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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLANHF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLANHF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER NORM, TRANSR, UPLO 00025 * INTEGER N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION WORK( 0: * ) 00029 * COMPLEX*16 A( 0: * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> ZLANHF returns the value of the one norm, or the Frobenius norm, or 00039 *> the infinity norm, or the element of largest absolute value of a 00040 *> complex Hermitian matrix A in RFP format. 00041 *> \endverbatim 00042 *> 00043 *> \return ZLANHF 00044 *> \verbatim 00045 *> 00046 *> ZLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm' 00047 *> ( 00048 *> ( norm1(A), NORM = '1', 'O' or 'o' 00049 *> ( 00050 *> ( normI(A), NORM = 'I' or 'i' 00051 *> ( 00052 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' 00053 *> 00054 *> where norm1 denotes the one norm of a matrix (maximum column sum), 00055 *> normI denotes the infinity norm of a matrix (maximum row sum) and 00056 *> normF denotes the Frobenius norm of a matrix (square root of sum of 00057 *> squares). Note that max(abs(A(i,j))) is not a matrix norm. 00058 *> \endverbatim 00059 * 00060 * Arguments: 00061 * ========== 00062 * 00063 *> \param[in] NORM 00064 *> \verbatim 00065 *> NORM is CHARACTER 00066 *> Specifies the value to be returned in ZLANHF as described 00067 *> above. 00068 *> \endverbatim 00069 *> 00070 *> \param[in] TRANSR 00071 *> \verbatim 00072 *> TRANSR is CHARACTER 00073 *> Specifies whether the RFP format of A is normal or 00074 *> conjugate-transposed format. 00075 *> = 'N': RFP format is Normal 00076 *> = 'C': RFP format is Conjugate-transposed 00077 *> \endverbatim 00078 *> 00079 *> \param[in] UPLO 00080 *> \verbatim 00081 *> UPLO is CHARACTER 00082 *> On entry, UPLO specifies whether the RFP matrix A came from 00083 *> an upper or lower triangular matrix as follows: 00084 *> 00085 *> UPLO = 'U' or 'u' RFP A came from an upper triangular 00086 *> matrix 00087 *> 00088 *> UPLO = 'L' or 'l' RFP A came from a lower triangular 00089 *> matrix 00090 *> \endverbatim 00091 *> 00092 *> \param[in] N 00093 *> \verbatim 00094 *> N is INTEGER 00095 *> The order of the matrix A. N >= 0. When N = 0, ZLANHF is 00096 *> set to zero. 00097 *> \endverbatim 00098 *> 00099 *> \param[in] A 00100 *> \verbatim 00101 *> A is COMPLEX*16 array, dimension ( N*(N+1)/2 ); 00102 *> On entry, the matrix A in RFP Format. 00103 *> RFP Format is described by TRANSR, UPLO and N as follows: 00104 *> If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; 00105 *> K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If 00106 *> TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A 00107 *> as defined when TRANSR = 'N'. The contents of RFP A are 00108 *> defined by UPLO as follows: If UPLO = 'U' the RFP A 00109 *> contains the ( N*(N+1)/2 ) elements of upper packed A 00110 *> either in normal or conjugate-transpose Format. If 00111 *> UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements 00112 *> of lower packed A either in normal or conjugate-transpose 00113 *> Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When 00114 *> TRANSR is 'N' the LDA is N+1 when N is even and is N when 00115 *> is odd. See the Note below for more details. 00116 *> Unchanged on exit. 00117 *> \endverbatim 00118 *> 00119 *> \param[out] WORK 00120 *> \verbatim 00121 *> WORK is DOUBLE PRECISION array, dimension (LWORK), 00122 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00123 *> WORK is not referenced. 00124 *> \endverbatim 00125 * 00126 * Authors: 00127 * ======== 00128 * 00129 *> \author Univ. of Tennessee 00130 *> \author Univ. of California Berkeley 00131 *> \author Univ. of Colorado Denver 00132 *> \author NAG Ltd. 00133 * 00134 *> \date November 2011 00135 * 00136 *> \ingroup complex16OTHERcomputational 00137 * 00138 *> \par Further Details: 00139 * ===================== 00140 *> 00141 *> \verbatim 00142 *> 00143 *> We first consider Standard Packed Format when N is even. 00144 *> We give an example where N = 6. 00145 *> 00146 *> AP is Upper AP is Lower 00147 *> 00148 *> 00 01 02 03 04 05 00 00149 *> 11 12 13 14 15 10 11 00150 *> 22 23 24 25 20 21 22 00151 *> 33 34 35 30 31 32 33 00152 *> 44 45 40 41 42 43 44 00153 *> 55 50 51 52 53 54 55 00154 *> 00155 *> 00156 *> Let TRANSR = 'N'. RFP holds AP as follows: 00157 *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last 00158 *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of 00159 *> conjugate-transpose of the first three columns of AP upper. 