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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, 00002 $ KL, KU, PACK, A, LDA, WORK, INFO ) 00003 * 00004 * -- LAPACK test routine (version 3.1) -- 00005 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00006 * June 2010 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER DIST, PACK, SYM 00010 INTEGER INFO, KL, KU, LDA, M, MODE, N 00011 REAL COND, DMAX 00012 * .. 00013 * .. Array Arguments .. 00014 INTEGER ISEED( 4 ) 00015 REAL A( LDA, * ), D( * ), WORK( * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * SLATMS generates random matrices with specified singular values 00022 * (or symmetric/hermitian with specified eigenvalues) 00023 * for testing LAPACK programs. 00024 * 00025 * SLATMS operates by applying the following sequence of 00026 * operations: 00027 * 00028 * Set the diagonal to D, where D may be input or 00029 * computed according to MODE, COND, DMAX, and SYM 00030 * as described below. 00031 * 00032 * Generate a matrix with the appropriate band structure, by one 00033 * of two methods: 00034 * 00035 * Method A: 00036 * Generate a dense M x N matrix by multiplying D on the left 00037 * and the right by random unitary matrices, then: 00038 * 00039 * Reduce the bandwidth according to KL and KU, using 00040 * Householder transformations. 00041 * 00042 * Method B: 00043 * Convert the bandwidth-0 (i.e., diagonal) matrix to a 00044 * bandwidth-1 matrix using Givens rotations, "chasing" 00045 * out-of-band elements back, much as in QR; then 00046 * convert the bandwidth-1 to a bandwidth-2 matrix, etc. 00047 * Note that for reasonably small bandwidths (relative to 00048 * M and N) this requires less storage, as a dense matrix 00049 * is not generated. Also, for symmetric matrices, only 00050 * one triangle is generated. 00051 * 00052 * Method A is chosen if the bandwidth is a large fraction of the 00053 * order of the matrix, and LDA is at least M (so a dense 00054 * matrix can be stored.) Method B is chosen if the bandwidth 00055 * is small (< 1/2 N for symmetric, < .3 N+M for 00056 * non-symmetric), or LDA is less than M and not less than the 00057 * bandwidth. 00058 * 00059 * Pack the matrix if desired. Options specified by PACK are: 00060 * no packing 00061 * zero out upper half (if symmetric) 00062 * zero out lower half (if symmetric) 00063 * store the upper half columnwise (if symmetric or upper 00064 * triangular) 00065 * store the lower half columnwise (if symmetric or lower 00066 * triangular) 00067 * store the lower triangle in banded format (if symmetric 00068 * or lower triangular) 00069 * store the upper triangle in banded format (if symmetric 00070 * or upper triangular) 00071 * store the entire matrix in banded format 00072 * If Method B is chosen, and band format is specified, then the 00073 * matrix will be generated in the band format, so no repacking 00074 * will be necessary. 00075 * 00076 * Arguments 00077 * ========= 00078 * 00079 * M (input) INTEGER 00080 * The number of rows of A. Not modified. 00081 * 00082 * N (input) INTEGER 00083 * The number of columns of A. Not modified. 00084 * 00085 * DIST (input) CHARACTER*1 00086 * On entry, DIST specifies the type of distribution to be used 00087 * to generate the random eigen-/singular values. 00088 * 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) 00089 * 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) 00090 * 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) 00091 * Not modified. 00092 * 00093 * ISEED (input/output) INTEGER array, dimension ( 4 ) 00094 * On entry ISEED specifies the seed of the random number 00095 * generator. They should lie between 0 and 4095 inclusive, 00096 * and ISEED(4) should be odd. The random number generator 00097 * uses a linear congruential sequence limited to small 00098 * integers, and so should produce machine independent 00099 * random numbers. The values of ISEED are changed on 00100 * exit, and can be used in the next call to SLATMS 00101 * to continue the same random number sequence. 