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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 SLANSF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download SLANSF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slansf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slansf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slansf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION SLANSF( NORM, TRANSR, UPLO, N, A, WORK ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER NORM, TRANSR, UPLO 00025 * INTEGER N 00026 * .. 00027 * .. Array Arguments .. 00028 * REAL A( 0: * ), WORK( 0: * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> SLANSF 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 SLANSF 00043 *> \verbatim 00044 *> 00045 *> SLANSF = ( 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 SLANSF 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, SLANSF is 00091 *> set to zero. 00092 *> \endverbatim 00093 *> 00094 *> \param[in] A 00095 *> \verbatim 00096 *> A is REAL 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 REAL 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 realOTHERcomputational 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 REAL FUNCTION SLANSF( 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 REAL A( 0: * ), WORK( 0: * ) 00223 * .. 00224 * 00225 * ===================================================================== 00226 * 00227 * .. 00228 * .. Parameters .. 00229 REAL ONE, ZERO 00230 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00231 * .. 00232 * .. Local Scalars .. 00233 INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA 00234 REAL SCALE, S, VALUE, AA 00235 * .. 00236 * .. External Functions .. 00237 LOGICAL LSAME 00238 INTEGER ISAMAX 00239 EXTERNAL LSAME, ISAMAX 00240 * .. 00241 * .. External Subroutines .. 00242 EXTERNAL SLASSQ 00243 * .. 00244 * .. Intrinsic Functions .. 00245 INTRINSIC ABS, MAX, SQRT 00246 * .. 00247 * .. Executable Statements .. 00248 * 00249 IF( N.EQ.0 ) THEN 00250 SLANSF = ZERO 00251 RETURN 00252 END IF 00253 * 00254 * set noe = 1 if n is odd. if n is even set noe=0 00255 * 00256 NOE = 1 00257 IF( MOD( N, 2 ).EQ.0 ) 00258 $ NOE = 0 00259 * 00260 * set ifm = 0 when form='T or 't' and 1 otherwise 00261 * 00262 IFM = 1 00263 IF( LSAME( TRANSR, 'T' ) ) 00264 $ IFM = 0 00265 * 00266 * set ilu = 0 when uplo='U or 'u' and 1 otherwise 00267 * 00268 ILU = 1 00269 IF( LSAME( UPLO, 'U' ) ) 00270 $ ILU = 0 00271 * 00272 * set lda = (n+1)/2 when ifm = 0 00273 * set lda = n when ifm = 1 and noe = 1 00274 * set lda = n+1 when ifm = 1 and noe = 0 00275 * 00276 IF( IFM.EQ.1 ) THEN 00277 IF( NOE.EQ.1 ) THEN 00278 LDA = N 00279 ELSE 00280 * noe=0 00281 LDA = N + 1 00282 END IF 00283 ELSE 00284 * ifm=0 00285 LDA = ( N+1 ) / 2 00286 END IF 00287 * 00288 IF( LSAME( NORM, 'M' ) ) THEN 00289 * 00290 * Find max(abs(A(i,j))). 