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LAPACK
3.4.0
LAPACK: Linear Algebra PACKage
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LAPACK
3.4.0
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DLANSF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DLANSF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION DLANSF( 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 A( 0: * ), WORK( 0: * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DLANSF returns the value of the one norm, or the Frobenius norm, or 00038 *> the infinity norm, or the element of largest absolute value of a 00039 *> real symmetric matrix A in RFP format. 00040 *> \endverbatim 00041 *> 00042 *> \return DLANSF 00043 *> \verbatim 00044 *> 00045 *> DLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm' 00046 *> ( 00047 *> ( norm1(A), NORM = '1', 'O' or 'o' 00048 *> ( 00049 *> ( normI(A), NORM = 'I' or 'i' 00050 *> ( 00051 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' 00052 *> 00053 *> where norm1 denotes the one norm of a matrix (maximum column sum), 00054 *> normI denotes the infinity norm of a matrix (maximum row sum) and 00055 *> normF denotes the Frobenius norm of a matrix (square root of sum of 00056 *> squares). Note that max(abs(A(i,j))) is not a matrix norm. 00057 *> \endverbatim 00058 * 00059 * Arguments: 00060 * ========== 00061 * 00062 *> \param[in] NORM 00063 *> \verbatim 00064 *> NORM is CHARACTER*1 00065 *> Specifies the value to be returned in DLANSF as described 00066 *> above. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] TRANSR 00070 *> \verbatim 00071 *> TRANSR is CHARACTER*1 00072 *> Specifies whether the RFP format of A is normal or 00073 *> transposed format. 00074 *> = 'N': RFP format is Normal; 00075 *> = 'T': RFP format is Transpose. 00076 *> \endverbatim 00077 *> 00078 *> \param[in] UPLO 00079 *> \verbatim 00080 *> UPLO is CHARACTER*1 00081 *> On entry, UPLO specifies whether the RFP matrix A came from 00082 *> an upper or lower triangular matrix as follows: 00083 *> = 'U': RFP A came from an upper triangular matrix; 00084 *> = 'L': RFP A came from a lower triangular matrix. 00085 *> \endverbatim 00086 *> 00087 *> \param[in] N 00088 *> \verbatim 00089 *> N is INTEGER 00090 *> The order of the matrix A. N >= 0. When N = 0, DLANSF is 00091 *> set to zero. 00092 *> \endverbatim 00093 *> 00094 *> \param[in] A 00095 *> \verbatim 00096 *> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ); 00097 *> On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') 00098 *> part of the symmetric matrix A stored in RFP format. See the 00099 *> "Notes" below for more details. 00100 *> Unchanged on exit. 00101 *> \endverbatim 00102 *> 00103 *> \param[out] WORK 00104 *> \verbatim 00105 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), 00106 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00107 *> WORK is not referenced. 