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading 00072 *> n-by-n upper triangular part of A contains the upper 00073 *> triangular part of the matrix A, and the strictly lower 00074 *> triangular part of A is not referenced. If UPLO = 'L', the 00075 *> leading n-by-n lower triangular part of A contains the lower 00076 *> triangular part of the matrix A, and the strictly upper 00077 *> triangular part of A is not referenced. 00078 *> 00079 *> On exit, the block diagonal matrix D and the multipliers used 00080 *> to obtain the factor U or L (see below for further details). 00081 *> \endverbatim 00082 *> 00083 *> \param[in] LDA 00084 *> \verbatim 00085 *> LDA is INTEGER 00086 *> The leading dimension of the array A. LDA >= max(1,N). 00087 *> \endverbatim 00088 *> 00089 *> \param[out] IPIV 00090 *> \verbatim 00091 *> IPIV is INTEGER array, dimension (N) 00092 *> Details of the interchanges and the block structure of D. 00093 *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were 00094 *> interchanged and D(k,k) is a 1-by-1 diagonal block. 00095 *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and 00096 *> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) 00097 *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = 00098 *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were 00099 *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 00100 *> \endverbatim 00101 *> 00102 *> \param[out] INFO 00103 *> \verbatim 00104 *> INFO is INTEGER 00105 *> = 0: successful exit 00106 *> < 0: if INFO = -k, the k-th argument had an illegal value 00107 *> > 0: if INFO = k, D(k,k) is exactly zero. The factorization 00108 *> has been completed, but the block diagonal matrix D is 00109 *> exactly singular, and division by zero will occur if it 00110 *> is used to solve a system of equations. 00111 *> \endverbatim 00112 * 00113 * Authors: 00114 * ======== 00115 * 00116 *> \author Univ. of Tennessee 00117 *> \author Univ. of California Berkeley 00118 *> \author Univ. of Colorado Denver 00119 *> \author NAG Ltd. 00120 * 00121 *> \date November 2011 00122 * 00123 *> \ingroup complex16HEcomputational 00124 * 00125 *> \par Further Details: 00126 * ===================== 00127 *> 00128 *> \verbatim 00129 *> 00130 *> If UPLO = 'U', then A = U*D*U**H, where 00131 *> U = P(n)*U(n)* ... *P(k)U(k)* ..., 00132 *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to 00133 *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 00134 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 00135 *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such 00136 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then 00137 *> 00138 *> ( I v 0 ) k-s 00139 *> U(k) = ( 0 I 0 ) s 00140 *> ( 0 0 I ) n-k 00141 *> k-s s n-k 00142 *> 00143 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). 00144 *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), 00145 *> and A(k,k), and v overwrites A(1:k-2,k-1:k). 00146 *> 00147 *> If UPLO = 'L', then A = L*D*L**H, where 00148 *> L = P(1)*L(1)* ... *P(k)*L(k)* ..., 00149 *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to 00150 *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 00151 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 00152 *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such 00153 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then 00154 *> 00155 *> ( I 0 0 ) k-1 00156 *> L(k) = ( 0 I 0 ) s 00157 *> ( 0 v I ) n-k-s+1 00158 *> k-1 s n-k-s+1 00159 *> 00160 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). 