00102 * Changed on exit. 00103 * 00104 * SYM (input) CHARACTER*1 00105 * If SYM='S' or 'H', the generated matrix is symmetric, with 00106 * eigenvalues specified by D, COND, MODE, and DMAX; they 00107 * may be positive, negative, or zero. 00108 * If SYM='P', the generated matrix is symmetric, with 00109 * eigenvalues (= singular values) specified by D, COND, 00110 * MODE, and DMAX; they will not be negative. 00111 * If SYM='N', the generated matrix is nonsymmetric, with 00112 * singular values specified by D, COND, MODE, and DMAX; 00113 * they will not be negative. 00114 * Not modified. 00115 * 00116 * D (input/output) REAL array, dimension ( MIN( M , N ) ) 00117 * This array is used to specify the singular values or 00118 * eigenvalues of A (see SYM, above.) If MODE=0, then D is 00119 * assumed to contain the singular/eigenvalues, otherwise 00120 * they will be computed according to MODE, COND, and DMAX, 00121 * and placed in D. 00122 * Modified if MODE is nonzero. 00123 * 00124 * MODE (input) INTEGER 00125 * On entry this describes how the singular/eigenvalues are to 00126 * be specified: 00127 * MODE = 0 means use D as input 00128 * MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND 00129 * MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND 00130 * MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) 00131 * MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) 00132 * MODE = 5 sets D to random numbers in the range 00133 * ( 1/COND , 1 ) such that their logarithms 00134 * are uniformly distributed. 00135 * MODE = 6 set D to random numbers from same distribution 00136 * as the rest of the matrix. 00137 * MODE < 0 has the same meaning as ABS(MODE), except that 00138 * the order of the elements of D is reversed. 00139 * Thus if MODE is positive, D has entries ranging from 00140 * 1 to 1/COND, if negative, from 1/COND to 1, 00141 * If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then 00142 * the elements of D will also be multiplied by a random 00143 * sign (i.e., +1 or -1.) 00144 * Not modified. 00145 * 00146 * COND (input) REAL 00147 * On entry, this is used as described under MODE above. 00148 * If used, it must be >= 1. Not modified. 00149 * 00150 * DMAX (input) REAL 00151 * If MODE is neither -6, 0 nor 6, the contents of D, as 00152 * computed according to MODE and COND, will be scaled by 00153 * DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or 00154 * singular value (which is to say the norm) will be abs(DMAX). 00155 * Note that DMAX need not be positive: if DMAX is negative 00156 * (or zero), D will be scaled by a negative number (or zero). 00157 * Not modified. 00158 * 00159 * KL (input) INTEGER 00160 * This specifies the lower bandwidth of the matrix. For 00161 * example, KL=0 implies upper triangular, KL=1 implies upper 00162 * Hessenberg, and KL being at least M-1 means that the matrix 00163 * has full lower bandwidth. KL must equal KU if the matrix 00164 * is symmetric. 00165 * Not modified. 00166 * 00167 * KU (input) INTEGER 00168 * This specifies the upper bandwidth of the matrix. For 00169 * example, KU=0 implies lower triangular, KU=1 implies lower 00170 * Hessenberg, and KU being at least N-1 means that the matrix 00171 * has full upper bandwidth. KL must equal KU if the matrix 00172 * is symmetric. 00173 * Not modified. 