00108 *> \endverbatim 00109 * 00110 * Authors: 00111 * ======== 00112 * 00113 *> \author Univ. of Tennessee 00114 *> \author Univ. of California Berkeley 00115 *> \author Univ. of Colorado Denver 00116 *> \author NAG Ltd. 00117 * 00118 *> \date November 2011 00119 * 00120 *> \ingroup doubleOTHERcomputational 00121 * 00122 *> \par Further Details: 00123 * ===================== 00124 *> 00125 *> \verbatim 00126 *> 00127 *> We first consider Rectangular Full Packed (RFP) Format when N is 00128 *> even. We give an example where N = 6. 00129 *> 00130 *> AP is Upper AP is Lower 00131 *> 00132 *> 00 01 02 03 04 05 00 00133 *> 11 12 13 14 15 10 11 00134 *> 22 23 24 25 20 21 22 00135 *> 33 34 35 30 31 32 33 00136 *> 44 45 40 41 42 43 44 00137 *> 55 50 51 52 53 54 55 00138 *> 00139 *> 00140 *> Let TRANSR = 'N'. RFP holds AP as follows: 00141 *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last 00142 *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of 00143 *> the transpose of the first three columns of AP upper. 00144 *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first 00145 *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of 00146 *> the transpose of the last three columns of AP lower. 00147 *> This covers the case N even and TRANSR = 'N'. 00148 *> 00149 *> RFP A RFP A 00150 *> 00151 *> 03 04 05 33 43 53 00152 *> 13 14 15 00 44 54 00153 *> 23 24 25 10 11 55 00154 *> 33 34 35 20 21 22 00155 *> 00 44 45 30 31 32 00156 *> 01 11 55 40 41 42 00157 *> 02 12 22 50 51 52 00158 *> 00159 *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the 00160 *> transpose of RFP A above. One therefore gets: 00161 *> 00162 *> 00163 *> RFP A RFP A 00164 *> 00165 *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 00166 *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 00167 *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 00168 *> 00169 *> 00170 *> We then consider Rectangular Full Packed (RFP) Format when N is 00171 *> odd. We give an example where N = 5. 00172 *> 00173 *> AP is Upper AP is Lower 00174 *> 00175 *> 00 01 02 03 04 00 00176 *> 11 12 13 14 10 11 00177 *> 22 23 24 20 21 22 00178 *> 33 34 30 31 32 33 00179 *> 44 40 41 42 43 44 00180 *> 00181 *> 00182 *> Let TRANSR = 'N'. RFP holds AP as follows: 00183 *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last 00184 *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of 00185 *> the transpose of the first two columns of AP upper. 00186 *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first 00187 *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of 00188 *> the transpose of the last two columns of AP lower. 00189 *> This covers the case N odd and TRANSR = 'N'. 