00160 *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first 00161 *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of 00162 *> conjugate-transpose of the last three columns of AP lower. 00163 *> To denote conjugate we place -- above the element. This covers the 00164 *> case N even and TRANSR = 'N'. 00165 *> 00166 *> RFP A RFP A 00167 *> 00168 *> -- -- -- 00169 *> 03 04 05 33 43 53 00170 *> -- -- 00171 *> 13 14 15 00 44 54 00172 *> -- 00173 *> 23 24 25 10 11 55 00174 *> 00175 *> 33 34 35 20 21 22 00176 *> -- 00177 *> 00 44 45 30 31 32 00178 *> -- -- 00179 *> 01 11 55 40 41 42 00180 *> -- -- -- 00181 *> 02 12 22 50 51 52 00182 *> 00183 *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- 00184 *> transpose of RFP A above. One therefore gets: 00185 *> 00186 *> 00187 *> RFP A RFP A 00188 *> 00189 *> -- -- -- -- -- -- -- -- -- -- 00190 *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 00191 *> -- -- -- -- -- -- -- -- -- -- 00192 *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 00193 *> -- -- -- -- -- -- -- -- -- -- 00194 *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 00195 *> 00196 *> 00197 *> We next consider Standard Packed Format when N is odd. 00198 *> We give an example where N = 5. 00199 *> 00200 *> AP is Upper AP is Lower 00201 *> 00202 *> 00 01 02 03 04 00 00203 *> 11 12 13 14 10 11 00204 *> 22 23 24 20 21 22 00205 *> 33 34 30 31 32 33 00206 *> 44 40 41 42 43 44 00207 *> 00208 *> 00209 *> Let TRANSR = 'N'. RFP holds AP as follows: 00210 *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last 00211 *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of 00212 *> conjugate-transpose of the first two columns of AP upper. 00213 *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first 00214 *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of 00215 *> conjugate-transpose of the last two columns of AP lower. 00216 *> To denote conjugate we place -- above the element. This covers the 00217 *> case N odd and TRANSR = 'N'. 00218 *> 00219 *> RFP A RFP A 00220 *> 00221 *> -- -- 00222 *> 02 03 04 00 33 43 00223 *> -- 00224 *> 12 13 14 10 11 44 00225 *> 00226 *> 22 23 24 20 21 22 00227 *> -- 00228 *> 00 33 34 30 31 32 00229 *> -- -- 00230 *> 01 11 44 40 41 42 00231 *> 00232 *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- 00233 *> transpose of RFP A above. One therefore gets: 00234 *> 00235 *> 00236 *> RFP A RFP A 00237 *> 00238 *> -- -- -- -- -- -- -- -- -- 00239 *> 02 12 22 00 01 00 10 20 30 40 50 00240 *> -- -- -- -- -- -- -- -- -- 00241 *> 03 13 23 33 11 33 11 21 31 41 51 00242 *> -- -- -- -- -- -- -- -- -- 00243 *> 04 14 24 34 44 43 44 22 32 42 52 00244 *> \endverbatim 00245 *> 00246 * ===================================================================== 00247 DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK ) 00248 * 00249 * -- LAPACK computational routine (version 3.4.0) -- 00250 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00251 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00252 * November 2011 00253 * 00254 * .. Scalar Arguments .. 00255 CHARACTER NORM, TRANSR, UPLO 00256 INTEGER N 00257 * .. 00258 * .. Array Arguments .. 00259 DOUBLE PRECISION WORK( 0: * ) 00260 COMPLEX*16 A( 0: * ) 00261 * .. 00262 * 00263 * ===================================================================== 00264 * 00265 * .. Parameters .. 00266 DOUBLE PRECISION ONE, ZERO 00267 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00268 * .. 00269 * .. Local Scalars .. 00270 INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA 00271 DOUBLE PRECISION SCALE, S, VALUE, AA 00272 * .. 00273 * .. External Functions .. 00274 LOGICAL LSAME 00275 INTEGER IDAMAX 00276 EXTERNAL LSAME, IDAMAX 00277 * .. 00278 * .. External Subroutines .. 00279 EXTERNAL ZLASSQ 00280 * .. 00281 * .. Intrinsic Functions .. 00282 INTRINSIC ABS, DBLE, MAX, SQRT 00283 * .. 00284 * .. Executable Statements .. 00285 * 00286 IF( N.EQ.0 ) THEN 00287 ZLANHF = ZERO 00288 RETURN 00289 ELSE IF( N.EQ.1 ) THEN 00290 ZLANHF = ABS( A(0) ) 00291 RETURN 00292 END IF 00293 * 00294 * set noe = 1 if n is odd. if n is even set noe=0 00295 * 00296 NOE = 1 00297 IF( MOD( N, 2 ).EQ.0 ) 00298 $ NOE = 0 00299 * 00300 * set ifm = 0 when form='C' or 'c' and 1 otherwise 00301 * 00302 IFM = 1 00303 IF( LSAME( TRANSR, 'C' ) ) 00304 $ IFM = 0 00305 * 00306 * set ilu = 0 when uplo='U or 'u' and 1 otherwise 00307 * 00308 ILU = 1 00309 IF( LSAME( UPLO, 'U' ) ) 00310 $ ILU = 0 00311 * 00312 * set lda = (n+1)/2 when ifm = 0 00313 * set lda = n when ifm = 1 and noe = 1 00314 * set lda = n+1 when ifm = 1 and noe = 0 00315 * 00316 IF( IFM.EQ.1 ) THEN 00317 IF( NOE.EQ.1 ) THEN 00318 LDA = N 00319 ELSE 00320 * noe=0 00321 LDA = N + 1 00322 END IF 00323 ELSE 00324 * ifm=0 00325 LDA = ( N+1 ) / 2 00326 END IF 00327 * 00328 IF( LSAME( NORM, 'M' ) ) THEN 00329 * 00330 * Find max(abs(A(i,j))). 