00174 * 00175 * PACK (input) CHARACTER*1 00176 * This specifies packing of matrix as follows: 00177 * 'N' => no packing 00178 * 'U' => zero out all subdiagonal entries (if symmetric) 00179 * 'L' => zero out all superdiagonal entries (if symmetric) 00180 * 'C' => store the upper triangle columnwise 00181 * (only if the matrix is symmetric or upper triangular) 00182 * 'R' => store the lower triangle columnwise 00183 * (only if the matrix is symmetric or lower triangular) 00184 * 'B' => store the lower triangle in band storage scheme 00185 * (only if matrix symmetric or lower triangular) 00186 * 'Q' => store the upper triangle in band storage scheme 00187 * (only if matrix symmetric or upper triangular) 00188 * 'Z' => store the entire matrix in band storage scheme 00189 * (pivoting can be provided for by using this 00190 * option to store A in the trailing rows of 00191 * the allocated storage) 00192 * 00193 * Using these options, the various LAPACK packed and banded 00194 * storage schemes can be obtained: 00195 * GB - use 'Z' 00196 * PB, SB or TB - use 'B' or 'Q' 00197 * PP, SP or TP - use 'C' or 'R' 00198 * 00199 * If two calls to SLATMS differ only in the PACK parameter, 00200 * they will generate mathematically equivalent matrices. 00201 * Not modified. 00202 * 00203 * A (input/output) REAL array, dimension ( LDA, N ) 00204 * On exit A is the desired test matrix. A is first generated 00205 * in full (unpacked) form, and then packed, if so specified 00206 * by PACK. Thus, the first M elements of the first N 00207 * columns will always be modified. If PACK specifies a 00208 * packed or banded storage scheme, all LDA elements of the 00209 * first N columns will be modified; the elements of the 00210 * array which do not correspond to elements of the generated 00211 * matrix are set to zero. 00212 * Modified. 00213 * 00214 * LDA (input) INTEGER 00215 * LDA specifies the first dimension of A as declared in the 00216 * calling program. If PACK='N', 'U', 'L', 'C', or 'R', then 00217 * LDA must be at least M. If PACK='B' or 'Q', then LDA must 00218 * be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). 00219 * If PACK='Z', LDA must be large enough to hold the packed 00220 * array: MIN( KU, N-1) + MIN( KL, M-1) + 1. 00221 * Not modified. 00222 * 00223 * WORK (workspace) REAL array, dimension ( 3*MAX( N , M ) ) 00224 * Workspace. 00225 * Modified. 00226 * 00227 * INFO (output) INTEGER 00228 * Error code. On exit, INFO will be set to one of the 00229 * following values: 00230 * 0 => normal return 00231 * -1 => M negative or unequal to N and SYM='S', 'H', or 'P' 00232 * -2 => N negative 00233 * -3 => DIST illegal string 00234 * -5 => SYM illegal string 00235 * -7 => MODE not in range -6 to 6 00236 * -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 00237 * -10 => KL negative 00238 * -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL 00239 * -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; 00240 * or PACK='C' or 'Q' and SYM='N' and KL is not zero; 00241 * or PACK='R' or 'B' and SYM='N' and KU is not zero; 00242 * or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not 00243 * N. 00244 * -14 => LDA is less than M, or PACK='Z' and LDA is less than 00245 * MIN(KU,N-1) + MIN(KL,M-1) + 1. 00246 * 1 => Error return from SLATM1 00247 * 2 => Cannot scale to DMAX (max. sing. value is 0) 00248 * 3 => Error return from SLAGGE or SLAGSY 00249 * 00250 * ===================================================================== 00251 * 00252 * .. Parameters .. 00253 REAL ZERO 00254 PARAMETER ( ZERO = 0.0E0 ) 00255 REAL ONE 00256 PARAMETER ( ONE = 1.0E0 ) 00257 REAL TWOPI 00258 PARAMETER ( TWOPI = 6.2831853071795864769252867663E+0 ) 00259 * .. 00260 * .. Local Scalars .. 00261 LOGICAL GIVENS, ILEXTR, ILTEMP, TOPDWN 00262 INTEGER I, IC, ICOL, IDIST, IENDCH, IINFO, IL, ILDA, 00263 $ IOFFG, IOFFST, IPACK, IPACKG, IR, IR1, IR2, 00264 $ IROW, IRSIGN, ISKEW, ISYM, ISYMPK, J, JC, JCH, 00265 $ JKL, JKU, JR, K, LLB, MINLDA, MNMIN, MR, NC, 00266 $ UUB 00267 REAL ALPHA, ANGLE, C, DUMMY, EXTRA, S, TEMP 00268 * .. 00269 * .. External Functions .. 00270 LOGICAL LSAME 00271 REAL SLARND 00272 EXTERNAL LSAME, SLARND 00273 * .. 00274 * .. External Subroutines .. 00275 EXTERNAL SCOPY, SLAGGE, SLAGSY, SLAROT, SLARTG, SLATM1, 00276 $ SLASET, SSCAL, XERBLA 00277 * .. 00278 * .. Intrinsic Functions .. 00279 INTRINSIC ABS, COS, MAX, MIN, MOD, REAL, SIN 00280 * .. 00281 * .. Executable Statements .. 00282 * 00283 * 1) Decode and Test the input parameters. 