00190 *> 00191 *> RFP A RFP A 00192 *> 00193 *> 02 03 04 00 33 43 00194 *> 12 13 14 10 11 44 00195 *> 22 23 24 20 21 22 00196 *> 00 33 34 30 31 32 00197 *> 01 11 44 40 41 42 00198 *> 00199 *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the 00200 *> transpose of RFP A above. One therefore gets: 00201 *> 00202 *> RFP A RFP A 00203 *> 00204 *> 02 12 22 00 01 00 10 20 30 40 50 00205 *> 03 13 23 33 11 33 11 21 31 41 51 00206 *> 04 14 24 34 44 43 44 22 32 42 52 00207 *> \endverbatim 00208 * 00209 * ===================================================================== 00210 DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK ) 00211 * 00212 * -- LAPACK computational routine (version 3.4.0) -- 00213 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00214 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00215 * November 2011 00216 * 00217 * .. Scalar Arguments .. 00218 CHARACTER NORM, TRANSR, UPLO 00219 INTEGER N 00220 * .. 00221 * .. Array Arguments .. 00222 DOUBLE PRECISION A( 0: * ), WORK( 0: * ) 00223 * .. 00224 * 00225 * ===================================================================== 00226 * 00227 * .. Parameters .. 00228 DOUBLE PRECISION ONE, ZERO 00229 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00230 * .. 00231 * .. Local Scalars .. 00232 INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA 00233 DOUBLE PRECISION SCALE, S, VALUE, AA 00234 * .. 00235 * .. External Functions .. 00236 LOGICAL LSAME 00237 INTEGER IDAMAX 00238 EXTERNAL LSAME, IDAMAX 00239 * .. 00240 * .. External Subroutines .. 00241 EXTERNAL DLASSQ 00242 * .. 00243 * .. Intrinsic Functions .. 00244 INTRINSIC ABS, MAX, SQRT 00245 * .. 00246 * .. Executable Statements .. 00247 * 00248 IF( N.EQ.0 ) THEN 00249 DLANSF = ZERO 00250 RETURN 00251 END IF 00252 * 00253 * set noe = 1 if n is odd. if n is even set noe=0 00254 * 00255 NOE = 1 00256 IF( MOD( N, 2 ).EQ.0 ) 00257 $ NOE = 0 00258 * 00259 * set ifm = 0 when form='T or 't' and 1 otherwise 00260 * 00261 IFM = 1 00262 IF( LSAME( TRANSR, 'T' ) ) 00263 $ IFM = 0 00264 * 00265 * set ilu = 0 when uplo='U or 'u' and 1 otherwise 00266 * 00267 ILU = 1 00268 IF( LSAME( UPLO, 'U' ) ) 00269 $ ILU = 0 00270 * 00271 * set lda = (n+1)/2 when ifm = 0 00272 * set lda = n when ifm = 1 and noe = 1 00273 * set lda = n+1 when ifm = 1 and noe = 0 00274 * 00275 IF( IFM.EQ.1 ) THEN 00276 IF( NOE.EQ.1 ) THEN 00277 LDA = N 00278 ELSE 00279 * noe=0 00280 LDA = N + 1 00281 END IF 00282 ELSE 00283 * ifm=0 00284 LDA = ( N+1 ) / 2 00285 END IF 00286 * 00287 IF( LSAME( NORM, 'M' ) ) THEN 00288 * 00289 * Find max(abs(A(i,j))). 00290 * 00291 K = ( N+1 ) / 2 00292 VALUE = ZERO 00293 IF( NOE.EQ.1 ) THEN 00294 * n is odd 00295 IF( IFM.EQ.1 ) THEN 00296 * A is n by k 00297 DO J = 0, K - 1 00298 DO I = 0, N - 1 00299 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00300 END DO 00301 END DO 00302 ELSE 00303 * xpose case; A is k by n 00304 DO J = 0, N - 1 00305 DO I = 0, K - 1 00306 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00307 END DO 00308 END DO 00309 END IF 00310 ELSE 00311 * n is even 00312 IF( IFM.EQ.1 ) THEN 00313 * A is n+1 by k 00314 DO J = 0, K - 1 00315 DO I = 0, N 