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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CHETF2 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CHETF2 + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetf2.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetf2.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetf2.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CHETF2( 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 A( LDA, * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> CHETF2 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 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 complexHEcomputational 00124 * 00125 *> \par Further Details: 00126 * ===================== 00127 *> 00128 *> \verbatim 00129 *> 00130 *> 09-29-06 - patch from 00131 *> Bobby Cheng, MathWorks 00132 *> 00133 *> Replace l.210 and l.392 00134 *> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 00135 *> by 00136 *> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN 00137 *> 00138 *> 01-01-96 - Based on modifications by 00139 *> J. Lewis, Boeing Computer Services Company 00140 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA 00141 *> 00142 *> If UPLO = 'U', then A = U*D*U**H, where 00143 *> U = P(n)*U(n)* ... *P(k)U(k)* ..., 00144 *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to 00145 *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 00146 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 00147 *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such 00148 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then 00149 *> 00150 *> ( I v 0 ) k-s 00151 *> U(k) = ( 0 I 0 ) s 00152 *> ( 0 0 I ) n-k 00153 *> k-s s n-k 00154 *> 00155 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). 00156 *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), 00157 *> and A(k,k), and v overwrites A(1:k-2,k-1:k). 00158 *> 00159 *> If UPLO = 'L', then A = L*D*L**H, where 00160 *> L = P(1)*L(1)* ... *P(k)*L(k)* ..., 00161 *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to 00162 *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 00163 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 00164 *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such 00165 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then 00166 *> 00167 *> ( I 0 0 ) k-1 00168 *> L(k) = ( 0 I 0 ) s 00169 *> ( 0 v I ) n-k-s+1 00170 *> k-1 s n-k-s+1 00171 *> 00172 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). 00173 *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), 00174 *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). 00175 *> \endverbatim 00176 *> 00177 * ===================================================================== 00178 SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO ) 00179 * 00180 * -- LAPACK computational routine (version 3.4.0) -- 00181 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00182 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00183 * November 2011 00184 * 00185 * .. Scalar Arguments .. 00186 CHARACTER UPLO 00187 INTEGER INFO, LDA, N 00188 * .. 00189 * .. Array Arguments .. 00190 INTEGER IPIV( * ) 00191 COMPLEX A( LDA, * ) 00192 * .. 00193 * 00194 * ===================================================================== 00195 * 00196 * .. Parameters .. 00197 REAL ZERO, ONE 00198 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00199 REAL EIGHT, SEVTEN 00200 PARAMETER ( EIGHT = 8.0E+0, SEVTEN = 17.0E+0 ) 00201 * .. 00202 * .. Local Scalars .. 00203 LOGICAL UPPER 00204 INTEGER I, IMAX, J, JMAX, K, KK, KP, KSTEP 00205 REAL ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, ROWMAX, 00206 $ TT 00207 COMPLEX D12, D21, T, WK, WKM1, WKP1, ZDUM 00208 * .. 