numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/MATGEN/slatms.f | 40791B | -rw-r--r-- |
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*> \brief \b SLATMS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, * KL, KU, PACK, A, LDA, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER DIST, PACK, SYM * INTEGER INFO, KL, KU, LDA, M, MODE, N * REAL COND, DMAX * .. * .. Array Arguments .. * INTEGER ISEED( 4 ) * REAL A( LDA, * ), D( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLATMS generates random matrices with specified singular values *> (or symmetric/hermitian with specified eigenvalues) *> for testing LAPACK programs. *> *> SLATMS operates by applying the following sequence of *> operations: *> *> Set the diagonal to D, where D may be input or *> computed according to MODE, COND, DMAX, and SYM *> as described below. *> *> Generate a matrix with the appropriate band structure, by one *> of two methods: *> *> Method A: *> Generate a dense M x N matrix by multiplying D on the left *> and the right by random unitary matrices, then: *> *> Reduce the bandwidth according to KL and KU, using *> Householder transformations. *> *> Method B: *> Convert the bandwidth-0 (i.e., diagonal) matrix to a *> bandwidth-1 matrix using Givens rotations, "chasing" *> out-of-band elements back, much as in QR; then *> convert the bandwidth-1 to a bandwidth-2 matrix, etc. *> Note that for reasonably small bandwidths (relative to *> M and N) this requires less storage, as a dense matrix *> is not generated. Also, for symmetric matrices, only *> one triangle is generated. *> *> Method A is chosen if the bandwidth is a large fraction of the *> order of the matrix, and LDA is at least M (so a dense *> matrix can be stored.) Method B is chosen if the bandwidth *> is small (< 1/2 N for symmetric, < .3 N+M for *> non-symmetric), or LDA is less than M and not less than the *> bandwidth. *> *> Pack the matrix if desired. Options specified by PACK are: *> no packing *> zero out upper half (if symmetric) *> zero out lower half (if symmetric) *> store the upper half columnwise (if symmetric or upper *> triangular) *> store the lower half columnwise (if symmetric or lower *> triangular) *> store the lower triangle in banded format (if symmetric *> or lower triangular) *> store the upper triangle in banded format (if symmetric *> or upper triangular) *> store the entire matrix in banded format *> If Method B is chosen, and band format is specified, then the *> matrix will be generated in the band format, so no repacking *> will be necessary. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of A. Not modified. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of A. Not modified. *> \endverbatim *> *> \param[in] DIST *> \verbatim *> DIST is CHARACTER*1 *> On entry, DIST specifies the type of distribution to be used *> to generate the random eigen-/singular values. *> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) *> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) *> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) *> Not modified. *> \endverbatim *> *> \param[in,out] ISEED *> \verbatim *> ISEED is INTEGER array, dimension ( 4 ) *> On entry ISEED specifies the seed of the random number *> generator. They should lie between 0 and 4095 inclusive, *> and ISEED(4) should be odd. The random number generator *> uses a linear congruential sequence limited to small *> integers, and so should produce machine independent *> random numbers. The