00316 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00317 END DO 00318 END DO 00319 ELSE 00320 * xpose case; A is k by n+1 00321 DO J = 0, N 00322 DO I = 0, K - 1 00323 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00324 END DO 00325 END DO 00326 END IF 00327 END IF 00328 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00329 $ ( NORM.EQ.'1' ) ) THEN 00330 * 00331 * Find normI(A) ( = norm1(A), since A is symmetric). 00332 * 00333 IF( IFM.EQ.1 ) THEN 00334 K = N / 2 00335 IF( NOE.EQ.1 ) THEN 00336 * n is odd 00337 IF( ILU.EQ.0 ) THEN 00338 DO I = 0, K - 1 00339 WORK( I ) = ZERO 00340 END DO 00341 DO J = 0, K 00342 S = ZERO 00343 DO I = 0, K + J - 1 00344 AA = ABS( A( I+J*LDA ) ) 00345 * -> A(i,j+k) 00346 S = S + AA 00347 WORK( I ) = WORK( I ) + AA 00348 END DO 00349 AA = ABS( A( I+J*LDA ) ) 00350 * -> A(j+k,j+k) 00351 WORK( J+K ) = S + AA 00352 IF( I.EQ.K+K ) 00353 $ GO TO 10 00354 I = I + 1 00355 AA = ABS( A( I+J*LDA ) ) 00356 * -> A(j,j) 00357 WORK( J ) = WORK( J ) + AA 00358 S = ZERO 00359 DO L = J + 1, K - 1 00360 I = I + 1 00361 AA = ABS( A( I+J*LDA ) ) 00362 * -> A(l,j) 00363 S = S + AA 00364 WORK( L ) = WORK( L ) + AA 00365 END DO 00366 WORK( J ) = WORK( J ) + S 00367 END DO 00368 10 CONTINUE 00369 I = IDAMAX( N, WORK, 1 ) 00370 VALUE = WORK( I-1 ) 00371 ELSE 00372 * ilu = 1 00373 K = K + 1 00374 * k=(n+1)/2 for n odd and ilu=1 00375 DO I = K, N - 1 00376 WORK( I ) = ZERO 00377 END DO 00378 DO J = K - 1, 0, -1 00379 S = ZERO 00380 DO I = 0, J - 2 00381 AA = ABS( A( I+J*LDA ) ) 00382 * -> A(j+k,i+k) 00383 S = S + AA 00384 WORK( I+K ) = WORK( I+K ) + AA 00385 END DO 00386 IF( J.GT.0 ) THEN 00387 AA = ABS( A( I+J*LDA ) ) 00388 * -> A(j+k,j+k) 00389 S = S + AA 00390 WORK( I+K ) = WORK( I+K ) + S 00391 * i=j 00392 I = I + 1 00393 END IF 00394 AA = ABS( A( I+J*LDA ) ) 00395 * -> A(j,j) 00396 WORK( J ) = AA 00397 S = ZERO 00398 DO L = J + 1, N - 1 00399 I = I + 1 00400 AA = ABS( A( I+J*LDA ) ) 00401 * -> A(l,j) 00402 S = S + AA 00403 WORK( L ) = WORK( L ) + AA 00404 END DO 00405 WORK( J ) = WORK( J ) + S 00406 END DO 00407 I = IDAMAX( N, WORK, 1 ) 00408 VALUE = WORK( I-1 ) 00409 END IF 00410 ELSE 00411 * n is even 00412 IF( ILU.EQ.0 ) THEN 00413 DO I = 0, K - 1 00414 WORK( I ) = ZERO 00415 END DO 00416 DO J = 0, K - 1 00417 S = ZERO 00418 DO I = 0, K + J - 1 00419 AA = ABS( A( I+J*LDA ) ) 00420 * -> A(i,j+k) 00421 S = S + AA 00422 WORK( I ) = WORK( I ) + AA 00423 END DO 00424 AA = ABS( A( I+J*LDA ) ) 00425 * -> A(j+k,j+k) 00426 WORK( J+K ) = S + AA 00427 I = I + 1 00428 AA = ABS( A( I+J*LDA ) ) 00429 * -> A(j,j) 00430 WORK( J ) = WORK( J ) + AA 00431 S = ZERO 00432 DO L = J + 1, K - 1 00433 I = I + 1 00434 AA = ABS( A( I+J*LDA ) ) 00435 * -> A(l,j) 00436 S = S + AA 00437 WORK( L ) = WORK( L ) + AA 00438 END DO 00439 WORK( J ) = WORK( J ) + S 00440 END DO 00441 I = IDAMAX( N, WORK, 1 ) 00442 VALUE = WORK( I-1 ) 00443 ELSE 00444 * ilu = 1 00445 DO I = K, N - 1 00446 WORK( I ) = ZERO 00447 END DO 00448 DO J = K - 1, 0, -1 00449 S = ZERO 00450 DO I = 0, J - 1 00451 AA = ABS( A( I+J*LDA ) ) 00452 * -> A(j+k,i+k) 00453 S = S + AA 00454 WORK( I+K ) = WORK( I+K ) + AA 00455 END DO 00456 AA = ABS( A( I+J*LDA ) ) 00457 * -> A(j+k,j+k) 00458 S = S + AA 00459 WORK( I+K ) = WORK( I+K ) + S 00460 * i=j 00461 I = I + 1 00462 AA = ABS( A( I+J*LDA ) ) 00463 * -> A(j,j) 00464 WORK( J ) = AA 00465 S = ZERO 00466 DO L = J + 1, N - 1 00467 I = I + 1 00468 AA = ABS( A( I+J*LDA ) ) 00469 * -> A(l,j) 00470 S = S + AA 00471 WORK( L ) = WORK( L ) + AA 00472 END DO 00473 WORK( J ) = WORK( J ) + S 00474 END DO 00475 I = IDAMAX( N, WORK, 1 ) 00476 VALUE = WORK( I-1 ) 00477 END IF 00478 END IF 00479 ELSE 00480 * ifm=0 00481 K = N / 2 00482 IF( NOE.EQ.1 ) THEN 00483 * n is odd 00484 IF( ILU.EQ.0 ) THEN 00485 N1 = K 00486 * n/2 00487 K = K + 1 00488 * k is the row size and lda 00489 DO I = N1, N - 1 00490 WORK( I ) = ZERO 00491 END DO 00492 DO J = 0, N1 - 1 00493 S = ZERO 00494 DO I = 0, K - 1 00495 AA = ABS( A( I+J*LDA ) ) 00496 * A(j,n1+i) 00497 WORK( I+N1 ) = WORK( I+N1 ) + AA 00498 S = S + AA 00499 END DO 00500 WORK( J ) = S 00501 END DO 00502 * j=n1=k-1 is special 00503 S = ABS( A( 0+J*LDA ) ) 00504 * A(k-1,k-1) 00505 DO I = 1, K - 1 00506 AA = ABS( A( I+J*LDA ) ) 00507 * A(k-1,i+n1) 00508 WORK( I+N1 ) = WORK( I+N1 ) + AA 00509 S = S + AA 00510 END DO 00511 WORK( J ) = WORK( J ) + S 00512 DO J = K, N - 1 00513 S = ZERO 00514 DO I = 0, J - K - 1 00515 AA = ABS( A( I+J*LDA ) ) 00516 * A(i,j-k) 00517 WORK( I ) = WORK( I ) + AA 00518 S = S + AA 00519 END DO 00520 * i=j-k 00521 AA = ABS( A( I+J*LDA ) ) 00522 * A(j-k,j-k) 00523 S = S + AA 00524 WORK( J-K ) = WORK( J-K ) + S 00525 I = I + 1 00526 S = ABS( A( I+J*LDA ) ) 00527 * A(j,j) 00528 DO L = J + 1, N - 1 00529 I = I + 1 00530 AA = ABS( A( I+J*LDA ) ) 00531 * A(j,l) 00532 WORK( L ) = WORK( L ) + AA 00533 S = S + AA 00534 END DO 00535 WORK( J ) = WORK( J ) + S 00536 END DO 00537 I = IDAMAX( N, WORK, 1 ) 00538 VALUE = WORK( I-1 ) 00539 ELSE 00540 * ilu=1 00541 K = K + 1 00542 * k=(n+1)/2 for n odd and ilu=1 00543 DO I = K, N - 1 00544 WORK( I ) = ZERO 00545 END DO 00546 DO J = 0, K - 2 00547 * process 00548 S = ZERO 00549 DO I = 0, J - 1 00550 AA = ABS( A( I+J*LDA ) ) 00551 * A(j,i) 00552 WORK( I ) = WORK( I ) + AA 00553 S = S + AA 00554 END DO 00555 AA = ABS( A( I+J*LDA ) ) 00556 * i=j so process of A(j,j) 00557 S = S + AA 00558 WORK( J ) = S 00559 * is initialised here 00560 I = I + 1 00561 * i=j process A(j+k,j+k) 00562 AA = ABS( A( I+J*LDA ) ) 00563 S = AA 00564 DO L = K + J + 1, N - 1 00565 I = I + 1 00566 AA = ABS( A( I+J*LDA ) ) 00567 * A(l,k+j) 00568 S = S + AA 00569 WORK( L ) = WORK( L ) + AA 00570 END DO 00571 WORK( K+J ) = WORK( K+J ) + S 00572 END DO 00573 * j=k-1 is special :process col A(k-1,0:k-1) 00574 S = ZERO 00575 DO I = 0, K - 2 00576 AA = ABS( A( I+J*LDA ) ) 00577 * A(k,i) 00578 WORK( I ) = WORK( I ) + AA 00579 S = S + AA 00580 END DO 00581 * i=k-1 00582 AA = ABS( A( I+J*LDA ) ) 00583 * A(k-1,k-1) 00584 S = S + AA 00585 WORK( I ) = S 00586 * done with col j=k+1 00587 DO J = K, N - 1 00588 * process col j of A = A(j,0:k-1) 00589 S = ZERO 00590 DO I = 0, K - 1 00591 AA = ABS( A( I+J*LDA ) ) 00592 * A(j,i) 00593 WORK( I ) = WORK( I ) + AA 00594 S = S + AA 00595 END DO 00596 WORK( J ) = WORK( J ) + S 00597 END DO 00598 I = IDAMAX( N, WORK, 1 ) 00599 VALUE = WORK( I-1 ) 00600 END IF 00601 ELSE 00602 * n is even 00603 IF( ILU.EQ.0 ) THEN 00604 DO I = K, N - 1 00605 WORK( I ) = ZERO 00606 END DO 00607 DO J = 0, K - 1 00608 S = ZERO 00609 DO I = 0, K - 1 00610 AA = ABS( A( I+J*LDA ) ) 00611 * A(j,i+k) 00612 WORK( I+K ) = WORK( I+K ) + AA 00613 S = S + AA 00614 END DO 00615 WORK( J ) = S 00616 END DO 00617 * j=k 00618 AA = ABS( A( 0+J*LDA ) ) 00619 * A(k,k) 00620 S = AA 00621 DO I = 1, K - 1 00622 AA = ABS( A( I+J*LDA ) ) 00623 * A(k,k+i) 00624 WORK( I+K ) = WORK( I+K ) + AA 00625 S = S + AA 00626 END DO 00627 WORK( J ) = WORK( J ) + S 00628 DO J = K + 1, N - 1 00629 S = ZERO 00630 DO I = 0, J - 2 - K 00631 AA = ABS( A( I+J*LDA ) ) 00632 * A(i,j-k-1) 00633 WORK( I ) = WORK( I ) + AA 00634 S = S + AA 00635 END DO 00636 * i=j-1-k 00637 AA = ABS( A( I+J*LDA ) ) 00638 * A(j-k-1,j-k-1) 00639 S = S + AA 00640 WORK( J-K-1 ) = WORK( J-K-1 ) + S 00641 I = I + 1 00642 AA = ABS( A( I+J*LDA ) ) 00643 * A(j,j) 00644 S = AA 00645 DO L = J + 1, N - 1 00646 I = I + 1 00647 AA = ABS( A( I+J*LDA ) ) 00648 * A(j,l) 00649 WORK( L ) = WORK( L ) + AA 00650 S = S + AA 00651 END DO 00652 WORK( J ) = WORK( J ) + S 00653 END DO 00654 * j=n 00655 S = ZERO 00656 DO I = 0, K - 2 00657 AA = ABS( A( I+J*LDA ) ) 00658 * A(i,k-1) 00659 WORK( I ) = WORK( I ) + AA 00660 S = S + AA 00661 END DO 00662 * i=k-1 00663 AA = ABS( A( I+J*LDA ) ) 00664 * A(k-1,k-1) 00665 S = S + AA 00666 WORK( I ) = WORK( I ) + S 00667 I = IDAMAX( N, WORK, 1 ) 00668 VALUE = WORK( I-1 ) 00669 ELSE 00670 * ilu=1 00671 DO I = K, N - 1 00672 WORK( I ) = ZERO 00673 END DO 00674 * j=0 is special :process col A(k:n-1,k) 00675 S = ABS( A( 0 ) ) 00676 * A(k,k) 00677 DO I = 1, K - 1 00678 AA = ABS( A( I ) ) 00679 * A(k+i,k) 00680 WORK( I+K ) = WORK( I+K ) + AA 00681 S = S + AA 00682 END DO 00683 WORK( K ) = WORK( K ) + S 00684 DO J = 1, K - 1 00685 * process 00686 S = ZERO 00687 DO I = 0, J - 2 00688 AA = ABS( A( I+J*LDA ) ) 00689 * A(j-1,i) 00690 WORK( I ) = WORK( I ) + AA 00691 S = S + AA 00692 END DO 00693 AA = ABS( A( I+J*LDA ) ) 00694 * i=j-1 so process of A(j-1,j-1) 00695 S = S + AA 00696 WORK( J-1 ) = S 00697 * is initialised here 00698 I = I + 1 00699 * i=j process A(j+k,j+k) 00700 AA = ABS( A( I+J*LDA ) ) 00701 S = AA 00702 DO L = K + J + 1, N - 1 00703 I = I + 1 00704 AA = ABS( A( I+J*LDA ) ) 00705 * A(l,k+j) 00706 S = S + AA 00707 WORK( L ) = WORK( L ) + AA 00708 END DO 00709 WORK( K+J ) = WORK( K+J ) + S 00710 END DO 00711 * j=k is special :process col A(k,0:k-1) 00712 S = ZERO 00713 DO I = 0, K - 2 00714 AA = ABS( A( I+J*LDA ) ) 00715 * A(k,i) 00716 WORK( I ) = WORK( I ) + AA 00717 S = S + AA 00718 END DO 00719 * i=k-1 00720 AA = ABS( A( I+J*LDA ) ) 00721 * A(k-1,k-1) 00722 S = S + AA 00723 WORK( I ) = S 00724 * done with col j=k+1 00725 DO J = K + 1, N 00726 * process col j-1 of A = A(j-1,0:k-1) 00727 S = ZERO 00728 DO I = 0, K - 1 00729 AA = ABS( A( I+J*LDA ) ) 00730 * A(j-1,i) 00731 WORK( I ) = WORK( I ) + AA 00732 S = S + AA 00733 END DO 00734 WORK( J-1 ) = WORK( J-1 ) + S 00735 END DO 00736 I = IDAMAX( N, WORK, 1 ) 00737 VALUE = WORK( I-1 ) 00738 END IF 00739 END IF 00740 END IF 00741 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00742 * 00743 * Find normF(A). 00744 * 00745 K = ( N+1 ) / 2 00746 SCALE = ZERO 00747 S = ONE 00748 IF( NOE.EQ.1 ) THEN 00749 * n is odd 00750 IF( IFM.EQ.1 ) THEN 00751 * A is normal 00752 IF( ILU.EQ.0 ) THEN 00753 * A is upper 00754 DO J = 0, K - 3 00755 CALL DLASSQ( K-J-2, A( K+J+1+J*LDA ), 1, SCALE, S ) 00756 * L at A(k,0) 00757 END DO 00758 DO J = 0, K - 1 00759 CALL DLASSQ( K+J-1, A( 0+J*LDA ), 1, SCALE, S ) 00760 * trap U at A(0,0) 00761 END DO 00762 S = S + S 00763 * double s for the off diagonal elements 00764 CALL DLASSQ( K-1, A( K ), LDA+1, SCALE, S ) 00765 * tri L at A(k,0) 00766 CALL DLASSQ( K, A( K-1 ), LDA+1, SCALE, S ) 00767 * tri U at A(k-1,0) 00768 ELSE 00769 * ilu=1 & A is lower 00770 DO J = 0, K - 1 00771 CALL DLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S ) 00772 * trap L at A(0,0) 00773 END DO 00774 DO J = 0, K - 2 00775 CALL DLASSQ( J, A( 0+( 1+J )*LDA ), 1, SCALE, S ) 00776 * U at A(0,1) 00777 END DO 00778 S = S + S 00779 * double s for the off diagonal elements 00780 CALL DLASSQ( K, A( 0 ), LDA+1, SCALE, S ) 00781 * tri L at A(0,0) 00782 CALL DLASSQ( K-1, A( 0+LDA ), LDA+1, SCALE, S ) 00783 * tri U at A(0,1) 00784 END IF 00785 ELSE 00786 * A is xpose 00787 IF( ILU.EQ.0 ) THEN 00788 * A**T is upper 00789 DO J = 1, K - 2 00790 CALL DLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S ) 00791 * U at A(0,k) 00792 END DO 00793 DO J = 0, K - 2 00794 CALL DLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 00795 * k by k-1 rect. at A(0,0) 00796 END DO 00797 DO J = 0, K - 2 00798 CALL DLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1, 00799 $ SCALE, S ) 00800 * L at A(0,k-1) 00801 END DO 00802 S = S + S 00803 * double s for the off diagonal elements 00804 CALL DLASSQ( K-1, A( 0+K*LDA ), LDA+1, SCALE, S ) 00805 * tri U at A(0,k) 00806 CALL DLASSQ( K, A( 0+( K-1 )*LDA ), LDA+1, SCALE, S ) 00807 * tri L at A(0,k-1) 00808 ELSE 00809 * A**T is lower 00810 DO J = 1, K - 1 00811 CALL DLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) 00812 * U at A(0,0) 00813 END DO 00814 DO J = K, N - 1 00815 CALL DLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 00816 * k by k-1 rect. at