00161 *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), 00162 *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). 00163 *> \endverbatim 00164 * 00165 *> \par Contributors: 00166 * ================== 00167 *> 00168 *> \verbatim 00169 *> 09-29-06 - patch from 00170 *> Bobby Cheng, MathWorks 00171 *> 00172 *> Replace l.210 and l.393 00173 *> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00174 *> by 00175 *> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN 00176 *> 00177 *> 01-01-96 - Based on modifications by 00178 *> J. Lewis, Boeing Computer Services Company 00179 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA 00180 *> \endverbatim 00181 * 00182 * ===================================================================== 00183 SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO ) 00184 * 00185 * -- LAPACK computational routine (version 3.4.0) -- 00186 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00187 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00188 * November 2011 00189 * 00190 * .. Scalar Arguments .. 00191 CHARACTER UPLO 00192 INTEGER INFO, LDA, N 00193 * .. 00194 * .. Array Arguments .. 00195 INTEGER IPIV( * ) 00196 COMPLEX*16 A( LDA, * ) 00197 * .. 00198 * 00199 * ===================================================================== 00200 * 00201 * .. Parameters .. 00202 DOUBLE PRECISION ZERO, ONE 00203 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00204 DOUBLE PRECISION EIGHT, SEVTEN 00205 PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 ) 00206 * .. 00207 * .. Local Scalars .. 00208 LOGICAL UPPER 00209 INTEGER I, IMAX, J, JMAX, K, KK, KP, KSTEP 00210 DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, ROWMAX, 00211 $ TT 00212 COMPLEX*16 D12, D21, T, WK, WKM1, WKP1, ZDUM 00213 * .. 00214 * .. External Functions .. 00215 LOGICAL LSAME, DISNAN 00216 INTEGER IZAMAX 00217 DOUBLE PRECISION DLAPY2 00218 EXTERNAL LSAME, IZAMAX, DLAPY2, DISNAN 00219 * .. 00220 * .. External Subroutines .. 00221 EXTERNAL XERBLA, ZDSCAL, ZHER, ZSWAP 00222 * .. 00223 * .. Intrinsic Functions .. 00224 INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, SQRT 00225 * .. 00226 * .. Statement Functions .. 00227 DOUBLE PRECISION CABS1 00228 * .. 00229 * .. Statement Function definitions .. 00230 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00231 * .. 00232 * .. Executable Statements .. 00233 * 00234 * Test the input parameters. 00235 * 00236 INFO = 0 00237 UPPER = LSAME( UPLO, 'U' ) 00238 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00239 INFO = -1 00240 ELSE IF( N.LT.0 ) THEN 00241 INFO = -2 00242 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00243 INFO = -4 00244 END IF 00245 IF( INFO.NE.0 ) THEN 00246 CALL XERBLA( 'ZHETF2', -INFO ) 00247 RETURN 00248 END IF 00249 * 00250 * Initialize ALPHA for use in choosing pivot block size. 00251 * 00252 ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT 00253 * 00254 IF( UPPER ) THEN 00255 * 00256 * Factorize A as U*D*U**H using the