00291 * 00292 K = ( N+1 ) / 2 00293 VALUE = ZERO 00294 IF( NOE.EQ.1 ) THEN 00295 * n is odd 00296 IF( IFM.EQ.1 ) THEN 00297 * A is n by k 00298 DO J = 0, K - 1 00299 DO I = 0, N - 1 00300 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00301 END DO 00302 END DO 00303 ELSE 00304 * xpose case; A is k by n 00305 DO J = 0, N - 1 00306 DO I = 0, K - 1 00307 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00308 END DO 00309 END DO 00310 END IF 00311 ELSE 00312 * n is even 00313 IF( IFM.EQ.1 ) THEN 00314 * A is n+1 by k 00315 DO J = 0, K - 1 00316 DO I = 0, N 00317 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00318 END DO 00319 END DO 00320 ELSE 00321 * xpose case; A is k by n+1 00322 DO J = 0, N 00323 DO I = 0, K - 1 00324 VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) ) 00325 END DO 00326 END DO 00327 END IF 00328 END IF 00329 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00330 $ ( NORM.EQ.'1' ) ) THEN 00331 * 00332 * Find normI(A) ( = norm1(A), since A is symmetric). 00333 * 00334 IF( IFM.EQ.1 ) THEN 00335 K = N / 2 00336 IF( NOE.EQ.1 ) THEN 00337 * n is odd 00338 IF( ILU.EQ.0 ) THEN 00339 DO I = 0, K - 1 00340 WORK( I ) = ZERO 00341 END DO 00342 DO J = 0, K 00343 S = ZERO 00344 DO I = 0, K + J - 1 00345 AA = ABS( A( I+J*LDA ) ) 00346 * -> A(i,j+k) 00347 S = S + AA 00348 WORK( I ) = WORK( I ) + AA 00349 END DO 00350 AA = ABS( A( I+J*LDA ) ) 00351 * -> A(j+k,j+k) 00352 WORK( J+K ) = S + AA 00353 IF( I.EQ.K+K ) 00354 $ GO TO 10 00355 I = I + 1 00356 AA = ABS( A( I+J*LDA ) ) 00357 * -> A(j,j) 00358 WORK( J ) = WORK( J ) + AA 00359 S = ZERO 00360 DO L = J + 1, K - 1 00361 I = I + 1 00362 AA = ABS( A( I+J*LDA ) ) 00363 * -> A(l,j) 00364 S = S + AA 00365 WORK( L ) = WORK( L ) + AA 00366 END DO 00367 WORK( J ) = WORK( J ) + S 00368 END DO 00369 10 CONTINUE 00370 I = ISAMAX( N, WORK, 1 ) 00371 VALUE = WORK( I-1 ) 00372 ELSE 00373 * ilu = 1 00374 K = K + 1 00375 * k=(n+1)/2 for n odd and ilu=1 00376 DO I = K, N - 1 00377 WORK( I ) = ZERO 00378 END DO 00379 DO J = K - 1, 0, -1 00380 S = ZERO 00381 DO I = 0, J - 2 00382 AA = ABS( A( I+J*LDA ) ) 00383 * -> A(j+k,i+k) 00384 S = S + AA 00385 WORK( I+K ) = WORK( I+K ) + AA 00386 END DO 00387 IF( J.GT.0 ) THEN 00388 AA = ABS( A( I+J*LDA ) ) 00389 * -> A(j+k,j+k) 00390 S = S + AA 00391 WORK( I+K ) = WORK( I+K ) + S 00392 * i=j 00393 I = I + 1 00394 END IF 00395 AA = ABS( A( I+J*LDA ) ) 00396 * -> A(j,j) 00397 WORK( J ) = AA 00398 S = ZERO 00399 DO L = J + 1, N - 1 00400 I = I + 1 00401 AA = ABS( A( I+J*LDA ) ) 00402 * -> A(l,j) 00403 S = S + AA 00404 WORK( L ) = WORK( L ) + AA 00405 END DO 00406 WORK( J ) = WORK( J ) + S 00407 END DO 00408 I = ISAMAX( N, WORK, 1 ) 00409 VALUE = WORK( I-1 ) 00410 END IF 00411 ELSE 00412 * n is even 00413 IF( ILU.EQ.0 ) THEN 00414 DO I = 0, K - 1 00415 WORK( I ) = ZERO 00416 END DO 00417 DO J = 0, K - 1 00418 S = ZERO 00419 DO I = 0, K + J - 1 00420 AA = ABS( A( I+J*LDA ) ) 00421 * -> A(i,j+k) 00422 S = S + AA 00423 WORK( I ) = WORK( I ) + AA 00424 END DO 00425 AA = ABS( A( I+J*LDA ) ) 00426 * -> A(j+k,j+k) 00427 WORK( J+K ) = S + AA 00428 I = I + 1 00429 AA = ABS( A( I+J*LDA ) ) 00430 * -> A(j,j) 00431 WORK( J ) = WORK( J ) + AA 00432 S = ZERO 00433 DO L = J + 1, K - 1 00434 I = I + 1 00435 AA = ABS( A( I+J*LDA ) ) 00436 * -> A(l,j) 00437 S = S + AA 00438 WORK( L ) = WORK( L ) + AA 00439 END DO 00440 WORK( J ) = WORK( J ) + S 00441 END DO 00442 I = ISAMAX( N, WORK, 1 ) 00443 VALUE = WORK( I-1 ) 00444 ELSE 00445 * ilu = 1 00446 DO I = K, N - 1 00447 WORK( I ) = ZERO 00448 END DO 00449 DO J = K - 1, 0, -1 00450 S = ZERO 00451 DO I = 0, J - 1 00452 AA = ABS( A( I+J*LDA ) ) 00453 * -> A(j+k,i+k) 00454 S = S + AA 00455 WORK( I+K ) = WORK( I+K ) + AA 00456 END DO 00457 AA = ABS( A( I+J*LDA ) ) 00458 * -> A(j+k,j+k) 00459 S = S + AA 00460 WORK( I+K ) = WORK( I+K ) + S 00461 * i=j 00462 I = I + 1 00463 AA = ABS( A( I+J*LDA ) ) 00464 * -> A(j,j) 00465 WORK( J ) = AA 00466 S = ZERO 00467 DO L = J + 1, N - 1 00468 I = I + 1 00469 AA = ABS( A( I+J*LDA ) ) 00470 * -> A(l,j) 00471 S = S + AA 00472 WORK( L ) = WORK( L ) + AA 00473 END DO 00474 WORK( J ) = WORK( J ) + S 00475 END DO 00476 I = ISAMAX( N, WORK, 1 ) 00477 VALUE = WORK( I-1 ) 00478 END IF 00479 END IF 00480 ELSE 00481 * ifm=0 00482 K = N / 2 00483 IF( NOE.EQ.1 ) THEN 00484 * n is odd 00485 IF( ILU.EQ.0 ) THEN 00486 N1 = K 00487 * n/2 00488 K = K + 1 00489 * k is the row size and lda 00490 DO I = N1, N - 1 00491 WORK( I ) = ZERO 00492 END DO 00493 DO J = 0, N1 - 1 00494 S = ZERO 00495 DO I = 0, K - 1 00496 AA = ABS( A( I+J*LDA ) ) 00497 * A(j,n1+i) 00498 WORK( I+N1 ) = WORK( I+N1 ) + AA 00499 S = S + AA 00500 END DO 00501 WORK( J ) = S 00502 END DO 00503 * j=n1=k-1 is special 00504 S = ABS( A( 0+J*LDA ) ) 00505 * A(k-1,k-1) 00506 DO I = 1, K - 1 00507 AA = ABS( A( I+J*LDA ) ) 00508 * A(k-1,i+n1) 00509 WORK( I+N1 ) = WORK( I+N1 ) + AA 00510 S = S + AA 00511 END DO 00512 WORK( J ) = WORK( J ) + S 00513 DO J = K, N - 1 00514 S = ZERO 00515 DO I = 0, J - K - 1 00516 AA = ABS( A( I+J*LDA ) ) 00517 * A(i,j-k) 00518 WORK( I ) = WORK( I ) + AA 00519 S = S + AA 00520 END DO 00521 * i=j-k 00522 AA = ABS( A( I+J*LDA ) ) 00523 * A(j-k,j-k) 00524 S = S + AA 00525 WORK( J-K ) = WORK( J-K ) + S 00526 I = I + 1 00527 S = ABS( A( I+J*LDA ) ) 00528 * A(j,j) 00529 DO L = J + 1, N - 1 00530 I = I + 1 00531 AA = ABS( A( I+J*LDA ) ) 00532 * A(j,l) 00533 WORK( L ) = WORK( L ) + AA 00534 S = S + AA 00535 END DO 00536 WORK( J ) = WORK( J ) + S 00537 END DO 00538 I = ISAMAX( N, WORK, 1 ) 00539 VALUE = WORK( I-1 ) 00540 ELSE 00541 * ilu=1 00542 K = K + 1 00543 * k=(n+1)/2 for n odd and ilu=1 00544 DO I = K, N - 1 00545 WORK( I ) = ZERO 00546 END DO 00547 DO J = 0, K - 2 00548 * process 00549 S = ZERO 00550 DO I = 0, J - 1 00551 AA = ABS( A( I+J*LDA ) ) 00552 * A(j,i) 00553 WORK( I ) = WORK( I ) + AA 00554 S = S + AA 00555 END DO 00556 AA = ABS( A( I+J*LDA ) ) 00557 * i=j so process of A(j,j) 00558 S = S + AA 00559 WORK( J ) = S 00560 * is initialised here 00561 I = I + 1 00562 * i=j process A(j+k,j+k) 00563 AA = ABS( A( I+J*LDA ) ) 00564 S = AA 00565 DO L = K + J + 1, N - 1 00566 I = I + 1 00567 