00331 * 00332 K = ( N+1 ) / 2 00333 VALUE = ZERO 00334 IF( NOE.EQ.1 ) THEN 00335 * n is odd & n = k + k - 1 00336 IF( IFM.EQ.1 ) THEN 00337 * A is n by k 00338 IF( ILU.EQ.1 ) THEN 00339 * uplo ='L' 00340 J = 0 00341 * -> L(0,0) 00342 VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) ) 00343 DO I = 1, N - 1 00344 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00345 END DO 00346 DO J = 1, K - 1 00347 DO I = 0, J - 2 00348 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00349 END DO 00350 I = J - 1 00351 * L(k+j,k+j) 00352 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00353 I = J 00354 * -> L(j,j) 00355 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00356 DO I = J + 1, N - 1 00357 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00358 END DO 00359 END DO 00360 ELSE 00361 * uplo = 'U' 00362 DO J = 0, K - 2 00363 DO I = 0, K + J - 2 00364 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00365 END DO 00366 I = K + J - 1 00367 * -> U(i,i) 00368 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00369 I = I + 1 00370 * =k+j; i -> U(j,j) 00371 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00372 DO I = K + J + 1, N - 1 00373 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00374 END DO 00375 END DO 00376 DO I = 0, N - 2 00377 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00378 * j=k-1 00379 END DO 00380 * i=n-1 -> U(n-1,n-1) 00381 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00382 END IF 00383 ELSE 00384 * xpose case; A is k by n 00385 IF( ILU.EQ.1 ) THEN 00386 * uplo ='L' 00387 DO J = 0, K - 2 00388 DO I = 0, J - 1 00389 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00390 END DO 00391 I = J 00392 * L(i,i) 00393 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00394 I = J + 1 00395 * L(j+k,j+k) 00396 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00397 DO I = J + 2, K - 1 00398 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00399 END DO 00400 END DO 00401 J = K - 1 00402 DO I = 0, K - 2 00403 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00404 END DO 00405 I = K - 1 00406 * -> L(i,i) is at A(i,j) 00407 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00408 DO J = K, N - 1 00409 DO I = 0, K - 1 00410 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00411 END DO 00412 END DO 00413 ELSE 00414 * uplo = 'U' 00415 DO J = 0, K - 2 00416 DO I = 0, K - 1 00417 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00418 END DO 00419 END DO 00420 J = K - 1 00421 * -> U(j,j) is at A(0,j) 00422 VALUE = MAX( VALUE, ABS( DBLE( A( 0+J*LDA ) ) ) ) 00423 DO I = 1, K - 1 00424 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00425 END DO 00426 DO J = K, N - 1 00427 DO I = 0, J - K - 1 00428 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00429 END DO 00430 I = J - K 00431 * -> U(i,i) at A(i,j) 00432 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00433 I = J - K + 1 00434 * U(j,j) 00435 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00436 DO I = J - K + 2, K - 1 00437 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00438 END DO 00439 END DO 00440 END IF 00441 END IF 00442 ELSE 00443 * n is even & k = n/2 00444 IF( IFM.EQ.1 ) THEN 00445 * A is n+1 by k 00446 IF( ILU.EQ.1 ) THEN 00447 * uplo ='L' 00448 J = 0 00449 * -> L(k,k) & j=1 -> L(0,0) 00450 VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) ) 00451 VALUE = MAX( VALUE, ABS( DBLE( A( J+1+J*LDA ) ) ) ) 00452 DO I = 2, N 00453 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00454 END DO 00455 DO J = 1, K - 1 00456 DO I = 0, J - 1 00457 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00458 END DO 00459 I = J 00460 * L(k+j,k+j) 00461 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00462 I = J + 1 00463 * -> L(j,j) 00464 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00465 DO I = J + 2, N 00466 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00467 END DO 00468 END DO 00469 ELSE 00470 * uplo = 'U' 00471 DO J = 0, K - 2 00472 DO I = 0, K + J - 1 00473 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00474 END DO 00475 I = K + J 00476 * -> U(i,i) 00477 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00478 I = I + 1 00479 * =k+j+1; i -> U(j,j) 00480 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00481 