00209 * .. External Functions .. 00210 LOGICAL LSAME, SISNAN 00211 INTEGER ICAMAX 00212 REAL SLAPY2 00213 EXTERNAL LSAME, ICAMAX, SLAPY2, SISNAN 00214 * .. 00215 * .. External Subroutines .. 00216 EXTERNAL CHER, CSSCAL, CSWAP, XERBLA 00217 * .. 00218 * .. Intrinsic Functions .. 00219 INTRINSIC ABS, AIMAG, CMPLX, CONJG, MAX, REAL, SQRT 00220 * .. 00221 * .. Statement Functions .. 00222 REAL CABS1 00223 * .. 00224 * .. Statement Function definitions .. 00225 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00226 * .. 00227 * .. Executable Statements .. 00228 * 00229 * Test the input parameters. 00230 * 00231 INFO = 0 00232 UPPER = LSAME( UPLO, 'U' ) 00233 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00234 INFO = -1 00235 ELSE IF( N.LT.0 ) THEN 00236 INFO = -2 00237 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00238 INFO = -4 00239 END IF 00240 IF( INFO.NE.0 ) THEN 00241 CALL XERBLA( 'CHETF2', -INFO ) 00242 RETURN 00243 END IF 00244 * 00245 * Initialize ALPHA for use in choosing pivot block size. 00246 * 00247 ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT 00248 * 00249 IF( UPPER ) THEN 00250 * 00251 * Factorize A as U*D*U**H using the upper triangle of A 00252 * 00253 * K is the main loop index, decreasing from N to 1 in steps of 00254 * 1 or 2 00255 * 00256 K = N 00257 10 CONTINUE 00258 * 00259 * If K < 1, exit from loop 00260 * 00261 IF( K.LT.1 ) 00262 $ GO TO 90 00263 KSTEP = 1 00264 * 00265 * Determine rows and columns to be interchanged and whether 00266 * a 1-by-1 or 2-by-2 pivot block will be used 00267 * 00268 ABSAKK = ABS( REAL( A( K, K ) ) ) 00269 * 00270 * IMAX is the row-index of the largest off-diagonal element in 00271 * column K, and COLMAX is its absolute value 00272 * 00273 IF( K.GT.1 ) THEN 00274 IMAX = ICAMAX( K-1, A( 1, K ), 1 ) 00275 COLMAX = CABS1( A( IMAX, K ) ) 00276 ELSE 00277 COLMAX = ZERO 00278 END IF 00279 * 00280 IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN 00281 * 00282 * Column K is zero or contains a NaN: set INFO and continue 00283 * 00284 IF( INFO.EQ.0 ) 00285 $ INFO = K 00286 KP = K 00287 A( K, K ) = REAL( A( K, K ) ) 00288 ELSE 00289 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00290 * 00291 * no interchange, use 1-by-1 pivot block 00292 * 00293 KP = K 00294 ELSE 00295 * 00296 * JMAX is the column-index of the largest off-diagonal 00297 * element in row IMAX, and ROWMAX is its absolute value 00298 * 00299 JMAX = IMAX + ICAMAX( K-IMAX, A( IMAX, IMAX+1 ), LDA ) 00300 ROWMAX = CABS1( A( IMAX, JMAX ) ) 00301 IF( IMAX.GT.1 ) THEN 00302 JMAX = ICAMAX( IMAX-1, A( 1, IMAX ), 1 ) 00303 ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) ) 00304 END IF 00305 * 00306 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00307 * 00308 * no interchange, use 1-by-1 pivot block 00309 * 00310 KP = K 00311 ELSE IF( ABS( REAL( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX ) 00312 $ THEN 00313 * 00314 * interchange rows and columns K and IMAX, use 1-by-1 00315 * pivot block 00316 * 00317 KP = IMAX 00318 ELSE 00319 * 00320 * interchange rows and columns K-1 and IMAX, use 2-by-2 00321 * pivot block 00322 * 00323 KP = IMAX 00324 KSTEP = 2 00325 END IF 00326 END IF 00327 * 00328 KK = K - KSTEP + 1 00329 IF( KP.NE.KK ) THEN 00330 * 00331 * Interchange rows and columns KK and KP in the leading 00332 * submatrix A(1:k,1:k) 00333 * 00334 CALL CSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 ) 00335 DO 20 J = KP + 1, KK - 1 00336 T = CONJG( A( J, KK ) ) 00337 A( J, KK ) = CONJG( A( KP, J ) ) 00338 A( KP, J ) = T 00339 20 CONTINUE 00340 A( KP, KK ) = CONJG( A( KP, KK ) ) 00341 R1 = REAL( A( KK, KK ) ) 00342 A( KK, KK ) = REAL( A( KP, KP ) ) 00343 A( KP, KP ) = R1 00344 IF( KSTEP.EQ.2 ) THEN 00345 A( K, K ) = REAL( A( K, K ) ) 00346 T = A( K-1, K ) 00347 A( K-1, K ) = A( KP, K ) 00348 A( KP, K ) = T 00349 END IF 00350 ELSE 00351 A( K, K ) = REAL( A( K, K ) ) 00352 IF( KSTEP.EQ.2 ) 00353 $ A( K-1, K-1 ) = REAL( A( K-1, K-1 ) ) 00354 END IF 00355 * 00356 * Update the leading submatrix 00357 * 00358 IF( KSTEP.EQ.1 ) THEN 00359 * 00360 * 1-by-1 pivot block D(k): column k now holds 00361 * 00362 * W(k) = U(k)*D(k) 00363 * 00364 * where U(k) is the k-th column of U 00365 * 00366 * Perform a rank-1 update of A(1:k-1,1:k-1) as 00367 * 00368 * A := A - U(k)*D(k)*U(k)**H = A - W(k)*1/D(k)*W(k)**H 00369 * 00370 R1 = ONE / REAL( A( K, K ) ) 00371 CALL CHER( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA ) 00372 * 00373 * Store U(k) in column k 00374 * 00375 CALL CSSCAL( K-1, R1, A( 1, K ), 1 ) 00376 ELSE 00377 * 00378 * 2-by-2 pivot block D(k): columns k and k-1 now hold 00379 * 00380 * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) 00381 * 00382 * where U(k) and U(k-1) are the k-th and (k-1)-th columns 00383 * of U 00384 * 00385 * Perform a rank-2 update of A(1:k-2,1:k-2) as 00386 * 00387 * A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**H 00388 * = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**H 00389 * 00390 IF( K.GT.2 ) THEN 00391 * 00392 D = SLAPY2( REAL( A( K-1, K ) ), 00393 $ AIMAG( A( K-1, K ) ) ) 00394 D22 = REAL( A( K-1, K-1 ) ) / D 00395 D11 = REAL( A( K, K ) ) / D 00396 TT = ONE / ( D11*D22-ONE ) 00397 D12 = A( K-1, K ) / D 00398 D = TT / D 00399 * 00400 DO 40 J = K - 2, 1, -1 00401 WKM1 = D*( D11*A( J, K-1 )-CONJG( D12 )*A( J, K ) ) 00402 WK = D*( D22*A( J, K )-D12*A( J, K-1 ) ) 00403 DO 30 I = J, 1, -1 00404 A( I, J ) = A( I, J ) - A( I, K )*CONJG( WK ) - 00405 $ A( I, K-1 )*CONJG( WKM1 ) 00406 30 CONTINUE 00407 A( J, K ) = WK 00408 A( J, K-1 ) = WKM1 00409 A( J, J ) = CMPLX( REAL( A( J, J ) ), 0.0E+0 ) 00410 40 CONTINUE 00411 * 00412 END IF 00413 * 00414 END IF 00415 END IF 00416 * 00417 * Store details of the interchanges in IPIV 00418 * 00419 IF( KSTEP.EQ.1 ) THEN 00420 IPIV( K ) = KP 00421 ELSE 00422 IPIV( K ) = -KP 00423 IPIV( K-1 ) = -KP 00424 END IF 00425 * 00426 * Decrease K and return to the start of the main loop 00427 * 00428 K = K - KSTEP 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 50 CONTINUE 00440 * 00441 * If K > N, exit from loop 00442 * 00443 IF( K.GT.N ) 00444 $ GO TO 90 00445 KSTEP = 1 00446 * 00447 * Determine rows and columns to be interchanged and whether 00448 * a 1-by-1 or 2-by-2 pivot block will be used 00449 * 00450 ABSAKK = ABS( REAL( A( K, K ) ) ) 00451 * 00452 * IMAX is the row-index of the largest off-diagonal element in 00453 * column K, and COLMAX is its absolute value 00454 * 00455 IF( K.LT.N ) THEN 00456 IMAX = K + ICAMAX( N-K, A( K+1, K ), 1 ) 00457 COLMAX = CABS1( A( IMAX, K ) ) 00458 ELSE 00459 COLMAX = ZERO 00460 END IF 00461 * 00462 IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN 00463 * 00464 * Column K is zero or contains a NaN: set INFO and continue 00465 * 00466 IF( INFO.EQ.0 ) 00467 $ INFO = K 00468 KP = K 00469 A( K, K ) = REAL( A( K, K ) ) 00470 ELSE 00471 IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 00472 * 00473 * no interchange, use 1-by-1 pivot block 00474 * 00475 KP = K 00476 ELSE 00477 * 00478 * JMAX is the column-index of the largest off-diagonal 00479 * element in row IMAX, and ROWMAX is its absolute value 00480 * 