AA = ABS( A( I+J*LDA ) ) 00568 * A(l,k+j) 00569 S = S + AA 00570 WORK( L ) = WORK( L ) + AA 00571 END DO 00572 WORK( K+J ) = WORK( K+J ) + S 00573 END DO 00574 * j=k-1 is special :process col A(k-1,0:k-1) 00575 S = ZERO 00576 DO I = 0, K - 2 00577 AA = ABS( A( I+J*LDA ) ) 00578 * A(k,i) 00579 WORK( I ) = WORK( I ) + AA 00580 S = S + AA 00581 END DO 00582 * i=k-1 00583 AA = ABS( A( I+J*LDA ) ) 00584 * A(k-1,k-1) 00585 S = S + AA 00586 WORK( I ) = S 00587 * done with col j=k+1 00588 DO J = K, N - 1 00589 * process col j of A = A(j,0:k-1) 00590 S = ZERO 00591 DO I = 0, K - 1 00592 AA = ABS( A( I+J*LDA ) ) 00593 * A(j,i) 00594 WORK( I ) = WORK( I ) + AA 00595 S = S + AA 00596 END DO 00597 WORK( J ) = WORK( J ) + S 00598 END DO 00599 I = ISAMAX( N, WORK, 1 ) 00600 VALUE = WORK( I-1 ) 00601 END IF 00602 ELSE 00603 * n is even 00604 IF( ILU.EQ.0 ) THEN 00605 DO I = K, N - 1 00606 WORK( I ) = ZERO 00607 END DO 00608 DO J = 0, K - 1 00609 S = ZERO 00610 DO I = 0, K - 1 00611 AA = ABS( A( I+J*LDA ) ) 00612 * A(j,i+k) 00613 WORK( I+K ) = WORK( I+K ) + AA 00614 S = S + AA 00615 END DO 00616 WORK( J ) = S 00617 END DO 00618 * j=k 00619 AA = ABS( A( 0+J*LDA ) ) 00620 * A(k,k) 00621 S = AA 00622 DO I = 1, K - 1 00623 AA = ABS( A( I+J*LDA ) ) 00624 * A(k,k+i) 00625 WORK( I+K ) = WORK( I+K ) + AA 00626 S = S + AA 00627 END DO 00628 WORK( J ) = WORK( J ) + S 00629 DO J = K + 1, N - 1 00630 S = ZERO 00631 DO I = 0, J - 2 - K 00632 AA = ABS( A( I+J*LDA ) ) 00633 * A(i,j-k-1) 00634 WORK( I ) = WORK( I ) + AA 00635 S = S + AA 00636 END DO 00637 * i=j-1-k 00638 AA = ABS( A( I+J*LDA ) ) 00639 * A(j-k-1,j-k-1) 00640 S = S + AA 00641 WORK( J-K-1 ) = WORK( J-K-1 ) + S 00642 I = I + 1 00643 AA = ABS( A( I+J*LDA ) ) 00644 * A(j,j) 00645 S = AA 00646 DO L = J + 1, N - 1 00647 I = I + 1 00648 AA = ABS( A( I+J*LDA ) ) 00649 * A(j,l) 00650 WORK( L ) = WORK( L ) + AA 00651 S = S + AA 00652 END DO 00653 WORK( J ) = WORK( J ) + S 00654 END DO 00655 * j=n 00656 S = ZERO 00657 DO I = 0, K - 2 00658 AA = ABS( A( I+J*LDA ) ) 00659 * A(i,k-1) 00660 WORK( I ) = WORK( I ) + AA 00661 S = S + AA 00662 END DO 00663 * i=k-1 00664 AA = ABS( A( I+J*LDA ) ) 00665 * A(k-1,k-1) 00666 S = S + AA 00667 WORK( I ) = WORK( I ) + S 00668 I = ISAMAX( N, WORK, 1 ) 00669 VALUE = WORK( I-1 ) 00670 ELSE 00671 * ilu=1 00672 DO I = K, N - 1 00673 WORK( I ) = ZERO 00674 END DO 00675 * j=0 is special :process col A(k:n-1,k) 00676 S = ABS( A( 0 ) ) 00677 * A(k,k) 00678 DO I = 1, K - 1 00679 AA = ABS( A( I ) ) 00680 * A(k+i,k) 00681 WORK( I+K ) = WORK( I+K ) + AA 00682 S = S + AA 00683 END DO 00684 WORK( K ) = WORK( K ) + S 00685 DO J = 1, K - 1 00686 * process 00687 S = ZERO 00688 DO I = 0, J - 2 00689 AA = ABS( A( I+J*LDA ) ) 00690 * A(j-1,i) 00691 WORK( I ) = WORK( I ) + AA 00692 S = S + AA 00693 END DO 00694 AA = ABS( A( I+J*LDA ) ) 00695 * i=j-1 so process of A(j-1,j-1) 00696 S = S + AA 00697 WORK( J-1 ) = S 00698 * is initialised here 00699 I = I + 1 00700 * i=j process A(j+k,j+k) 00701 AA = ABS( A( I+J*LDA ) ) 00702 S = AA 00703 DO L = K + J + 1, N - 1 00704 I = I + 1 00705 AA = ABS( A( I+J*LDA ) ) 00706 * A(l,k+j) 00707 S = S + AA 00708 WORK( L ) = WORK( L ) + AA 00709 END DO 00710 WORK( K+J ) = WORK( K+J ) + S 00711 END DO 00712 * j=k is special :process col A(k,0:k-1) 00713 S = ZERO 00714 DO I = 0, K - 2 00715 AA = ABS( A( I+J*LDA ) ) 00716 * A(k,i) 00717 WORK( I ) = WORK( I ) + AA 00718 S = S + AA 00719 END DO 00720 * i=k-1 00721 AA = ABS( A( I+J*LDA ) ) 00722 * A(k-1,k-1) 00723 S = S + AA 00724 WORK( I ) = S 00725 * done with col j=k+1 00726 DO J = K + 1, N 00727 * process col j-1 of A = A(j-1,0:k-1) 00728 S = ZERO 00729 DO I = 0, K - 1 00730 AA = ABS( A( I+J*LDA ) ) 00731 * A(j-1,i) 00732 WORK( I ) = WORK( I ) + AA 00733 S = S + AA 00734 END DO 00735 WORK( J-1 ) = WORK( J-1 ) + S 00736 END DO 00737 I = ISAMAX( N, WORK, 1 ) 00738 VALUE = WORK( I-1 ) 00739 END IF 00740 END IF 00741 END IF 00742 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00743 * 00744 * Find normF(A). 00745 * 00746 K = ( N+1 ) / 2 00747 SCALE = ZERO 00748 S = ONE 00749 IF( NOE.EQ.1 ) THEN 00750 * n is odd 00751 IF( IFM.EQ.1 ) THEN 00752 * A is normal 00753 IF( ILU.EQ.0 ) THEN 00754 * A is upper 00755 DO J = 0, K - 3 00756 CALL SLASSQ( K-J-2, A( K+J+1+J*LDA ), 1, SCALE, S ) 00757 * L at A(k,0) 00758 END DO 00759 DO J = 0, K - 1 00760 CALL SLASSQ( K+J-1, A( 0+J*LDA ), 1, SCALE, S ) 00761 * trap U at A(0,0) 00762 END DO 00763 S = S + S 00764 * double s for the off diagonal elements 00765 CALL SLASSQ( K-1, A( K ), LDA+1, SCALE, S ) 00766 * tri L at A(k,0) 00767 CALL SLASSQ( K, A( K-1 ), LDA+1, SCALE, S ) 00768 * tri U at A(k-1,0) 00769 ELSE 00770 * ilu=1 & A is lower 00771 DO J = 0, K - 1 00772 CALL SLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S ) 00773 * trap L at A(0,0) 00774 END DO 00775 DO J = 0, K - 2 00776 CALL SLASSQ( J, A( 0+( 1+J )*LDA ), 1, SCALE, S ) 00777 * U at A(0,1) 00778 END DO 00779 S = S + S 00780 * double s for the off diagonal elements 00781 CALL SLASSQ( K, A( 0 ), LDA+1, SCALE, S ) 00782 * tri L at A(0,0) 00783 CALL SLASSQ( K-1, A( 0+LDA ), LDA+1, SCALE, S ) 00784 * tri U at A(0,1) 00785 END IF 00786 ELSE 00787 * A is xpose 00788 IF( ILU.EQ.0 ) THEN 00789 * A**T is upper 00790 DO J = 1, K - 2 00791 CALL SLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S ) 00792 * U at A(0,k) 00793 END DO 00794 DO J = 0, K - 2 00795 CALL SLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 00796 * k by k-1 rect. at A(0,0) 00797 END DO 00798 DO J = 0, K - 2 00799 CALL SLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1, 00800 $ SCALE, S ) 00801 * L at A(0,k-1) 00802 END DO 00803 S = S + S 00804 * double s for the off diagonal elements 00805 CALL SLASSQ( K-1, A( 0+K*LDA ), LDA+1, SCALE, S ) 00806 * tri U at A(0,k) 00807 CALL SLASSQ( K, A( 0+( K-1 )*LDA ), LDA+1, SCALE, S ) 00808 * tri L at A(0,k-1) 00809 ELSE 00810 * A**T is lower 00811 DO J = 1, K - 1 00812 CALL SLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) 00813 * U at A(0,0) 00814 END