DO I = K + J + 2, N 00482 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00483 END DO 00484 END DO 00485 DO I = 0, N - 2 00486 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00487 * j=k-1 00488 END DO 00489 * i=n-1 -> U(n-1,n-1) 00490 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00491 I = N 00492 * -> U(k-1,k-1) 00493 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00494 END IF 00495 ELSE 00496 * xpose case; A is k by n+1 00497 IF( ILU.EQ.1 ) THEN 00498 * uplo ='L' 00499 J = 0 00500 * -> L(k,k) at A(0,0) 00501 VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) ) 00502 DO I = 1, K - 1 00503 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00504 END DO 00505 DO J = 1, K - 1 00506 DO I = 0, J - 2 00507 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00508 END DO 00509 I = J - 1 00510 * L(i,i) 00511 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00512 I = J 00513 * L(j+k,j+k) 00514 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00515 DO I = J + 1, K - 1 00516 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00517 END DO 00518 END DO 00519 J = K 00520 DO I = 0, K - 2 00521 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00522 END DO 00523 I = K - 1 00524 * -> L(i,i) is at A(i,j) 00525 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00526 DO J = K + 1, N 00527 DO I = 0, K - 1 00528 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00529 END DO 00530 END DO 00531 ELSE 00532 * uplo = 'U' 00533 DO J = 0, K - 1 00534 DO I = 0, K - 1 00535 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00536 END DO 00537 END DO 00538 J = K 00539 * -> U(j,j) is at A(0,j) 00540 VALUE = MAX( VALUE, ABS( DBLE( A( 0+J*LDA ) ) ) ) 00541 DO I = 1, K - 1 00542 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00543 END DO 00544 DO J = K + 1, N - 1 00545 DO I = 0, J - K - 2 00546 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00547 END DO 00548 I = J - K - 1 00549 * -> U(i,i) at A(i,j) 00550 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00551 I = J - K 00552 * U(j,j) 00553 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00554 DO I = J - K + 1, K - 1 00555 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00556 END DO 00557 END DO 00558 J = N 00559 DO I = 0, K - 2 00560 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00561 END DO 00562 I = K - 1 00563 * U(k,k) at A(i,j) 00564 VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) ) 00565 END IF 00566 END IF 00567 END IF 00568 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00569 $ ( NORM.EQ.'1' ) ) THEN 00570 * 00571 * Find normI(A) ( = norm1(A), since A is Hermitian). 00572 * 00573 IF( IFM.EQ.1 ) THEN 00574 * A is 'N' 00575 K = N / 2 00576 IF( NOE.EQ.1 ) THEN 00577 * n is odd & A is n by (n+1)/2 00578 IF( ILU.EQ.0 ) THEN 00579 * uplo = 'U' 00580 DO I = 0, K - 1 00581 WORK( I ) = ZERO 00582 END DO 00583 DO J = 0, K 00584 S = ZERO 00585 DO I = 0, K + J - 1 00586 AA = ABS( A( I+J*LDA ) ) 00587 * -> A(i,j+k) 00588 S = S + AA 00589 WORK( I ) = WORK( I ) + AA 00590 END DO 00591 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00592 * -> A(j+k,j+k) 00593 WORK( J+K ) = S + AA 00594 IF( I.EQ.K+K ) 00595 $ GO TO 10 00596 I = I + 1 00597 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00598 * -> A(j,j) 00599 WORK( J ) = WORK( J ) + AA 00600 S = ZERO 00601 DO L = J + 1, K - 1 00602 I = I + 1 00603 AA = ABS( A( I+J*LDA ) ) 00604 * -> A(l,j) 00605 S = S + AA 00606 WORK( L ) = WORK( L ) + AA 00607 END DO 00608 WORK( J ) = WORK( J ) + S 00609 END DO 00610 10 CONTINUE 00611 I = IDAMAX( N, WORK, 1 ) 00612 VALUE = WORK( I-1 ) 00613 ELSE 00614 * ilu = 1 & uplo = 'L' 00615 K = K + 1 00616 * k=(n+1)/2 for n odd and ilu=1 00617 DO I = K, N - 1 00618 WORK( I ) = ZERO 00619 END DO 00620 DO J = K - 1, 0, -1 00621 S = ZERO 00622 DO I = 0, J - 2 00623 AA = ABS( A( I+J*LDA ) ) 00624 * -> A(j+k,i+k) 00625 S = S + AA 00626 WORK( I+K ) = WORK( I+K ) + AA 00627 END DO 00628 IF( J.GT.0 ) THEN 00629 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00630 * -> A(j+k,j+k) 00631 S = S + AA 00632 WORK( I+K ) = WORK( I+K ) + S 00633 * i=j 00634 I = I + 1 00635 END IF 00636 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00637 * -> A(j,j) 00638 WORK( J ) = AA 00639 S = ZERO 00640 DO L = J + 1, N - 1 00641 I = I + 1 00642 AA = ABS( A( I+J*LDA ) ) 00643 * -> A(l,j) 00644 S = S + AA 00645 WORK( L ) = WORK( L ) + AA 00646 END DO 00647 WORK( J ) = WORK( J ) + S 00648 END DO 00649 I = IDAMAX( N, WORK, 1 ) 00650 VALUE = WORK( I-1 ) 00651 END IF 00652 ELSE 00653 * n is even & A is n+1 by k = n/2 00654 IF( ILU.EQ.0 ) THEN 00655 * uplo = 'U' 00656 DO I = 0, K - 1 00657 WORK( I ) = ZERO 00658 END DO 00659 DO J = 0, K - 1 00660 S = ZERO 00661 DO I = 0, K + J - 1 00662 AA = ABS( A( I+J*LDA ) ) 00663 * -> A(i,j+k) 00664 S = S + AA 00665 WORK( I ) = WORK( I ) + AA 00666 END DO 00667 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00668 * -> A(j+k,j+k) 00669 WORK( J+K ) = S + AA 00670 I = I + 1 00671 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00672 * -> A(j,j) 00673 WORK( J ) = WORK( J ) + AA 00674 S = ZERO 00675 DO L = J + 1, K - 1 00676 I = I + 1 00677 AA = ABS( A( I+J*LDA ) ) 00678 * -> A(l,j) 00679 S = S + AA 00680 WORK( L ) = WORK( L ) + AA 00681 END DO 00682 WORK( J ) = WORK( J ) + S 00683 END DO 00684 I = IDAMAX( N, WORK, 1 ) 00685 VALUE = WORK( I-1 ) 00686 ELSE 00687 * ilu = 1 & uplo = 'L' 00688 DO I = K, N - 1 00689 WORK( I ) = ZERO 00690 END DO 00691 DO J = K - 1, 0, -1 00692 S = ZERO 00693 DO I = 0, J - 1 00694 AA = ABS( A( I+J*LDA ) ) 00695 * -> A(j+k,i+k) 00696 S = S + AA 00697 WORK( I+K ) = WORK( I+K ) + AA 00698 END DO 00699 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00700 * -> A(j+k,j+k) 00701 S = S + AA 00702 WORK( I+K ) = WORK( I+K ) + S 00703 * i=j 00704 I = I + 1 00705 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00706 * -> A(j,j) 00707 WORK( J ) = AA 00708 S = ZERO 00709 DO L = J + 1, N - 1 00710 I = I + 1 00711 AA = ABS( A( I+J*LDA ) ) 00712 * -> A(l,j) 00713 S = S + AA 00714 WORK( L ) = WORK( L ) + AA 00715 END DO 00716 WORK( J ) = WORK( J ) + S 00717 END DO 00718 I = IDAMAX( N, WORK, 1 ) 00719 VALUE = WORK( I-1 ) 00720 END IF 00721 END IF 00722 ELSE 00723 * ifm=0 00724 K = N / 2 00725 IF( NOE.EQ.1 ) THEN 00726 * n is odd & A is (n+1)/2 by n 00727 IF( ILU.EQ.0 ) THEN 00728 * uplo = 'U' 00729 N1 = K 00730 * n/2 00731 K = K + 1 00732 * k is the row size and lda 00733 DO I = N1, N - 1 00734 WORK( I ) = ZERO 00735 END DO 00736 DO J = 0, N1 - 1 00737 S = ZERO 00738 DO I = 0, K - 1 00739 AA = ABS( A( I+J*LDA ) ) 00740 * A(j,n1+i) 00741 WORK( I+N1 ) = WORK( I+N1 ) + AA 00742 S = S + AA 00743 END DO 00744 WORK( J ) = S 00745 END DO 00746 * j=n1=k-1 is special 00747 S = ABS( DBLE( A( 0+J*LDA ) ) ) 00748 * A(k-1,k-1) 00749 DO I = 1, K - 1 00750 AA = ABS( A( I+J*LDA ) ) 00751 * A(k-1,i+n1) 00752 WORK( I+N1 ) = WORK( I+N1 ) + AA 00753 S = S + AA 00754 END DO 00755 WORK( J ) = WORK( J ) + S 00756 DO J = K, N - 1 00757 S = ZERO 00758 DO I = 0, J - K - 1 00759 AA = ABS( A( I+J*LDA ) ) 00760 * A(i,j-k) 00761 WORK( I ) = WORK( I ) + AA 00762 S = S + AA 00763 END DO 00764 * i=j-k 00765 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00766 * A(j-k,j-k) 00767 S = S + AA 00768 WORK( J-K ) = WORK( J-K ) + S 00769 I = I + 1 00770 S = ABS( DBLE( A( I+J*LDA ) ) ) 00771 * A(j,j) 00772 DO L = J + 1, N - 1 00773 I = I + 1 00774 AA = ABS( A( I+J*LDA ) ) 00775 * A(j,l) 00776 WORK( L ) = WORK( L ) + AA 00777 S = S + AA 00778 END DO 00779 WORK( J ) = WORK( J ) + S 00780 END DO 00781 I = IDAMAX( N, WORK, 1 ) 00782 VALUE = WORK( I-1 ) 00783 ELSE 00784 * ilu=1 & uplo = 'L' 00785 K = K + 1 00786 * k=(n+1)/2 for n odd and ilu=1 00787 DO I = K, N - 1 00788 WORK( I ) = ZERO 00789 END DO 00790 DO J = 0, K - 2 00791 * process 00792 S = ZERO 00793 DO I = 0, J - 1 00794 AA = ABS( A( I+J*LDA ) ) 00795 * A(j,i) 00796 WORK( I ) = WORK( I ) + AA 00797 S = S + AA 00798 END DO 00799 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00800 * i=j so process of A(j,j) 00801 S = S + AA 00802 WORK( J ) = S 00803 * is initialised here 00804 I = I + 1 00805 * i=j process A(j+k,j+k) 00806 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00807 S = AA 00808 DO L = K + J + 1, N - 1 00809 I = I + 1 00810 AA = ABS( A( I+J*LDA ) ) 00811 * A(l,k+j) 00812 S = S + AA 00813 WORK( L ) = WORK( L ) + AA 00814 END DO 00815 WORK( K+J ) = WORK( K+J ) + S 00816 END DO 00817 * j=k-1 is special :process col A(k-1,0:k-1) 00818 S = ZERO 00819 DO I = 0, K - 2 00820 AA = ABS( A( I+J*LDA ) ) 00821 * A(k,i) 00822 WORK( I ) = WORK( I ) + AA 00823 S = S + AA 00824 END DO 00825 * i=k-1 00826 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00827 * A(k-1,k-1) 00828 S = S + AA 00829 WORK( I ) = S 00830 * done with col j=k+1 00831 DO J = K, N - 1 00832 * process col j of A = A(j,0:k-1) 00833 S = ZERO 00834 DO I = 0, K - 1 00835 AA = ABS( A( I+J*LDA ) ) 00836 * A(j,i) 00837 WORK( I ) = WORK( I ) + AA 00838 S = S + AA 00839 END DO 00840 WORK( J ) = WORK( J ) + S 00841 END DO 00842 I = IDAMAX( N, WORK, 1 ) 00843 VALUE = WORK( I-1 ) 00844 END IF 00845 ELSE 00846 * n is even & A is k=n/2 by