00284 * Initialize flags & seed. 00285 * 00286 INFO = 0 00287 * 00288 * Quick return if possible 00289 * 00290 IF( M.EQ.0 .OR. N.EQ.0 ) 00291 $ RETURN 00292 * 00293 * Decode DIST 00294 * 00295 IF( LSAME( DIST, 'U' ) ) THEN 00296 IDIST = 1 00297 ELSE IF( LSAME( DIST, 'S' ) ) THEN 00298 IDIST = 2 00299 ELSE IF( LSAME( DIST, 'N' ) ) THEN 00300 IDIST = 3 00301 ELSE 00302 IDIST = -1 00303 END IF 00304 * 00305 * Decode SYM 00306 * 00307 IF( LSAME( SYM, 'N' ) ) THEN 00308 ISYM = 1 00309 IRSIGN = 0 00310 ELSE IF( LSAME( SYM, 'P' ) ) THEN 00311 ISYM = 2 00312 IRSIGN = 0 00313 ELSE IF( LSAME( SYM, 'S' ) ) THEN 00314 ISYM = 2 00315 IRSIGN = 1 00316 ELSE IF( LSAME( SYM, 'H' ) ) THEN 00317 ISYM = 2 00318 IRSIGN = 1 00319 ELSE 00320 ISYM = -1 00321 END IF 00322 * 00323 * Decode PACK 00324 * 00325 ISYMPK = 0 00326 IF( LSAME( PACK, 'N' ) ) THEN 00327 IPACK = 0 00328 ELSE IF( LSAME( PACK, 'U' ) ) THEN 00329 IPACK = 1 00330 ISYMPK = 1 00331 ELSE IF( LSAME( PACK, 'L' ) ) THEN 00332 IPACK = 2 00333 ISYMPK = 1 00334 ELSE IF( LSAME( PACK, 'C' ) ) THEN 00335 IPACK = 3 00336 ISYMPK = 2 00337 ELSE IF( LSAME( PACK, 'R' ) ) THEN 00338 IPACK = 4 00339 ISYMPK = 3 00340 ELSE IF( LSAME( PACK, 'B' ) ) THEN 00341 IPACK = 5 00342 ISYMPK = 3 00343 ELSE IF( LSAME( PACK, 'Q' ) ) THEN 00344 IPACK = 6 00345 ISYMPK = 2 00346 ELSE IF( LSAME( PACK, 'Z' ) ) THEN 00347 IPACK = 7 00348 ELSE 00349 IPACK = -1 00350 END IF 00351 * 00352 * Set certain internal parameters 00353 * 00354 MNMIN = MIN( M, N ) 00355 LLB = MIN( KL, M-1 ) 00356 UUB = MIN( KU, N-1 ) 00357 MR = MIN( M, N+LLB ) 00358 NC = MIN( N, M+UUB ) 00359 * 00360 IF( IPACK.EQ.5 .OR. IPACK.EQ.6 ) THEN 00361 MINLDA = UUB + 1 00362 ELSE IF( IPACK.EQ.7 ) THEN 00363 MINLDA = LLB + UUB + 1 00364 ELSE 00365 MINLDA = M 00366 END IF 00367 * 00368 * Use Givens rotation method if bandwidth small enough, 00369 * or if LDA is too small to store the matrix unpacked. 00370 * 00371 GIVENS = .FALSE. 00372 IF( ISYM.EQ.1 ) THEN 00373 IF( REAL( LLB+UUB ).LT.0.3*REAL( MAX( 1, MR+NC ) ) ) 00374 $ GIVENS = .TRUE. 00375 ELSE 00376 IF( 2*LLB.LT.M ) 00377 $ GIVENS = .TRUE. 00378 END IF 00379 IF( LDA.LT.M .AND. LDA.GE.MINLDA ) 00380 $ GIVENS = .TRUE. 00381 * 00382 * Set INFO if an error 00383 * 00384 IF( M.LT.0 ) THEN 00385 INFO = -1 00386 ELSE IF( M.NE.N .AND. ISYM.NE.1 ) THEN 00387 INFO = -1 00388 ELSE IF( N.LT.0 ) THEN 00389 INFO = -2 00390 ELSE IF( IDIST.EQ.-1 ) THEN 00391 INFO = -3 00392 ELSE IF( ISYM.EQ.-1 ) THEN 00393 INFO = -5 00394 ELSE IF( ABS( MODE ).GT.6 ) THEN 00395 INFO = -7 00396 ELSE IF( ( MODE.NE.0 .AND. ABS( MODE ).NE.6 ) .AND. COND.LT.ONE ) 00397 $ THEN 00398 INFO = -8 00399 ELSE IF( KL.LT.0 ) THEN 00400 INFO = -10 00401 ELSE IF( KU.LT.0 .OR. ( ISYM.NE.1 .AND. KL.NE.KU ) ) THEN 00402 INFO = -11 00403 ELSE IF( IPACK.EQ.-1 .OR. ( ISYMPK.EQ.1 .AND. ISYM.EQ.1 ) .OR. 00404 $ ( ISYMPK.EQ.2 .AND. ISYM.EQ.1 .AND. KL.GT.0 ) .OR. 00405 $ ( ISYMPK.EQ.3 .AND. ISYM.EQ.1 .AND. KU.GT.0 ) .OR. 00406 $ ( ISYMPK.NE.0 .AND. M.NE.N ) ) THEN 00407 INFO = -12 00408 ELSE IF( LDA.LT.MAX( 1, MINLDA ) ) THEN 00409 INFO = -14 00410 END IF 00411 * 00412 IF( INFO.NE.0 ) THEN 00413 CALL XERBLA( 'SLATMS', -INFO ) 00414 RETURN 00415 END IF 00416 * 00417 * Initialize random number generator 00418 * 00419 DO 10 I = 1, 4 00420 ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 ) 00421 10 CONTINUE 00422 * 00423 IF( MOD( ISEED( 4 ), 2 ).NE.1 ) 00424 $ ISEED( 4 ) = ISEED( 4 ) + 1 00425 * 00426 * 2) Set up D if indicated. 00427 * 00428 * Compute D according to COND and MODE 00429 * 00430 CALL SLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, MNMIN, IINFO ) 00431 IF( IINFO.NE.0 ) THEN 00432 INFO = 1 00433 RETURN 00434 END IF 00435 * 00436 * Choose Top-Down if D is (apparently) increasing, 00437 * Bottom-Up if D is (apparently) decreasing. 00438 * 00439 IF( ABS( D( 1 ) ).LE.ABS( D( MNMIN ) ) ) THEN 00440 TOPDWN = .TRUE. 00441 ELSE 00442 TOPDWN = .FALSE. 