DO 00815 DO J = K, N - 1 00816 CALL SLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 00817 * k by k-1 rect. at A(0,k) 00818 END DO 00819 DO J = 0, K - 3 00820 CALL SLASSQ( K-J-2, A( J+2+J*LDA ), 1, SCALE, S ) 00821 * L at A(1,0) 00822 END DO 00823 S = S + S 00824 * double s for the off diagonal elements 00825 CALL SLASSQ( K, A( 0 ), LDA+1, SCALE, S ) 00826 * tri U at A(0,0) 00827 CALL SLASSQ( K-1, A( 1 ), LDA+1, SCALE, S ) 00828 * tri L at A(1,0) 00829 END IF 00830 END IF 00831 ELSE 00832 * n is even 00833 IF( IFM.EQ.1 ) THEN 00834 * A is normal 00835 IF( ILU.EQ.0 ) THEN 00836 * A is upper 00837 DO J = 0, K - 2 00838 CALL SLASSQ( K-J-1, A( K+J+2+J*LDA ), 1, SCALE, S ) 00839 * L at A(k+1,0) 00840 END DO 00841 DO J = 0, K - 1 00842 CALL SLASSQ( K+J, A( 0+J*LDA ), 1, SCALE, S ) 00843 * trap U at A(0,0) 00844 END DO 00845 S = S + S 00846 * double s for the off diagonal elements 00847 CALL SLASSQ( K, A( K+1 ), LDA+1, SCALE, S ) 00848 * tri L at A(k+1,0) 00849 CALL SLASSQ( K, A( K ), LDA+1, SCALE, S ) 00850 * tri U at A(k,0) 00851 ELSE 00852 * ilu=1 & A is lower 00853 DO J = 0, K - 1 00854 CALL SLASSQ( N-J-1, A( J+2+J*LDA ), 1, SCALE, S ) 00855 * trap L at A(1,0) 00856 END DO 00857 DO J = 1, K - 1 00858 CALL SLASSQ( J, A( 0+J*LDA ), 1, SCALE, S ) 00859 * U at A(0,0) 00860 END DO 00861 S = S + S 00862 * double s for the off diagonal elements 00863 CALL SLASSQ( K, A( 1 ), LDA+1, SCALE, S ) 00864 * tri L at A(1,0) 00865 CALL SLASSQ( K, A( 0 ), LDA+1, SCALE, S ) 00866 * tri U at A(0,0) 00867 END IF 00868 ELSE 00869 * A is xpose 00870 IF( ILU.EQ.0 ) THEN 00871 * A**T is upper 00872 DO J = 1, K - 1 00873 CALL SLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S ) 00874 * U at A(0,k+1) 00875 END DO 00876 DO J = 0, K - 1 00877 CALL SLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 00878 * k by k rect. at A(0,0) 00879 END DO 00880 DO J = 0, K - 2 00881 CALL SLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE, 00882 $ S ) 00883 * L at A(0,k) 00884 END DO 00885 S = S + S 00886 * double s for the off diagonal elements 00887 CALL SLASSQ( K, A( 0+( K+1 )*LDA ), LDA+1, SCALE, S ) 00888 * tri U at A(0,k+1) 00889 CALL SLASSQ( K, A( 0+K*LDA ), LDA+1, SCALE, S ) 00890 * tri L at A(0,k) 00891 ELSE 00892 * A**T is lower 00893 DO J = 1, K - 1 00894 CALL SLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S ) 00895 * U at A(0,1) 00896 END DO 00897 DO J = K + 1, N 00898 CALL SLASSQ( K, A( 0+J*LDA ), 1, SCALE, S ) 00899 * k by k rect. at A(0,k+1) 00900 END DO 00901 DO J = 0, K - 2 00902 CALL SLASSQ( K-J-1, A( J+1+J*LDA ), 1, SCALE, S ) 00903 * L at A(0,0) 00904 END DO 00905 S = S + S 00906 * double s for the off diagonal elements 00907 CALL SLASSQ( K, A( LDA ), LDA+1, SCALE, S ) 00908 * tri L at A(0,1) 00909 CALL SLASSQ( K, A( 0 ), LDA+1, SCALE, S ) 00910 * tri U at A(0,0) 00911 END IF 00912 END IF 00913 END IF 00914 VALUE = SCALE*SQRT( S ) 00915 END IF 00916 * 00917 SLANSF = VALUE 00918 RETURN 00919 * 00920 * End of SLANSF 00921 * 00922 END
1.7.6.1 