n+1 00847 IF( ILU.EQ.0 ) THEN 00848 * uplo = 'U' 00849 DO I = K, N - 1 00850 WORK( I ) = ZERO 00851 END DO 00852 DO J = 0, K - 1 00853 S = ZERO 00854 DO I = 0, K - 1 00855 AA = ABS( A( I+J*LDA ) ) 00856 * A(j,i+k) 00857 WORK( I+K ) = WORK( I+K ) + AA 00858 S = S + AA 00859 END DO 00860 WORK( J ) = S 00861 END DO 00862 * j=k 00863 AA = ABS( DBLE( A( 0+J*LDA ) ) ) 00864 * A(k,k) 00865 S = AA 00866 DO I = 1, K - 1 00867 AA = ABS( A( I+J*LDA ) ) 00868 * A(k,k+i) 00869 WORK( I+K ) = WORK( I+K ) + AA 00870 S = S + AA 00871 END DO 00872 WORK( J ) = WORK( J ) + S 00873 DO J = K + 1, N - 1 00874 S = ZERO 00875 DO I = 0, J - 2 - K 00876 AA = ABS( A( I+J*LDA ) ) 00877 * A(i,j-k-1) 00878 WORK( I ) = WORK( I ) + AA 00879 S = S + AA 00880 END DO 00881 * i=j-1-k 00882 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00883 * A(j-k-1,j-k-1) 00884 S = S + AA 00885 WORK( J-K-1 ) = WORK( J-K-1 ) + S 00886 I = I + 1 00887 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00888 * A(j,j) 00889 S = AA 00890 DO L = J + 1, N - 1 00891 I = I + 1 00892 AA = ABS( A( I+J*LDA ) ) 00893 * A(j,l) 00894 WORK( L ) = WORK( L ) + AA 00895 S = S + AA 00896 END DO 00897 WORK( J ) = WORK( J ) + S 00898 END DO 00899 * j=n 00900 S = ZERO 00901 DO I = 0, K - 2 00902 AA = ABS( A( I+J*LDA ) ) 00903 * A(i,k-1) 00904 WORK( I ) = WORK( I ) + AA 00905 S = S + AA 00906 END DO 00907 * i=k-1 00908 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00909 * A(k-1,k-1) 00910 S = S + AA 00911 WORK( I ) = WORK( I ) + S 00912 I = IDAMAX( N, WORK, 1 ) 00913 VALUE = WORK( I-1 ) 00914 ELSE 00915 * ilu=1 & uplo = 'L' 00916 DO I = K, N - 1 00917 WORK( I ) = ZERO 00918 END DO 00919 * j=0 is special :process col A(k:n-1,k) 00920 S = ABS( DBLE( A( 0 ) ) ) 00921 * A(k,k) 00922 DO I = 1, K - 1 00923 AA = ABS( A( I ) ) 00924 * A(k+i,k) 00925 WORK( I+K ) = WORK( I+K ) + AA 00926 S = S + AA 00927 END DO 00928 WORK( K ) = WORK( K ) + S 00929 DO J = 1, K - 1 00930 * process 00931 S = ZERO 00932 DO I = 0, J - 2 00933 AA = ABS( A( I+J*LDA ) ) 00934 * A(j-1,i) 00935 WORK( I ) = WORK( I ) + AA 00936 S = S + AA 00937 END DO 00938 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00939 * i=j-1 so process of A(j-1,j-1) 00940 S = S + AA 00941 WORK( J-1 ) = S 00942 * is initialised here 00943 I = I + 1 00944 * i=j process A(j+k,j+k) 00945 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00946 S = AA 00947 DO L = K + J + 1, N - 1 00948 I = I + 1 00949 AA = ABS( A( I+J*LDA ) ) 00950 * A(l,k+j) 00951 S = S + AA 00952 WORK( L ) = WORK( L ) + AA 00953 END DO 00954 WORK( K+J ) = WORK( K+J ) + S 00955 END DO 00956 * j=k is special :process col A(k,0:k-1) 00957 S = ZERO 00958 DO I = 0, K - 2 00959 AA = ABS( A( I+J*LDA ) ) 00960 * A(k,i) 00961 WORK( I ) = WORK( I ) + AA 00962 S = S + AA 00963 END DO 00964 * 00965 * i=k-1 00966 AA = ABS( DBLE( A( I+J*LDA ) ) ) 00967 * A(k-1,k-1) 00968 S = S + AA 00969 WORK( I ) = S 00970 * done with col j=k+1 00971 DO J = K + 1, N 00972 * 00973 * process col j-1 of A = A(j-1,0:k-1) 00974 S = ZERO 00975 DO I = 0, K - 1 00976 AA = ABS( A( I+J*LDA ) ) 00977 * A(j-1,i) 00978 WORK( I ) = WORK( I ) + AA 00979 S = S + AA 00980 END DO 00981 WORK( J-1 ) = WORK( J-1 ) + S 00982 END DO 00983 I = IDAMAX( N, WORK, 1 ) 00984 VALUE = WORK( I-1 ) 00985 END IF 00986 END IF 00987 END IF 00988 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00989 * 00990 * Find normF(A). 00991 * 00992 K = ( N+1 ) / 2 00993 SCALE = ZERO 00994 S = ONE 00995 IF( NOE.EQ.1 ) THEN 00996 * n is odd 00997 IF( IFM.EQ.1 ) THEN 00998 * A is normal & A is n by k 00999 IF( ILU.EQ.0 ) THEN 01000 * A is upper 01001 DO J = 0, K - 3 01002 CALL ZLASSQ( K-J-2, A( K+J+1+J*LDA ), 1, SCALE, S ) 01003 * L at A(k,0) 01004 END DO 01005 DO J = 0, K - 1 01006 CALL ZLASSQ( K+J-1, A( 0+J*LDA ), 1, SCALE, S ) 01007 * trap U at A(0,0) 01008 END DO 01009 S = S + S 01010 * double s for the off diagonal elements 01011 L = K - 1 01012 * -> U(k,k) at A(k-1,0) 01013 DO I = 0, K - 2 01014 AA = DBLE( A( L ) ) 01015 * U(k+i,k+i) 01016 IF( AA.NE.ZERO ) THEN 01017 IF( SCALE.LT.AA ) THEN 01018 S = ONE + S*( SCALE / AA )**2 01019 SCALE = AA 01020 ELSE 01021 S = S + ( AA / SCALE )**2 01022 END IF 01023 END IF 01024 AA = DBLE( A( L+1 ) ) 01025 * U(i,i) 01026 IF( AA.NE.ZERO ) THEN 01027 IF( SCALE.LT.AA ) THEN 01028 S = ONE + S*( SCALE / AA )**2 01029 SCALE = AA 01030 ELSE 01031 S = S + ( AA / SCALE )**2 01032 END IF 01033 END IF 01034 L = L + LDA + 1 01035 END DO 01036 AA = DBLE( A( L ) ) 01037 * U(n-1,n-1) 01038 IF( AA.NE.ZERO ) THEN 01039 IF( SCALE.LT.AA ) THEN 01040 S = ONE + S*( SCALE / AA )**2 01041 SCALE = AA 01042 ELSE 01043 S = S + ( AA / SCALE )**2 01044 END IF 01045 END IF 01046 ELSE 01047 * ilu=1 & A is lower 01048 DO J = 0, K - 1 01049 CALL ZLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S ) 01050 * trap L at A(0,0) 01051 END DO 01052 DO J = 1, K - 2 01053 CALL ZLASSQ( J, A( 0+( 1+J )*LDA ), 1, SCALE, S ) 01054 * U at A(0,1) 01055 END DO 01056 S = S + S 01057 * double s for the off diagonal elements 01058 AA = DBLE( A( 0 ) ) 01059 * L(0,0) at A(0,0) 01060 IF( AA.NE.ZERO ) THEN 01061 IF( SCALE.LT.AA ) THEN 01062 S = ONE + S*( SCALE / AA )**2 01063 SCALE = AA 01064 ELSE 01065 S = S + ( AA / SCALE )**2 01066 END IF 01067 END IF 01068 L = LDA 01069 * -> L(k,k) at A(0,1) 01070 DO I = 1, K - 1 01071 AA = DBLE( A( L ) ) 01072 * L(k-1+i,k-1+i) 01073 IF( AA.NE.ZERO ) THEN 01074 IF( SCALE.LT.AA ) THEN 01075 S = ONE + S*( SCALE / AA )**2 01076 SCALE = AA 01077 ELSE 01078 S = S + ( AA / SCALE )**2 01079 END IF 01080 END IF 01081 AA = DBLE( A( L+1 ) ) 01082 * L(i,i) 01083 IF( AA.NE.ZERO ) THEN 01084 IF( SCALE.LT.AA ) THEN 01085 S = ONE + S*( SCALE / AA )**2 01086 SCALE = AA 01087 ELSE 01088 S = S + ( AA / SCALE )**2 01089 END IF 01090 END IF 01091 L = L + LDA + 1 01092 END DO 01093 END IF 01094 ELSE 01095 * A is xpose & A is k by n 01096 IF( ILU.EQ.0 ) THEN 01097 * A**H is upper 01098 DO J = 1, K - 2 01099 CALL ZLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S ) 01100 * U at A(0,k) 01101 END DO 01102 DO J = 0, K - 2 01103 CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 01104 * k by k-1 rect. at A(0,0) 01105 END DO 01106 DO J = 0, K - 2 01107 CALL ZLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1, 01108 $ SCALE, S ) 01109 * L at A(0,k-1) 01110 END DO 01111 S = S + S 01112 * double s for the off diagonal elements 01113 L = 0 + K*LDA - LDA 01114 * -> U(k-1,k-1) at A(0,k-1) 01115 AA = DBLE( A( L ) ) 01116 * U(k-1,k-1) 01117 IF( AA.NE.ZERO ) THEN 01118 IF( SCALE.LT.AA ) THEN 01119 S = ONE + S*( SCALE / AA )**2 01120 SCALE = AA 01121 ELSE 01122 S = S + ( AA / SCALE )**2 01123 END IF 01124 END IF 01125 L = L + LDA 01126 * -> U(0,0) at A(0,k) 01127 DO J = K, N - 1 01128 AA = DBLE( A( L ) ) 01129 * -> U(j-k,j-k) 01130 IF( AA.NE.ZERO ) THEN 01131 IF( SCALE.LT.AA ) THEN 01132 S = ONE + S*( SCALE / AA )**2 01133 SCALE = AA 01134 ELSE 01135 S = S + ( AA / SCALE )**2 01136 END IF 01137 END IF 01138 AA = DBLE( A( L+1 ) ) 01139 * -> U(j,j) 01140 IF( AA.NE.ZERO ) THEN 01141 IF( SCALE.LT.AA ) THEN 01142 S = ONE + S*( SCALE / AA )**2 01143 SCALE = AA 01144 ELSE 01145 S = S + ( AA / SCALE )**2 01146 END IF 01147 END IF 01148 L = L + LDA + 1 01149 END DO 01150 ELSE 01151 * A**H is lower 01152 DO J = 1, K - 1 01153 CALL ZLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) 01154 * U at A(0,0) 01155 END DO 01156 DO J = K, N - 1 01157 CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 01158 * k by k-1 rect. at A(0,k) 01159 END DO 01160 DO J = 0, K - 3 01161 CALL ZLASSQ( K-J-2, A( J+2+J*LDA ), 1, SCALE, S ) 01162 * L at A(1,0) 01163 END DO 01164 S = S + S 01165 * double s for the off diagonal elements 01166 L = 0 01167 * -> L(0,0) at A(0,0) 01168 DO I = 0, K - 2 01169 AA = DBLE( A( L ) ) 01170 * L(i,i) 01171 IF( AA.NE.ZERO ) THEN 01172 IF( SCALE.LT.AA ) THEN 01173 S = ONE + S*( SCALE / AA )**2 01174 SCALE = AA 01175 ELSE 01176 S = S + ( AA / SCALE )**2 01177 END IF 01178 END IF 01179 AA = DBLE( A( L+1 ) ) 01180 * L(k+i,k+i) 01181 IF( AA.NE.ZERO ) THEN 01182 IF( SCALE.LT.AA ) THEN 01183 S = ONE + S*( SCALE / AA )**2 01184 SCALE = AA 01185 ELSE 01186 S = S + ( AA / SCALE )**2 01187 END IF 01188 END IF 01189 L = L + LDA + 1 01190 END DO 01191 * L-> k-1 + (k-1)*lda or L(k-1,k-1) at A(k-1,k-1) 01192 AA = DBLE( A( L ) ) 01193 * L(k-1,k-1) at A(k-1,k-1) 01194 IF( AA.NE.ZERO ) THEN 01195 IF( SCALE.LT.AA ) THEN 01196 S = ONE + S*( SCALE / AA )**2 01197 SCALE = AA 01198 ELSE 01199 S = S + ( AA / SCALE )**2 01200 END IF 01201 END IF 01202 END IF 01203 END IF 01204 ELSE 01205 * n is even 01206 IF( IFM.EQ.1 ) THEN 01207 * A is normal 01208 IF( ILU.EQ.0 ) THEN 01209 * A is upper 01210 DO J = 0, K - 2 01211 CALL ZLASSQ( K-J-1, A( K+J+2+J*LDA ), 1, SCALE, S ) 01212 * L at A(k+1,0) 01213 END DO 01214 DO J = 0, K - 1 01215 CALL ZLASSQ( K+J, A( 0+J*LDA ), 1, SCALE, S ) 01216 * trap U at A(0,0) 01217 END DO 01218 S = S + S 01219 * double s for the off diagonal elements 01220 L = K 01221 * -> U(k,k) at A(k,0) 01222 DO I = 0, K - 1 01223 AA = DBLE( A( L ) ) 01224 * U(k+i,k+i) 01225 IF( AA.NE.ZERO ) THEN 01226 IF( SCALE.LT.AA ) THEN 01227 S = ONE + S*( SCALE / AA )**2 01228 SCALE = AA 01229 ELSE 01230 S = S + ( AA / SCALE )**2 01231 END IF 01232 END IF 01233 AA = DBLE( A( L+1 ) ) 01234 * U(i,i) 01235 IF( AA.NE.ZERO ) THEN 01236 IF( SCALE.LT.AA ) THEN 01237 S = ONE + S*( SCALE / AA )**2 01238 SCALE = AA 01239 ELSE 01240 S = S + ( AA / SCALE )**2 01241 END IF 01242 END IF 01243 L = L + LDA + 1 01244 END DO 01245 ELSE 01246 * ilu=1 & A is lower 01247 DO J = 0, K - 1 01248 CALL ZLASSQ( N-J-1, A( J+2+J*LDA ), 1, SCALE, S ) 01249 * trap L at A(1,0) 01250 END DO 01251 DO J = 1, K - 1 01252 CALL ZLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) 01253 * U at A(0,0) 01254 END DO 01255 S = S + S 01256 * double s for the off diagonal elements 01257 L = 0 01258 * -> L(k,k) at A(0,0) 01259 DO I = 0, K - 1 01260 AA = DBLE( A( L ) ) 01261 * L(k-1+i,k-1+i) 01262 IF( AA.NE.ZERO ) THEN 01263 IF( SCALE.LT.AA ) THEN 01264 S = ONE + S*( SCALE / AA )**2 01265 SCALE = AA 01266 ELSE 01267 S = S + ( AA / SCALE )**2 01268 END IF 01269 END IF 01270 AA = DBLE( A( L+1 ) ) 01271 * L(i,i) 01272 IF( AA.NE.ZERO ) THEN 01273 IF( SCALE.LT.AA ) THEN 01274 S = ONE + S*( SCALE / AA )**2 01275 SCALE = AA 01276 ELSE 01277 S = S + ( AA / SCALE )**2 01278 END IF 01279 END IF 01280 L = L + LDA + 1 01281 END DO 01282 END IF 01283 ELSE 01284 * A is xpose 01285 IF( ILU.EQ.0 ) THEN 01286 * A**H is upper 01287 DO J = 1, K - 1 01288 CALL ZLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S ) 01289 * U at A(0,k+1) 01290 END DO 01291 DO J = 0, K - 1 01292 CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 01293 * k by k rect. at A(0,0) 01294 END DO 01295 DO J = 0, K - 2 01296 CALL ZLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE, 01297 $ S ) 01298 * L at A(0,k) 01299 END DO 01300 S = S + S 01301 * double s for the off diagonal elements 01302 L = 0 + K*LDA 01303 * -> U(k,k) at A(0,k) 01304 AA = DBLE( A( L ) ) 01305 * U(k,k) 01306 IF( AA.NE.ZERO ) THEN 01307 IF( SCALE.LT.AA ) THEN 01308 S = ONE + S*( SCALE / AA )**2 01309 SCALE = AA 01310 ELSE 01311 S = S + ( AA / SCALE )**2 01312 END IF 01313 END IF 01314 L = L + LDA 01315 * -> U(0,0) at A(0,k+1) 01316 DO J = K + 1, N - 1 01317 AA = DBLE( A( L ) ) 01318 * -> U(j-k-1,j-k-1) 01319 IF( AA.NE.ZERO ) THEN 01320 IF( SCALE.LT.AA ) THEN 01321 S = ONE + S*( SCALE / AA )**2 01322 SCALE = AA 01323 ELSE 01324 S = S + ( AA / SCALE )**2 01325 END IF 01326 END IF 01327 AA = DBLE( A( L+1 ) ) 01328 * -> U(j,j) 01329 IF( AA.NE.ZERO ) THEN 01330 IF( SCALE.LT.AA ) THEN 01331 S = ONE + S*( SCALE / AA )**2 01332 SCALE = AA 01333 ELSE 01334 S = S + ( AA / SCALE )**2 01335 END IF 01336 END IF 01337 L = L + LDA + 1 01338 END DO 01339 * L=k-1+n*lda 01340 * -> U(k-1,k-1) at A(k-1,n) 01341 AA = DBLE( A( L ) ) 01342 * U(k,k) 01343 IF( AA.NE.ZERO ) THEN 01344 IF( SCALE.LT.AA ) THEN 01345 S = ONE + S*( SCALE / AA )**2 01346 SCALE = AA 01347 ELSE 01348 S = S + ( AA / SCALE )**2 01349 END IF 01350 END IF 01351 ELSE 01352 * A**H is lower 01353 DO J = 1, K - 1 01354 CALL ZLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S ) 01355 * U at A(0,1) 01356 END DO 01357 DO J = K + 1, N 01358 CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 01359 * k by k rect. at A(0,k+1) 01360 END DO 01361 DO J = 0, K - 2 01362 CALL ZLASSQ( K-J-1, A( J+1+J*LDA ), 1, SCALE, S ) 01363 * L at A(0,0) 01364 END DO 01365 S = S + S 01366 * double s for the off diagonal elements 01367 L = 0 01368 * -> L(k,k) at A(0,0) 01369 AA = DBLE( A( L ) ) 01370 * L(k,k) at A(0,0) 01371 IF( AA.NE.ZERO ) THEN 01372 IF( SCALE.LT.AA ) THEN 01373 S = ONE + S*( SCALE / AA )**2 01374 SCALE = AA 01375 ELSE 01376 S = S + ( AA / SCALE )**2 01377 END IF 01378 END IF 01379 L = LDA 01380 * -> L(0,0) at A(0,1) 01381 DO I = 0, K - 2 01382 AA = DBLE( A( L ) ) 01383 * L(i,i) 01384 IF( AA.NE.ZERO ) THEN 01385 IF( SCALE.LT.AA ) THEN 01386 S = ONE + S*( SCALE / AA )**2 01387 SCALE = AA 01388 ELSE 01389 S = S + ( AA / SCALE )**2 01390 END IF 01391 END IF 01392 AA = DBLE( A( L+1 ) ) 01393 * L(k+i+1,k+i+1) 01394 IF( AA.NE.ZERO ) THEN 01395 IF( SCALE.LT.AA ) THEN 01396 S = ONE + S*( SCALE / AA )**2 01397 SCALE = AA 01398 ELSE 01399 S = S + ( AA / SCALE )**2 01400 END IF 01401 END IF 01402 L = L + LDA + 1 01403 END DO 01404 * L-> k - 1 + k*lda or L(k-1,k-1) at A(k-1,k) 01405 AA = DBLE( A( L ) ) 01406 * L(k-1,k-1) at A(k-1,k) 01407 IF( AA.NE.ZERO ) THEN 01408 IF( SCALE.LT.AA ) THEN 01409 S = ONE + S*( SCALE / AA )**2 01410 SCALE = AA 01411 ELSE 01412 S = S + ( AA / SCALE )**2 01413 END IF 01414 END IF 01415 END IF 01416 END IF 01417 END IF 01418 VALUE = SCALE*SQRT( S ) 01419 END IF 01420 * 01421 ZLANHF = VALUE 01422 RETURN 01423 * 01424 * End of ZLANHF 01425 * 01426 END