A(0,k) 00817 END DO 00818 DO J = 0, K - 3 00819 CALL DLASSQ( K-J-2, A( J+2+J*LDA ), 1, SCALE, S ) 00820 * L at A(1,0) 00821 END DO 00822 S = S + S 00823 * double s for the off diagonal elements 00824 CALL DLASSQ( K, A( 0 ), LDA+1, SCALE, S ) 00825 * tri U at A(0,0) 00826 CALL DLASSQ( K-1, A( 1 ), LDA+1, SCALE, S ) 00827 * tri L at A(1,0) 00828 END IF 00829 END IF 00830 ELSE 00831 * n is even 00832 IF( IFM.EQ.1 ) THEN 00833 * A is normal 00834 IF( ILU.EQ.0 ) THEN 00835 * A is upper 00836 DO J = 0, K - 2 00837 CALL DLASSQ( K-J-1, A( K+J+2+J*LDA ), 1, SCALE, S ) 00838 * L at A(k+1,0) 00839 END DO 00840 DO J = 0, K - 1 00841 CALL DLASSQ( K+J, A( 0+J*LDA ), 1, SCALE, S ) 00842 * trap U at A(0,0) 00843 END DO 00844 S = S + S 00845 * double s for the off diagonal elements 00846 CALL DLASSQ( K, A( K+1 ), LDA+1, SCALE, S ) 00847 * tri L at A(k+1,0) 00848 CALL DLASSQ( K, A( K ), LDA+1, SCALE, S ) 00849 * tri U at A(k,0) 00850 ELSE 00851 * ilu=1 & A is lower 00852 DO J = 0, K - 1 00853 CALL DLASSQ( N-J-1, A( J+2+J*LDA ), 1, SCALE, S ) 00854 * trap L at A(1,0) 00855 END DO 00856 DO J = 1, K - 1 00857 CALL DLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) 00858 * U at A(0,0) 00859 END DO 00860 S = S + S 00861 * double s for the off diagonal elements 00862 CALL DLASSQ( K, A( 1 ), LDA+1, SCALE, S ) 00863 * tri L at A(1,0) 00864 CALL DLASSQ( K, A( 0 ), LDA+1, SCALE, S ) 00865 * tri U at A(0,0) 00866 END IF 00867 ELSE 00868 * A is xpose 00869 IF( ILU.EQ.0 ) THEN 00870 * A**T is upper 00871 DO J = 1, K - 1 00872 CALL DLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S ) 00873 * U at A(0,k+1) 00874 END DO 00875 DO J = 0, K - 1 00876 CALL DLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 00877 * k by k rect. at A(0,0) 00878 END DO 00879 DO J = 0, K - 2 00880 CALL DLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE, 00881 $ S ) 00882 * L at A(0,k) 00883 END DO 00884 S = S + S 00885 * double s for the off diagonal elements 00886 CALL DLASSQ( K, A( 0+( K+1 )*LDA ), LDA+1, SCALE, S ) 00887 * tri U at A(0,k+1) 00888 CALL DLASSQ( K, A( 0+K*LDA ), LDA+1, SCALE, S ) 00889 * tri L at A(0,k) 00890 ELSE 00891 * A**T is lower 00892 DO J = 1, K - 1 00893 CALL DLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S ) 00894 * U at A(0,1) 00895 END DO 00896 DO J = K + 1, N 00897 CALL DLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 00898 * k by k rect. at A(0,k+1) 00899 END DO 00900 DO J = 0, K - 2 00901 CALL DLASSQ( K-J-1, A( J+1+J*LDA ), 1, SCALE, S ) 00902 * L at A(0,0) 00903 END DO 00904 S = S + S 00905 * double s for the off diagonal elements 00906 CALL DLASSQ( K, A( LDA ), LDA+1, SCALE, S ) 00907 * tri L at A(0,1) 00908 CALL DLASSQ( K, A( 0 ), LDA+1, SCALE, S ) 00909 * tri U at A(0,0) 00910 END IF 00911 END IF 00912 END IF 00913 VALUE = SCALE*SQRT( S ) 00914 END IF 00915 * 00916 DLANSF = VALUE 00917 RETURN 00918 * 00919 * End of DLANSF 00920 * 00921 END
1.7.6.1 