upper triangle of A 00257 * 00258 * K is the main loop index, decreasing from N to 1 in steps of 00259 * 1 or 2 00260 * 00261 K = N 00262 10 CONTINUE 00263 * 00264 * If K < 1, exit from loop 00265 * 00266 IF( K.LT.1 ) 00267 $ GO TO 90 00268 KSTEP = 1 00269 * 00270 * Determine rows and columns to be interchanged and whether 00271 * a 1-by-1 or 2-by-2 pivot block will be used 00272 * 00273 ABSAKK = ABS( DBLE( A( K, K ) ) ) 00274 * 00275 * IMAX is the row-index of the largest off-diagonal element in 00276 * column K, and COLMAX is its absolute value 00277 * 00278 IF( K.GT.1 ) THEN 00279 IMAX = IZAMAX( K-1, A( 1, K ), 1 ) 00280 COLMAX = CABS1( A( IMAX, K ) ) 00281 ELSE 00282 COLMAX = ZERO 00283 END IF 00284 * 00285 IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN 00286 * 00287 * Column K is zero or contains a NaN: set INFO and continue 00288 * 00289 IF( INFO.EQ.0 ) 00290 $ INFO = K 00291 KP = K 00292 A( K, K ) = DBLE( A( K, K ) ) 00293 ELSE 00294 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00295 * 00296 * no interchange, use 1-by-1 pivot block 00297 * 00298 KP = K 00299 ELSE 00300 * 00301 * JMAX is the column-index of the largest off-diagonal 00302 * element in row IMAX, and ROWMAX is its absolute value 00303 * 00304 JMAX = IMAX + IZAMAX( K-IMAX, A( IMAX, IMAX+1 ), LDA ) 00305 ROWMAX = CABS1( A( IMAX, JMAX ) ) 00306 IF( IMAX.GT.1 ) THEN 00307 JMAX = IZAMAX( IMAX-1, A( 1, IMAX ), 1 ) 00308 ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) ) 00309 END IF 00310 * 00311 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00312 * 00313 * no interchange, use 1-by-1 pivot block 00314 * 00315 KP = K 00316 ELSE IF( ABS( DBLE( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX ) 00317 $ THEN 00318 * 00319 * interchange rows and columns K and IMAX, use 1-by-1 00320 * pivot block 00321 * 00322 KP = IMAX 00323 ELSE 00324 * 00325 * interchange rows and columns K-1 and IMAX, use 2-by-2 00326 * pivot block 00327 * 00328 KP = IMAX 00329 KSTEP = 2 00330 END IF 00331 END IF 00332 * 00333 KK = K - KSTEP + 1 00334 IF( KP.NE.KK ) THEN 00335 * 00336 * Interchange rows and columns KK and KP in the leading 00337 * submatrix A(1:k,1:k) 00338 * 00339 CALL ZSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 ) 00340 DO 20 J = KP + 1, KK - 1 00341 T = DCONJG( A( J, KK ) ) 00342 A( J, KK ) = DCONJG( A( KP, J ) ) 00343 A( KP, J ) = T 00344 20 CONTINUE 00345 A( KP, KK ) = DCONJG( A( KP, KK ) ) 00346 R1 = DBLE( A( KK, KK ) ) 00347 A( KK, KK ) = DBLE( A( KP, KP ) ) 00348 A( KP, KP ) = R1 00349 IF( KSTEP.EQ.2 ) THEN 00350 A( K, K ) = DBLE( A( K, K ) ) 00351 T = A( K-1, K ) 00352 A( K-1, K ) = A( KP, K ) 00353 A( KP, K ) = T 00354 END IF 00355 ELSE 00356 A( K, K ) = DBLE( A( K, K ) ) 00357 IF( KSTEP.EQ.2 ) 00358 $ A( K-1, K-1 ) = DBLE( A( K-1, K-1 ) ) 00359 END IF 00360 * 00361 * Update the leading submatrix 00362 * 00363 IF( KSTEP.EQ.1 ) THEN 00364 * 00365 * 1-by-1 pivot block D(k): column k now holds 00366 * 00367 * W(k) = U(k)*D(k) 00368 * 00369 * where U(k) is the k-th column of U 00370 * 00371 * Perform a rank-1 update of A(1:k-1,1:k-1) as 00372 * 00373 * A := A - U(k)*D(k)*U(k)**H = A - W(k)*1/D(k)*W(k)**H 00374 * 00375 R1 = ONE / DBLE( A( K, K ) ) 00376 CALL ZHER( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA ) 00377 * 00378 * Store U(k) in column k 00379 * 00380 CALL ZDSCAL( K-1, R1, A( 1, K ), 1 ) 00381 ELSE 00382 * 00383 * 2-by-2 pivot block D(k): columns k and k-1 now hold 00384 * 00385 * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) 00386 * 00387 * where U(k) and U(k-1) are the k-th and (k-1)-th columns 00388 * of U 00389 * 00390 * Perform a rank-2 update of A(1:k-2,1:k-2) as 00391 * 00392 * A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**H 00393 * = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**H 00394 * 00395 IF( K.GT.2 ) THEN 00396 * 00397 D = DLAPY2( DBLE( A( K-1, K ) ), 00398 $ DIMAG( A( K-1, K ) ) ) 00399 D22 = DBLE( A( K-1, K-1 ) ) / D 00400 D11 = DBLE( A( K, K ) ) / D 00401 TT = ONE / ( D11*D22-ONE ) 00402 D12 = A( K-1, K ) / D 00403 D = TT / D 00404 * 00405 DO 40 J = K - 2, 1, -1 00406 WKM1 = D*( D11*A( J, K-1 )-DCONJG( D12 )* 00407 $ A( J, K ) ) 00408 WK = D*( D22*A( J, K )-D12*A( J, K-1 ) ) 00409 DO 30 I = J, 1, -1 00410 A( I, J ) = A( I, J ) - A( I, K )*DCONJG( WK ) - 00411 $ A( I, K-1 )*DCONJG( WKM1 ) 00412 30 CONTINUE 00413 A( J, K ) = WK 00414 A( J, K-1 ) = WKM1 00415 A( J, J ) = DCMPLX( DBLE( A( J, J ) ), 0.0D+0 ) 00416 40 CONTINUE 00417 * 00418 END IF 00419 * 00420 END IF 00421 END IF 00422 * 00423 * Store details of the interchanges in IPIV 00424 * 00425 IF( KSTEP.EQ.1 ) THEN 00426 IPIV( K ) = KP 00427 ELSE 00428 IPIV( K ) = -KP 00429 IPIV( K-1 ) = -KP 00430 END IF 00431 * 00432 * Decrease K and return to the start of the main loop 00433 * 00434 K = K - KSTEP 00435 GO TO 10 00436 * 00437 ELSE 00438 * 00439 * Factorize A as L*D*L**H using the lower triangle of A 00440 * 00441 * K is the main loop index, increasing from 1 to N in steps of 00442 * 1 or 2 00443 * 00444 K = 1 00445 50 CONTINUE 00446 * 00447 * If K > N, exit from loop 00448 * 00449 IF( K.GT.N ) 00450 $ GO TO 90 00451 KSTEP = 1 00452 * 00453 * Determine rows and columns to be interchanged and whether 00454 * a 1-by-1 or 2-by-2 pivot block will be used 00455 * 00456 ABSAKK = ABS( DBLE( A( K, K ) ) ) 00457 * 00458 * IMAX is the row-index of the largest off-diagonal element in 00459 * column K, and COLMAX is its absolute value 00460 * 00461 IF( K.LT.N ) THEN 00462 IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 ) 00463 COLMAX = CABS1( A( IMAX, K ) ) 00464 ELSE 00465 COLMAX = ZERO 00466 END IF 00467 * 00468 IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN 00469 * 00470 * Column K is zero or contains a NaN: set INFO and continue 00471 * 00472 IF( INFO.EQ.0 ) 00473 $ INFO = K 00474 KP = K 00475 A( K, K ) = DBLE( A( K, K ) ) 00476 ELSE 00477 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00478 * 00479 * no interchange, use 1-by-1 pivot block 00480 * 00481 KP = K 00482 ELSE 00483 * 00484 * JMAX is the column-index of the largest off-diagonal 00485 * element in row IMAX, and ROWMAX is its absolute value 00486 * 00487 JMAX = K - 1 + IZAMAX( IMAX-K, A( IMAX, K ), LDA ) 00488 ROWMAX = CABS1( A( IMAX, JMAX ) ) 00489 IF( IMAX.LT.N ) THEN 00490 JMAX = IMAX + IZAMAX( N-IMAX, A( IMAX+1, IMAX ), 1 ) 00491 ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) ) 00492 END IF 00493 * 00494 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00495 * 00496 * no interchange, use 1-by-1 pivot block 