00443 END IF 00444 * 00445 IF( MODE.NE.0 .AND. ABS( MODE ).NE.6 ) THEN 00446 * 00447 * Scale by DMAX 00448 * 00449 TEMP = ABS( D( 1 ) ) 00450 DO 20 I = 2, MNMIN 00451 TEMP = MAX( TEMP, ABS( D( I ) ) ) 00452 20 CONTINUE 00453 * 00454 IF( TEMP.GT.ZERO ) THEN 00455 ALPHA = DMAX / TEMP 00456 ELSE 00457 INFO = 2 00458 RETURN 00459 END IF 00460 * 00461 CALL SSCAL( MNMIN, ALPHA, D, 1 ) 00462 * 00463 END IF 00464 * 00465 * 3) Generate Banded Matrix using Givens rotations. 00466 * Also the special case of UUB=LLB=0 00467 * 00468 * Compute Addressing constants to cover all 00469 * storage formats. Whether GE, SY, GB, or SB, 00470 * upper or lower triangle or both, 00471 * the (i,j)-th element is in 00472 * A( i - ISKEW*j + IOFFST, j ) 00473 * 00474 IF( IPACK.GT.4 ) THEN 00475 ILDA = LDA - 1 00476 ISKEW = 1 00477 IF( IPACK.GT.5 ) THEN 00478 IOFFST = UUB + 1 00479 ELSE 00480 IOFFST = 1 00481 END IF 00482 ELSE 00483 ILDA = LDA 00484 ISKEW = 0 00485 IOFFST = 0 00486 END IF 00487 * 00488 * IPACKG is the format that the matrix is generated in. If this is 00489 * different from IPACK, then the matrix must be repacked at the 00490 * end. It also signals how to compute the norm, for scaling. 00491 * 00492 IPACKG = 0 00493 CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) 00494 * 00495 * Diagonal Matrix -- We are done, unless it 00496 * is to be stored SP/PP/TP (PACK='R' or 'C') 00497 * 00498 IF( LLB.EQ.0 .AND. UUB.EQ.0 ) THEN 00499 CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFST, 1 ), ILDA+1 ) 00500 IF( IPACK.LE.2 .OR. IPACK.GE.5 ) 00501 $ IPACKG = IPACK 00502 * 00503 ELSE IF( GIVENS ) THEN 00504 * 00505 * Check whether to use Givens rotations, 00506 * Householder transformations, or nothing. 00507 * 00508 IF( ISYM.EQ.1 ) THEN 00509 * 00510 * Non-symmetric -- A = U D V 00511 * 00512 IF( IPACK.GT.4 ) THEN 00513 IPACKG = IPACK 00514 ELSE 00515 IPACKG = 0 00516 END IF 00517 * 00518 CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFST, 1 ), ILDA+1 ) 00519 * 00520 IF( TOPDWN ) THEN 00521 JKL = 0 00522 DO 50 JKU = 1, UUB 00523 * 00524 * Transform from bandwidth JKL, JKU-1 to JKL, JKU 00525 * 00526 * Last row actually rotated is M 00527 * Last column actually rotated is MIN( M+JKU, N ) 00528 * 00529 DO 40 JR = 1, MIN( M+JKU, N ) + JKL - 1 00530 EXTRA = ZERO 00531 ANGLE = TWOPI*SLARND( 1, ISEED ) 00532 C = COS( ANGLE ) 00533 S = SIN( ANGLE ) 00534 ICOL = MAX( 1, JR-JKL ) 00535 IF( JR.LT.M ) THEN 00536 IL = MIN( N, JR+JKU ) + 1 - ICOL 00537 CALL SLAROT( .TRUE., JR.GT.JKL, .FALSE., IL, C, 00538 $ S, A( JR-ISKEW*ICOL+IOFFST, ICOL ), 00539 $ ILDA, EXTRA, DUMMY ) 00540 END IF 00541 * 00542 * Chase "EXTRA" back up 00543 * 00544 IR = JR 00545 IC = ICOL 00546 DO 30 JCH = JR - JKL, 1, -JKL - JKU 00547 IF( IR.LT.M ) THEN 00548 CALL SLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST, 00549 $ IC+1 ), EXTRA, C, S, DUMMY ) 00550 END IF 00551 IROW = MAX( 1, JCH-JKU ) 00552 IL = IR + 2 - IROW 00553 TEMP = ZERO 00554 ILTEMP = JCH.GT.JKU 00555 CALL SLAROT( .FALSE., ILTEMP, .TRUE., IL, C, -S, 00556 $ A( IROW-ISKEW*IC+IOFFST, IC ), 00557 $ ILDA, TEMP, EXTRA ) 00558 IF( ILTEMP ) THEN 00559 CALL SLARTG( A( IROW+1-ISKEW*( IC+1 )+IOFFST, 00560 $ IC+1 ), TEMP, C, S, DUMMY ) 00561 ICOL = MAX( 1, JCH-JKU-JKL ) 00562 IL = IC + 2 - ICOL 00563 EXTRA = ZERO 00564 CALL SLAROT( .TRUE., JCH.GT.JKU+JKL, .TRUE., 00565 $ IL, C, -S, A( IROW-ISKEW*ICOL+ 00566 $ IOFFST, ICOL ), ILDA, EXTRA, 00567 $ TEMP ) 00568 IC = ICOL 00569 IR = IROW 00570 END IF 00571 30 CONTINUE 00572 40 CONTINUE 00573 50 CONTINUE 00574 * 00575 JKU = UUB 00576 DO 80 JKL = 1, LLB 00577 * 00578 * Transform from bandwidth JKL-1, JKU to JKL, JKU 00579 * 00580 DO 70 JC = 1, MIN( N+JKL, M ) + JKU - 1 00581 EXTRA = ZERO 00582 ANGLE = TWOPI*SLARND( 1, ISEED ) 00583 C = COS( ANGLE ) 00584 S = SIN( ANGLE ) 00585 IROW = MAX( 1, JC-JKU ) 00586 IF( JC.LT.N ) THEN 00587 IL = MIN( M, JC+JKL ) + 1 - IROW 00588 CALL SLAROT( .FALSE., JC.GT.JKU, .FALSE., IL, C, 00589 $ S, A( IROW-ISKEW*JC+IOFFST, JC ), 00590 $ ILDA, EXTRA, DUMMY ) 00591 END IF 00592 * 00593 * Chase "EXTRA" back