00481 JMAX = K - 1 + ICAMAX( IMAX-K, A( IMAX, K ), LDA ) 00482 ROWMAX = CABS1( A( IMAX, JMAX ) ) 00483 IF( IMAX.LT.N ) THEN 00484 JMAX = IMAX + ICAMAX( N-IMAX, A( IMAX+1, IMAX ), 1 ) 00485 ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) ) 00486 END IF 00487 * 00488 IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 00489 * 00490 * no interchange, use 1-by-1 pivot block 00491 * 00492 KP = K 00493 ELSE IF( ABS( REAL( A( IMAX, IMAX ) ) ).GE.ALPHA*ROWMAX ) 00494 $ THEN 00495 * 00496 * interchange rows and columns K and IMAX, use 1-by-1 00497 * pivot block 00498 * 00499 KP = IMAX 00500 ELSE 00501 * 00502 * interchange rows and columns K+1 and IMAX, use 2-by-2 00503 * pivot block 00504 * 00505 KP = IMAX 00506 KSTEP = 2 00507 END IF 00508 END IF 00509 * 00510 KK = K + KSTEP - 1 00511 IF( KP.NE.KK ) THEN 00512 * 00513 * Interchange rows and columns KK and KP in the trailing 00514 * submatrix A(k:n,k:n) 00515 * 00516 IF( KP.LT.N ) 00517 $ CALL CSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 ) 00518 DO 60 J = KK + 1, KP - 1 00519 T = CONJG( A( J, KK ) ) 00520 A( J, KK ) = CONJG( A( KP, J ) ) 00521 A( KP, J ) = T 00522 60 CONTINUE 00523 A( KP, KK ) = CONJG( A( KP, KK ) ) 00524 R1 = REAL( A( KK, KK ) ) 00525 A( KK, KK ) = REAL( A( KP, KP ) ) 00526 A( KP, KP ) = R1 00527 IF( KSTEP.EQ.2 ) THEN 00528 A( K, K ) = REAL( A( K, K ) ) 00529 T = A( K+1, K ) 00530 A( K+1, K ) = A( KP, K ) 00531 A( KP, K ) = T 00532 END IF 00533 ELSE 00534 A( K, K ) = REAL( A( K, K ) ) 00535 IF( KSTEP.EQ.2 ) 00536 $ A( K+1, K+1 ) = REAL( A( K+1, K+1 ) ) 00537 END IF 00538 * 00539 * Update the trailing submatrix 00540 * 00541 IF( KSTEP.EQ.1 ) THEN 00542 * 00543 * 1-by-1 pivot block D(k): column k now holds 00544 * 00545 * W(k) = L(k)*D(k) 00546 * 00547 * where L(k) is the k-th column of L 00548 * 00549 IF( K.LT.N ) THEN 00550 * 00551 * Perform a rank-1 update of A(k+1:n,k+1:n) as 00552 * 00553 * A := A - L(k)*D(k)*L(k)**H = A - W(k)*(1/D(k))*W(k)**H 00554 * 00555 R1 = ONE / REAL( A( K, K ) ) 00556 CALL CHER( UPLO, N-K, -R1, A( K+1, K ), 1, 00557 $ A( K+1, K+1 ), LDA ) 00558 * 00559 * Store L(k) in column K 00560 * 00561 CALL CSSCAL( N-K, R1, A( K+1, K ), 1 ) 00562 END IF 00563 ELSE 00564 * 00565 * 2-by-2 pivot block D(k) 00566 * 00567 IF( K.LT.N-1 ) THEN 00568 * 00569 * Perform a rank-2 update of A(k+2:n,k+2:n) as 00570 * 00571 * A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**H 00572 * = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**H 00573 * 00574 * where L(k) and L(k+1) are the k-th and (k+1)-th 00575 * columns of L 00576 * 00577 D = SLAPY2( REAL( A( K+1, K ) ), 00578 $ AIMAG( A( K+1, K ) ) ) 00579 D11 = REAL( A( K+1, K+1 ) ) / D 00580 D22 = REAL( A( K, K ) ) / D 00581 TT = ONE / ( D11*D22-ONE ) 00582 D21 = A( K+1, K ) / D 00583 D = TT / D 00584 * 00585 DO 80 J = K + 2, N 00586 WK = D*( D11*A( J, K )-D21*A( J, K+1 ) ) 00587 WKP1 = D*( D22*A( J, K+1 )-CONJG( D21 )*A( J, K ) ) 00588 DO 70 I = J, N 00589 A( I, J ) = A( I, J ) - A( I, K )*CONJG( WK ) - 00590 $ A( I, K+1 )*CONJG( WKP1 ) 00591 70 CONTINUE 00592 A( J, K ) = WK 00593 A( J, K+1 ) = WKP1 00594 A( J, J ) = CMPLX( REAL( A( J, J ) ), 0.0E+0 ) 00595 80 CONTINUE 00596 END IF 00597 END IF 00598 END IF 00599 * 00600 * Store details of the interchanges in IPIV 00601 * 00602 IF( KSTEP.EQ.1 ) THEN 00603 IPIV( K ) = KP 00604 ELSE 00605 IPIV( K ) = -KP 00606 IPIV( K+1 ) = -KP 00607 END IF 00608 * 00609 * Increase K and return to the start of the main loop 00610 * 00611 K = K + KSTEP 00612 GO TO 50 00613 * 00614 END IF 00615 * 00616 90 CONTINUE 00617 RETURN 00618 * 00619 * End of CHETF2 00620 * 00621 END