00497 * 00498 KP = K 00499 ELSE IF( ABS( DBLE( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX ) 00500 $ THEN 00501 * 00502 * interchange rows and columns K and IMAX, use 1-by-1 00503 * pivot block 00504 * 00505 KP = IMAX 00506 ELSE 00507 * 00508 * interchange rows and columns K+1 and IMAX, use 2-by-2 00509 * pivot block 00510 * 00511 KP = IMAX 00512 KSTEP = 2 00513 END IF 00514 END IF 00515 * 00516 KK = K + KSTEP - 1 00517 IF( KP.NE.KK ) THEN 00518 * 00519 * Interchange rows and columns KK and KP in the trailing 00520 * submatrix A(k:n,k:n) 00521 * 00522 IF( KP.LT.N ) 00523 $ CALL ZSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 ) 00524 DO 60 J = KK + 1, KP - 1 00525 T = DCONJG( A( J, KK ) ) 00526 A( J, KK ) = DCONJG( A( KP, J ) ) 00527 A( KP, J ) = T 00528 60 CONTINUE 00529 A( KP, KK ) = DCONJG( A( KP, KK ) ) 00530 R1 = DBLE( A( KK, KK ) ) 00531 A( KK, KK ) = DBLE( A( KP, KP ) ) 00532 A( KP, KP ) = R1 00533 IF( KSTEP.EQ.2 ) THEN 00534 A( K, K ) = DBLE( A( K, K ) ) 00535 T = A( K+1, K ) 00536 A( K+1, K ) = A( KP, K ) 00537 A( KP, K ) = T 00538 END IF 00539 ELSE 00540 A( K, K ) = DBLE( A( K, K ) ) 00541 IF( KSTEP.EQ.2 ) 00542 $ A( K+1, K+1 ) = DBLE( A( K+1, K+1 ) ) 00543 END IF 00544 * 00545 * Update the trailing submatrix 00546 * 00547 IF( KSTEP.EQ.1 ) THEN 00548 * 00549 * 1-by-1 pivot block D(k): column k now holds 00550 * 00551 * W(k) = L(k)*D(k) 00552 * 00553 * where L(k) is the k-th column of L 00554 * 00555 IF( K.LT.N ) THEN 00556 * 00557 * Perform a rank-1 update of A(k+1:n,k+1:n) as 00558 * 00559 * A := A - L(k)*D(k)*L(k)**H = A - W(k)*(1/D(k))*W(k)**H 00560 * 00561 R1 = ONE / DBLE( A( K, K ) ) 00562 CALL ZHER( UPLO, N-K, -R1, A( K+1, K ), 1, 00563 $ A( K+1, K+1 ), LDA ) 00564 * 00565 * Store L(k) in column K 00566 * 00567 CALL ZDSCAL( N-K, R1, A( K+1, K ), 1 ) 00568 END IF 00569 ELSE 00570 * 00571 * 2-by-2 pivot block D(k) 00572 * 00573 IF( K.LT.N-1 ) THEN 00574 * 00575 * Perform a rank-2 update of A(k+2:n,k+2:n) as 00576 * 00577 * A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**H 00578 * = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**H 00579 * 00580 * where L(k) and L(k+1) are the k-th and (k+1)-th 00581 * columns of L 00582 * 00583 D = DLAPY2( DBLE( A( K+1, K ) ), 00584 $ DIMAG( A( K+1, K ) ) ) 00585 D11 = DBLE( A( K+1, K+1 ) ) / D 00586 D22 = DBLE( A( K, K ) ) / D 00587 TT = ONE / ( D11*D22-ONE ) 00588 D21 = A( K+1, K ) / D 00589 D = TT / D 00590 * 00591 DO 80 J = K + 2, N 00592 WK = D*( D11*A( J, K )-D21*A( J, K+1 ) ) 00593 WKP1 = D*( D22*A( J, K+1 )-DCONJG( D21 )* 00594 $ A( J, K ) ) 00595 DO 70 I = J, N 00596 A( I, J ) = A( I, J ) - A( I, K )*DCONJG( WK ) - 00597 $ A( I, K+1 )*DCONJG( WKP1 ) 00598 70 CONTINUE 00599 A( J, K ) = WK 00600 A( J, K+1 ) = WKP1 00601 A( J, J ) = DCMPLX( DBLE( A( J, J ) ), 0.0D+0 ) 00602 80 CONTINUE 00603 END IF 00604 END IF 00605 END IF 00606 * 00607 * Store details of the interchanges in IPIV 00608 * 00609 IF( KSTEP.EQ.1 ) THEN 00610 IPIV( K ) = KP 00611 ELSE 00612 IPIV( K ) = -KP 00613 IPIV( K+1 ) = -KP 00614 END IF 00615 * 00616 * Increase K and return to the start of the main loop 00617 * 00618 K = K + KSTEP 00619 GO TO 50 00620 * 00621 END IF 00622 * 00623 90 CONTINUE 00624 RETURN 00625 * 00626 * End of ZHETF2 00627 * 00628 END