up 00594 * 00595 IC = JC 00596 IR = IROW 00597 DO 60 JCH = JC - JKU, 1, -JKL - JKU 00598 IF( IC.LT.N ) THEN 00599 CALL SLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST, 00600 $ IC+1 ), EXTRA, C, S, DUMMY ) 00601 END IF 00602 ICOL = MAX( 1, JCH-JKL ) 00603 IL = IC + 2 - ICOL 00604 TEMP = ZERO 00605 ILTEMP = JCH.GT.JKL 00606 CALL SLAROT( .TRUE., ILTEMP, .TRUE., IL, C, -S, 00607 $ A( IR-ISKEW*ICOL+IOFFST, ICOL ), 00608 $ ILDA, TEMP, EXTRA ) 00609 IF( ILTEMP ) THEN 00610 CALL SLARTG( A( IR+1-ISKEW*( ICOL+1 )+IOFFST, 00611 $ ICOL+1 ), TEMP, C, S, DUMMY ) 00612 IROW = MAX( 1, JCH-JKL-JKU ) 00613 IL = IR + 2 - IROW 00614 EXTRA = ZERO 00615 CALL SLAROT( .FALSE., JCH.GT.JKL+JKU, .TRUE., 00616 $ IL, C, -S, A( IROW-ISKEW*ICOL+ 00617 $ IOFFST, ICOL ), ILDA, EXTRA, 00618 $ TEMP ) 00619 IC = ICOL 00620 IR = IROW 00621 END IF 00622 60 CONTINUE 00623 70 CONTINUE 00624 80 CONTINUE 00625 * 00626 ELSE 00627 * 00628 * Bottom-Up -- Start at the bottom right. 00629 * 00630 JKL = 0 00631 DO 110 JKU = 1, UUB 00632 * 00633 * Transform from bandwidth JKL, JKU-1 to JKL, JKU 00634 * 00635 * First row actually rotated is M 00636 * First column actually rotated is MIN( M+JKU, N ) 00637 * 00638 IENDCH = MIN( M, N+JKL ) - 1 00639 DO 100 JC = MIN( M+JKU, N ) - 1, 1 - JKL, -1 00640 EXTRA = ZERO 00641 ANGLE = TWOPI*SLARND( 1, ISEED ) 00642 C = COS( ANGLE ) 00643 S = SIN( ANGLE ) 00644 IROW = MAX( 1, JC-JKU+1 ) 00645 IF( JC.GT.0 ) THEN 00646 IL = MIN( M, JC+JKL+1 ) + 1 - IROW 00647 CALL SLAROT( .FALSE., .FALSE., JC+JKL.LT.M, IL, 00648 $ C, S, A( IROW-ISKEW*JC+IOFFST, 00649 $ JC ), ILDA, DUMMY, EXTRA ) 00650 END IF 00651 * 00652 * Chase "EXTRA" back down 00653 * 00654 IC = JC 00655 DO 90 JCH = JC + JKL, IENDCH, JKL + JKU 00656 ILEXTR = IC.GT.0 00657 IF( ILEXTR ) THEN 00658 CALL SLARTG( A( JCH-ISKEW*IC+IOFFST, IC ), 00659 $ EXTRA, C, S, DUMMY ) 00660 END IF 00661 IC = MAX( 1, IC ) 00662 ICOL = MIN( N-1, JCH+JKU ) 00663 ILTEMP = JCH + JKU.LT.N 00664 TEMP = ZERO 00665 CALL SLAROT( .TRUE., ILEXTR, ILTEMP, ICOL+2-IC, 00666 $ C, S, A( JCH-ISKEW*IC+IOFFST, IC ), 00667 $ ILDA, EXTRA, TEMP ) 00668 IF( ILTEMP ) THEN 00669 CALL SLARTG( A( JCH-ISKEW*ICOL+IOFFST, 00670 $ ICOL ), TEMP, C, S, DUMMY ) 00671 IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH 00672 EXTRA = ZERO 00673 CALL SLAROT( .FALSE., .TRUE., 00674 $ JCH+JKL+JKU.LE.IENDCH, IL, C, S, 00675 $ A( JCH-ISKEW*ICOL+IOFFST, 00676 $ ICOL ), ILDA, TEMP, EXTRA ) 00677 IC = ICOL 00678 END IF 00679 90 CONTINUE 00680 100 CONTINUE 00681 110 CONTINUE 00682 * 00683 JKU = UUB 00684 DO 140 JKL = 1, LLB 00685 * 00686 * Transform from bandwidth JKL-1, JKU to JKL, JKU 00687 * 00688 * First row actually rotated is MIN( N+JKL, M ) 00689 * First column actually rotated is N 00690 * 00691 IENDCH = MIN( N, M+JKU ) - 1 00692 DO 130 JR = MIN( N+JKL, M ) - 1, 1 - JKU, -1 00693 EXTRA = ZERO 00694 ANGLE = TWOPI*SLARND( 1, ISEED ) 00695 C = COS( ANGLE ) 00696 S = SIN( ANGLE ) 00697 ICOL = MAX( 1, JR-JKL+1 ) 00698 IF( JR.GT.0 ) THEN 00699 IL = MIN( N, JR+JKU+1 ) + 1 - ICOL 00700 CALL SLAROT( .TRUE., .FALSE., JR+JKU.LT.N, IL, 00701 $ C, S, A( JR-ISKEW*ICOL+IOFFST, 00702 $ ICOL ), ILDA, DUMMY, EXTRA ) 00703 END IF 00704 * 00705 * Chase "EXTRA" back down 00706 * 00707 IR = JR 00708 DO 120 JCH = JR + JKU, IENDCH, JKL + JKU 00709 ILEXTR = IR.GT.0 00710 IF( ILEXTR ) THEN 00711 CALL SLARTG( A( IR-ISKEW*JCH+IOFFST, JCH ), 00712 $ EXTRA, C, S, DUMMY ) 00713 END IF 00714 IR = MAX( 1, IR ) 00715 IROW = MIN( M-1, JCH+JKL ) 00716 ILTEMP = JCH + JKL.LT.M 00717 TEMP = ZERO 00718 CALL SLAROT( .FALSE., ILEXTR, ILTEMP, IROW+2-IR, 00719 $ C, S, A( IR-ISKEW*JCH+IOFFST, 00720 $ JCH ), ILDA, EXTRA, TEMP ) 00721 IF( ILTEMP ) THEN 00722 CALL SLARTG( A( IROW-ISKEW*JCH+IOFFST, JCH ), 00723 $ TEMP, C, S, DUMMY ) 00724 IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH 00725 EXTRA = ZERO 00726 CALL SLAROT( .TRUE., .TRUE., 00727 $ JCH+JKL+JKU.LE.IENDCH, IL, C, S, 00728 $ A( IROW-ISKEW*JCH+IOFFST, JCH ), 00729 $ ILDA, TEMP, EXTRA ) 00730 IR = IROW 00731 END IF 00732 120 CONTINUE 00733 130 CONTINUE 00734 140 CONTINUE 00735 END IF 00736 * 00737 ELSE 00738 * 00739 * Symmetric -- A = U D U' 00740 * 00741 IPACKG = IPACK 00742 IOFFG = IOFFST 00743 * 00744 IF( TOPDWN ) THEN 00745 * 00746 * Top-Down -- Generate Upper triangle only 00747 * 00748 IF( IPACK.GE.5 ) THEN 00749 IPACKG = 6 00750 IOFFG = UUB + 1 00751 ELSE 00752 IPACKG = 1 00753 END IF 00754 CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFG, 1 ), ILDA+1 ) 00755 * 00756 DO 170 K = 1, UUB 00757 DO 160 JC = 1, N - 1 00758 IROW = MAX( 1, JC-K ) 00759 IL = MIN( JC+1, K+2 ) 00760 EXTRA = ZERO 00761 TEMP = A( JC-ISKEW*( JC+1 )+IOFFG, JC+1 ) 00762 ANGLE = TWOPI*SLARND( 1, ISEED ) 00763 C = COS( ANGLE ) 00764 S = SIN( ANGLE ) 00765 CALL SLAROT( .FALSE., JC.GT.K, .TRUE., IL, C, S, 00766 $ A( IROW-ISKEW*JC+IOFFG, JC ), ILDA, 00767 $ EXTRA, TEMP ) 00768 CALL SLAROT( .TRUE., .TRUE., .FALSE., 00769 $ MIN( K, N-JC )+1, C, S, 00770 $ A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA, 00771 $ TEMP, DUMMY ) 00772 * 00773 * Chase EXTRA back up the matrix 00774 * 00775 ICOL = JC 00776 DO 150 JCH = JC - K, 1, -K 00777 CALL SLARTG( A( JCH+1-ISKEW*( ICOL+1 )+IOFFG, 00778 $ ICOL+1 ), EXTRA, C, S, DUMMY ) 00779 TEMP = A( JCH-ISKEW*( JCH+1 )+IOFFG, JCH+1 ) 00780 CALL SLAROT( .TRUE., .TRUE., .TRUE., K+2, C, -S, 00781 $ A( ( 1-ISKEW )*JCH+IOFFG, JCH ), 00782 $ ILDA, TEMP, EXTRA ) 00783 IROW = MAX( 1, JCH-K ) 00784 IL = MIN( JCH+1, K+2 ) 00785 EXTRA = ZERO 00786 CALL SLAROT( .FALSE., JCH.GT.K, .TRUE., IL, C, 00787 $ -S, A( IROW-ISKEW*JCH+IOFFG, JCH ), 00788 $ ILDA, EXTRA, TEMP ) 00789 ICOL = JCH 00790 150 CONTINUE 00791 160 CONTINUE 00792 170 CONTINUE 00793 * 00794 * If we need lower triangle, copy from upper. Note that 00795 * the order of copying is chosen to work for 'q' -> 'b' 00796 * 00797 IF( IPACK.NE.IPACKG .AND. IPACK.NE.3 ) THEN 00798 DO 190 JC = 1, N 00799 IROW = IOFFST - ISKEW*JC 00800 DO 180 JR = JC, MIN( N, JC+UUB ) 00801 A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR ) 00802 180 CONTINUE 00803 190 CONTINUE 00804 IF( IPACK.EQ.5 ) THEN 00805 DO 210 JC = N - UUB + 1, N 00806 DO 200 JR = N + 2 - JC, UUB + 1 00807 A( JR, JC ) = ZERO 00808 200 CONTINUE 00809 210 CONTINUE 00810 END IF 00811 IF( IPACKG.EQ.6 ) THEN 00812 IPACKG = IPACK 00813 ELSE 00814 IPACKG = 0 00815 END IF 00816 END IF 00817 ELSE 00818 * 00819 * Bottom-Up -- Generate Lower triangle only 00820 * 00821 IF( IPACK.GE.5 ) THEN 00822 IPACKG = 5 00823 IF( IPACK.EQ.6 ) 00824 $ IOFFG = 1 00825 ELSE 00826 IPACKG = 2 00827 END IF 00828 CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFG, 1 ), ILDA+1 ) 00829 * 00830 DO 240 K = 1, UUB 00831 DO 230 JC = N - 1, 1, -1 00832 IL = MIN( N+1-JC, K+2 ) 00833 EXTRA = ZERO 00834 TEMP = A( 1+( 1-ISKEW )*JC+IOFFG, JC ) 00835 ANGLE = TWOPI*SLARND( 1, ISEED ) 00836 C = COS( ANGLE ) 00837 S = -SIN( ANGLE ) 00838 CALL SLAROT( .FALSE., .TRUE., N-JC.GT.K, IL, C, S, 00839 $ A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA, 00840 $ TEMP, EXTRA ) 00841 ICOL = MAX( 1, JC-K+1 ) 00842 CALL SLAROT( .TRUE., .FALSE., .TRUE., JC+2-ICOL, C, 00843 $ S, A( JC-ISKEW*ICOL+IOFFG, ICOL ), 00844 $ ILDA, DUMMY, TEMP ) 00845 * 00846 * Chase EXTRA back down the matrix 00847 * 00848 ICOL = JC 00849 DO 220 JCH = JC + K, N - 1, K 00850 CALL SLARTG( A( JCH-ISKEW*ICOL+IOFFG, ICOL ), 00851 $ EXTRA, C, S, DUMMY ) 00852 TEMP = A( 1+( 1-ISKEW )*JCH+IOFFG, JCH ) 00853 CALL SLAROT( .TRUE., .TRUE., .TRUE., K+2, C, S, 00854 $ A( JCH-ISKEW*ICOL+IOFFG, ICOL ), 00855 $ ILDA, EXTRA, TEMP ) 00856 IL = MIN( N+1-JCH, K+2 ) 00857 EXTRA = ZERO 00858 CALL SLAROT( .FALSE., .TRUE., N-JCH.GT.K, IL, C, 00859 $ S, A( ( 1-ISKEW )*JCH+IOFFG, JCH ), 00860 $ ILDA, TEMP, EXTRA ) 00861 ICOL = JCH 00862 220 CONTINUE 00863 230 CONTINUE 00864 240 CONTINUE 00865 * 00866 * If we need upper triangle, copy from lower. Note that 00867 * the order of copying is chosen to work for 'b' -> 'q' 00868 * 00869 IF( IPACK.NE.IPACKG .AND. IPACK.NE.4 ) THEN 00870 DO 260 JC = N, 1, -1 00871 IROW = IOFFST - ISKEW*JC 00872 DO 250 JR = JC, MAX( 1, JC-UUB ), -1 00873 A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR ) 00874 250 CONTINUE 00875 260 CONTINUE 00876 IF( IPACK.EQ.6 ) THEN 00877 DO 280 JC = 1, UUB 00878 DO 270 JR = 1, UUB + 1 - JC 00879 A( JR, JC ) = ZERO 00880 270 CONTINUE 00881 280 CONTINUE 00882 END IF 00883 IF( IPACKG.EQ.5 ) THEN 00884 IPACKG = IPACK 00885 ELSE 00886 IPACKG = 0 00887 END IF 00888 END IF 00889 END IF 00890 END IF 00891 * 00892 ELSE 00893 * 00894 * 4) Generate Banded Matrix by first 00895 * Rotating by random Unitary matrices, 00896 * then reducing the bandwidth using Householder 00897 * transformations. 00898 * 00899 * Note: we should get here only if LDA .ge. N 00900 * 00901 IF( ISYM.EQ.1 ) THEN 00902 * 00903 * Non-symmetric -- A = U D V 00904 * 00905 CALL SLAGGE( MR, NC, LLB, UUB, D, A, LDA, ISEED, WORK, 00906 $ IINFO ) 00907 ELSE 00908 * 00909 * Symmetric -- A = U D U' 00910 * 00911 CALL SLAGSY( M, LLB, D, A, LDA, ISEED, WORK, IINFO ) 00912 * 00913 END IF 00914 IF( IINFO.NE.0 ) THEN 00915 INFO = 3 00916 RETURN 00917 END IF 00918 END IF 00919 * 00920 * 5) Pack the matrix 00921 * 00922 IF( IPACK.NE.IPACKG ) THEN 00923 IF( IPACK.EQ.1 ) THEN 00924 * 00925 * 'U' -- Upper triangular, not packed 00926 * 00927 DO 300 J = 1, M 00928 DO 290 I = J + 1, M 00929 A( I, J ) = ZERO 00930 290 CONTINUE 00931 300 CONTINUE 00932 * 00933 ELSE IF( IPACK.EQ.2 ) THEN 00934 * 00935 * 'L' -- Lower triangular, not packed 00936 * 00937 DO 320 J = 2, M 00938 DO 310 I = 1, J - 1 00939 A( I, J ) = ZERO 00940 310 CONTINUE 00941 320 CONTINUE 00942 * 00943 ELSE IF( IPACK.EQ.3 ) THEN 00944 * 00945 * 'C' -- Upper triangle packed Columnwise. 00946 * 00947 ICOL = 1 00948 IROW = 0 00949 DO 340 J = 1, M 00950 DO 330 I = 1, J 00951 IROW = IROW + 1 00952 IF( IROW.GT.LDA ) THEN 00953 IROW = 1 00954 ICOL = ICOL + 1 00955 END IF 00956 A( IROW, ICOL ) = A( I, J ) 00957 330 CONTINUE 00958 340 CONTINUE 00959 * 00960 ELSE IF( IPACK.EQ.4 ) THEN 00961 * 00962 * 'R' -- Lower triangle packed Columnwise. 00963 * 00964 ICOL = 1 00965 IROW = 0 00966 DO 360 J = 1, M 00967 DO 350 I = J, M 00968 IROW = IROW + 1 00969 IF( IROW.GT.LDA ) THEN 00970 IROW = 1 00971 ICOL = ICOL + 1 00972 END IF 00973 A( IROW, ICOL ) = A( I, J ) 00974 350 CONTINUE 00975 360 CONTINUE 00976 * 00977 ELSE IF( IPACK.GE.5 ) THEN 00978 * 00979 * 'B' -- The lower triangle is packed as a band matrix. 00980 * 'Q' -- The upper triangle is packed as a band matrix. 00981 * 'Z' -- The whole matrix is packed as a band matrix. 00982 * 00983 IF( IPACK.EQ.5 ) 00984 $ UUB = 0 00985 IF( IPACK.EQ.6 ) 00986 $ LLB = 0 00987 * 00988 DO 380 J = 1, UUB 00989 DO 370 I = MIN( J+LLB, M ), 1, -1 00990 A( I-J+UUB+1, J ) = A( I, J ) 00991 370 CONTINUE 00992 380 CONTINUE 00993 * 00994 DO 400 J = UUB + 2, N 00995 DO 390 I = J - UUB, MIN( J+LLB, M ) 00996 A( I-J+UUB+1, J ) = A( I, J ) 00997 390 CONTINUE 00998 400 CONTINUE 00999 END IF 01000 * 01001 * If packed, zero out extraneous elements. 01002 * 01003 * Symmetric/Triangular Packed -- 01004 * zero out everything after A(IROW,ICOL) 01005 * 01006 IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN 01007 DO 420 JC = ICOL, M 01008 DO 410 JR = IROW + 1, LDA 01009 A( JR, JC ) = ZERO 01010 410 CONTINUE 01011 IROW = 0 01012 420 CONTINUE 01013 * 01014 ELSE IF( IPACK.GE.5 ) THEN 01015 * 01016 * Packed Band -- 01017 * 1st row is now in A( UUB+2-j, j), zero above it 01018 * m-th row is now in A( M+UUB-j,j), zero below it 01019 * last non-zero diagonal is now in A( UUB+LLB+1,j ), 01020 * zero below it, too. 01021 * 01022 IR1 = UUB + LLB + 2 01023 IR2 = UUB + M + 2 01024 DO 450 JC = 1, N 01025 DO 430 JR = 1, UUB + 1 - JC 01026 A( JR, JC ) = ZERO 01027 430 CONTINUE 01028 DO 440 JR = MAX( 1, MIN( IR1, IR2-JC ) ), LDA 01029 A( JR, JC ) = ZERO 01030 440 CONTINUE 01031 450 CONTINUE 01032 END IF 01033 END IF 01034 * 01035 RETURN 01036 * 01037 * End of SLATMS 01038 * 01039 END
1.7.3 