values of ISEED are changed on *> exit, and can be used in the next call to SLATMS *> to continue the same random number sequence. *> Changed on exit. *> \endverbatim *> *> \param[in] SYM *> \verbatim *> SYM is CHARACTER*1 *> If SYM='S' or 'H', the generated matrix is symmetric, with *> eigenvalues specified by D, COND, MODE, and DMAX; they *> may be positive, negative, or zero. *> If SYM='P', the generated matrix is symmetric, with *> eigenvalues (= singular values) specified by D, COND, *> MODE, and DMAX; they will not be negative. *> If SYM='N', the generated matrix is nonsymmetric, with *> singular values specified by D, COND, MODE, and DMAX; *> they will not be negative. *> Not modified. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is REAL array, dimension ( MIN( M , N ) ) *> This array is used to specify the singular values or *> eigenvalues of A (see SYM, above.) If MODE=0, then D is *> assumed to contain the singular/eigenvalues, otherwise *> they will be computed according to MODE, COND, and DMAX, *> and placed in D. *> Modified if MODE is nonzero. *> \endverbatim *> *> \param[in] MODE *> \verbatim *> MODE is INTEGER *> On entry this describes how the singular/eigenvalues are to *> be specified: *> MODE = 0 means use D as input *> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND *> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND *> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) *> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) *> MODE = 5 sets D to random numbers in the range *> ( 1/COND , 1 ) such that their logarithms *> are uniformly distributed. *> MODE = 6 set D to random numbers from same distribution *> as the rest of the matrix. *> MODE < 0 has the same meaning as ABS(MODE), except that *> the order of the elements of D is reversed. *> Thus if MODE is positive, D has entries ranging from *> 1 to 1/COND, if negative, from 1/COND to 1, *> If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then *> the elements of D will also be multiplied by a random *> sign (i.e., +1 or -1.) *> Not modified. *> \endverbatim *> *> \param[in] COND *> \verbatim *> COND is REAL *> On entry, this is used as described under MODE above. *> If used, it must be >= 1. Not modified. *> \endverbatim *> *> \param[in] DMAX *> \verbatim *> DMAX is REAL *> If MODE is neither -6, 0 nor 6, the contents of D, as *> computed according to MODE and COND, will be scaled by *> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or *> singular value (which is to say the norm) will be abs(DMAX). *> Note that DMAX need not be positive: if DMAX is negative *> (or zero), D will be scaled by a negative number (or zero). *> Not modified. *> \endverbatim *> *> \param[in] KL *> \verbatim *> KL is INTEGER *> This specifies the lower bandwidth of the matrix. For *> example, KL=0 implies upper triangular, KL=1 implies upper *> Hessenberg, and KL being at least M-1 means that the matrix *> has full lower bandwidth. KL must equal KU if the matrix *> is symmetric. *> Not modified. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is INTEGER *> This specifies the upper bandwidth of the matrix. For *> example, KU=0 implies lower triangular, KU=1 implies lower *> Hessenberg, and KU being at least N-1 means that the matrix *> has full upper bandwidth. KL must equal KU if the matrix *> is symmetric. *> Not modified. *> \endverbatim *> *> \param[in] PACK *> \verbatim *> PACK is CHARACTER*1 *> This specifies packing of matrix as follows: *> 'N' => no packing *> 'U' => zero out all subdiagonal entries (if symmetric) *> 'L' => zero out all superdiagonal entries (if symmetric) *> 'C' => store the upper triangle columnwise *> (only if the matrix is symmetric or upper triangular) *> 'R' => store the lower triangle columnwise *> (only if the matrix is symmetric or lower triangular) *> 'B' => store the lower triangle in band storage scheme *> (only if matrix symmetric or lower triangular) *> 'Q' => store the upper triangle in band storage scheme *> (only if matrix symmetric or upper triangular) *> 'Z' => store the entire matrix in band storage scheme *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) *> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB or TB - use 'B' or 'Q' *> PP, SP or TP - use 'C' or 'R' *> *> If two calls to SLATMS differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is REAL array, dimension ( LDA, N ) *> On exit A is the desired test matrix. A is first generated *> in full (unpacked) form, and then packed, if so specified *> by PACK. Thus, the first M elements of the first N *> columns will always be modified. If PACK specifies a *> packed or banded storage scheme, all LDA elements of the *> first N columns will be modified; the elements of the *> array which do not correspond to elements of the generated *> matrix are set to zero. *> Modified. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> LDA specifies the first dimension of A as declared in the *> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then *> LDA must be at least M. If PACK='B' or 'Q', then LDA must *> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). *> If PACK='Z', LDA must be large enough to hold the packed *> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. *> Not modified. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension ( 3*MAX( N , M ) ) *> Workspace. *> Modified. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> Error code. On exit, INFO will be set to one of the *> following values: *> 0 => normal return *> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' *> -2 => N negative *> -3 => DIST illegal string *> -5 => SYM illegal string *> -7 => MODE not in range -6 to 6 *> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 *> -10 => KL negative *> -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL *> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; *> or PACK='C' or 'Q' and SYM='N' and KL is not zero; *> or PACK='R' or 'B' and SYM='N' and KU is not zero; *> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not *> N. *> -14 => LDA is less than M, or PACK='Z' and LDA is less than *> MIN(KU,N-1) + MIN(KL,M-1) + 1. *> 1 => Error return from SLATM1 *> 2 => Cannot scale to DMAX (max. sing. value is 0) *> 3 => Error return from SLAGGE or SLAGSY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup real_matgen * * ===================================================================== SUBROUTINE SLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ KL, KU, PACK, A, LDA, WORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER DIST, PACK, SYM INTEGER INFO, KL, KU, LDA, M, MODE, N REAL COND, DMAX * .. * .. Array Arguments .. INTEGER ISEED( 4 ) REAL A( LDA, * ), D( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) REAL ONE PARAMETER ( ONE = 1.0E0 ) REAL TWOPI PARAMETER ( TWOPI = 6.28318530717958647692528676655900576839E+0 ) * .. * .. Local Scalars .. LOGICAL GIVENS, ILEXTR, ILTEMP, TOPDWN INTEGER I, IC, ICOL, IDIST, IENDCH, IINFO, IL, ILDA, $ IOFFG, IOFFST, IPACK, IPACKG, IR, IR1, IR2, $ IROW, IRSIGN, ISKEW, ISYM, ISYMPK, J, JC, JCH, $ JKL, JKU, JR, K, LLB, MINLDA, MNMIN, MR, NC, $ UUB REAL ALPHA, ANGLE, C, DUMMY, EXTRA, S, TEMP * .. * .. External Functions .. LOGICAL LSAME REAL SLARND EXTERNAL LSAME, SLARND * .. * .. External Subroutines .. EXTERNAL SCOPY, SLAGGE, SLAGSY, $ SLAROT, SLARTG, SLATM1, $ SLASET, SSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, COS, MAX, MIN, MOD, REAL, SIN * .. * .. Executable Statements .. * * 1) Decode and Test the input parameters. * Initialize flags & seed. * INFO = 0 * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * * Decode DIST * IF( LSAME( DIST, 'U' ) ) THEN IDIST = 1 ELSE IF( LSAME( DIST, 'S' ) ) THEN IDIST = 2 ELSE IF( LSAME( DIST, 'N' ) ) THEN IDIST = 3 ELSE IDIST = -1 END IF * * Decode SYM * IF( LSAME( SYM, 'N' ) ) THEN ISYM = 1 IRSIGN = 0 ELSE IF( LSAME( SYM, 'P' ) ) THEN ISYM = 2 IRSIGN = 0 ELSE IF( LSAME( SYM, 'S' ) ) THEN ISYM = 2 IRSIGN = 1 ELSE IF( LSAME( SYM, 'H' ) ) THEN ISYM = 2 IRSIGN = 1 ELSE ISYM = -1 END IF * * Decode PACK * ISYMPK = 0 IF( LSAME( PACK, 'N' ) ) THEN IPACK = 0 ELSE IF( LSAME( PACK, 'U' ) ) THEN IPACK = 1 ISYMPK = 1 ELSE IF( LSAME( PACK, 'L' ) ) THEN IPACK = 2 ISYMPK = 1 ELSE IF( LSAME( PACK, 'C' ) ) THEN IPACK = 3 ISYMPK = 2 ELSE IF( LSAME( PACK, 'R' ) ) THEN IPACK = 4 ISYMPK = 3 ELSE IF( LSAME( PACK, 'B' ) ) THEN IPACK = 5 ISYMPK = 3 ELSE IF( LSAME( PACK, 'Q' ) ) THEN IPACK = 6 ISYMPK = 2 ELSE IF( LSAME( PACK, 'Z' ) ) THEN IPACK = 7 ELSE IPACK = -1 END IF * * Set certain internal parameters * MNMIN = MIN( M, N ) LLB = MIN( KL, M-1 ) UUB = MIN( KU, N-1 ) MR = MIN( M, N+LLB ) NC = MIN( N, M+UUB ) * IF( IPACK.EQ.5 .OR. IPACK.EQ.6 ) THEN MINLDA = UUB + 1 ELSE IF( IPACK.EQ.7 ) THEN MINLDA = LLB + UUB + 1 ELSE MINLDA = M END IF * * Use Givens rotation method if bandwidth small enough, * or if LDA is too small to store the matrix unpacked. * GIVENS = .FALSE. IF( ISYM.EQ.1 ) THEN IF( REAL( LLB+UUB ).LT.0.3*REAL( MAX( 1, MR+NC ) ) ) $ GIVENS = .TRUE. ELSE IF( 2*LLB.LT.M ) $ GIVENS = .TRUE. END IF IF( LDA.LT.M .AND. LDA.GE.MINLDA ) $ GIVENS = .TRUE. * * Set INFO if an error * IF( M.LT.0 ) THEN INFO = -1 ELSE IF( M.NE.N .AND. ISYM.NE.1 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( IDIST.EQ.-1 ) THEN INFO = -3 ELSE IF( ISYM.EQ.-1 ) THEN INFO = -5 ELSE IF( ABS( MODE ).GT.6 ) THEN INFO = -7 ELSE IF( ( MODE.NE.0 .AND. ABS( MODE ).NE.6 ) .AND. COND.LT.ONE ) $ THEN INFO = -8 ELSE IF( KL.LT.0 ) THEN INFO = -10 ELSE IF( KU.LT.0 .OR. ( ISYM.NE.1 .AND. KL.NE.KU ) ) THEN INFO = -11 ELSE IF( IPACK.EQ.-1 .OR. ( ISYMPK.EQ.1 .AND. ISYM.EQ.1 ) .OR. $ ( ISYMPK.EQ.2 .AND. ISYM.EQ.1 .AND. KL.GT.0 ) .OR. $ ( ISYMPK.EQ.3 .AND. ISYM.EQ.1 .AND. KU.GT.0 ) .OR. $ ( ISYMPK.NE.0 .AND. M.NE.N ) ) THEN INFO = -12 ELSE IF( LDA.LT.MAX( 1, MINLDA ) ) THEN INFO = -14 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SLATMS', -INFO ) RETURN END IF * * Initialize random number generator * DO 10 I = 1, 4 ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 ) 10 CONTINUE * IF( MOD( ISEED( 4 ), 2 ).NE.1 ) $ ISEED( 4 ) = ISEED( 4 ) + 1 * * 2) Set up D if indicated. * * Compute D according to COND and MODE * CALL SLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, MNMIN, $ IINFO ) IF( IINFO.NE.0 ) THEN INFO = 1 RETURN END IF * * Choose Top-Down if D is (apparently) increasing, * Bottom-Up if D is (apparently) decreasing. * IF( ABS( D( 1 ) ).LE.ABS( D( MNMIN ) ) ) THEN TOPDWN = .TRUE. ELSE TOPDWN = .FALSE. END IF * IF( MODE.NE.0 .AND. ABS( MODE ).NE.6 ) THEN * * Scale by DMAX * TEMP = ABS( D( 1 ) ) DO 20 I = 2, MNMIN TEMP = MAX( TEMP, ABS( D( I ) ) ) 20 CONTINUE * IF( TEMP.GT.ZERO ) THEN ALPHA = DMAX / TEMP ELSE INFO = 2 RETURN END IF * CALL SSCAL( MNMIN, ALPHA, D, 1 ) * END IF * * 3) Generate Banded Matrix using Givens rotations. * Also the special case of UUB=LLB=0 * * Compute Addressing constants to cover all * storage formats. Whether GE, SY, GB, or SB, * upper or lower triangle or both, * the (i,j)-th element is in * A( i - ISKEW*j + IOFFST, j ) * IF( IPACK.GT.4 ) THEN ILDA = LDA - 1 ISKEW = 1 IF( IPACK.GT.5 ) THEN IOFFST = UUB + 1 ELSE IOFFST = 1 END IF ELSE ILDA = LDA ISKEW = 0 IOFFST = 0 END IF * * IPACKG is the format that the matrix is generated in. If this is * different from IPACK, then the matrix must be repacked at the * end. It also signals how to compute the norm, for scaling. * IPACKG = 0 CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) * * Diagonal Matrix -- We are done, unless it * is to be stored SP/PP/TP (PACK='R' or 'C') * IF( LLB.EQ.0 .AND. UUB.EQ.0 ) THEN CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFST, 1 ), ILDA+1 ) IF( IPACK.LE.2 .OR. IPACK.GE.5 ) $ IPACKG = IPACK * ELSE IF( GIVENS ) THEN * * Check whether to use Givens rotations, * Householder transformations, or nothing. * IF( ISYM.EQ.1 ) THEN * * Non-symmetric -- A = U D V * IF( IPACK.GT.4 ) THEN IPACKG = IPACK ELSE IPACKG = 0 END IF * CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFST, 1 ), ILDA+1 ) * IF( TOPDWN ) THEN JKL = 0 DO 50 JKU = 1, UUB * * Transform from bandwidth JKL, JKU-1 to JKL, JKU * * Last row actually rotated is M * Last column actually rotated is MIN( M+JKU, N ) * DO 40 JR = 1, MIN( M+JKU, N ) + JKL - 1 EXTRA = ZERO ANGLE = TWOPI*SLARND( 1, ISEED ) C = COS( ANGLE ) S = SIN( ANGLE ) ICOL = MAX( 1, JR-JKL ) IF( JR.LT.M ) THEN IL = MIN( N, JR+JKU ) + 1 - ICOL CALL SLAROT( .TRUE., JR.GT.JKL, .FALSE., IL, $ C, $ S, A( JR-ISKEW*ICOL+IOFFST, ICOL ), $ ILDA, EXTRA, DUMMY ) END IF * * Chase "EXTRA" back up * IR = JR IC = ICOL DO 30 JCH = JR - JKL, 1, -JKL - JKU IF( IR.LT.M ) THEN CALL SLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST, $ IC+1 ), EXTRA, C, S, DUMMY ) END IF IROW = MAX( 1, JCH-JKU ) IL = IR + 2 - IROW TEMP = ZERO ILTEMP = JCH.GT.JKU CALL SLAROT( .FALSE., ILTEMP, .TRUE., IL, C, $ -S, $ A( IROW-ISKEW*IC+IOFFST, IC ), $ ILDA, TEMP, EXTRA ) IF( ILTEMP ) THEN CALL SLARTG( A( IROW+1-ISKEW*( IC+1 )+IOFFST, $ IC+1 ), TEMP, C, S, DUMMY ) ICOL = MAX( 1, JCH-JKU-JKL ) IL = IC + 2 - ICOL EXTRA = ZERO CALL SLAROT( .TRUE., JCH.GT.JKU+JKL, $ .TRUE., $ IL, C, -S, A( IROW-ISKEW*ICOL+ $ IOFFST, ICOL ), ILDA, EXTRA, $ TEMP ) IC = ICOL IR = IROW END IF 30 CONTINUE 40 CONTINUE 50 CONTINUE * JKU = UUB DO 80 JKL = 1, LLB * * Transform from bandwidth JKL-1, JKU to JKL, JKU * DO 70 JC = 1, MIN( N+JKL, M ) + JKU - 1 EXTRA = ZERO ANGLE = TWOPI*SLARND( 1, ISEED ) C = COS( ANGLE ) S = SIN( ANGLE ) IROW = MAX( 1, JC-JKU ) IF( JC.LT.N ) THEN IL = MIN( M, JC+JKL ) + 1 - IROW CALL SLAROT( .FALSE., JC.GT.JKU, .FALSE., IL, $ C, $ S, A( IROW-ISKEW*JC+IOFFST, JC ), $ ILDA, EXTRA, DUMMY ) END IF * * Chase "EXTRA" back up * IC = JC IR = IROW DO 60 JCH = JC - JKU, 1, -JKL - JKU IF( IC.LT.N ) THEN CALL SLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST, $ IC+1 ), EXTRA, C, S, DUMMY ) END IF ICOL = MAX( 1, JCH-JKL ) IL = IC + 2 - ICOL TEMP = ZERO ILTEMP = JCH.GT.JKL CALL SLAROT( .TRUE., ILTEMP, .TRUE., IL, C, $ -S, $ A( IR-ISKEW*ICOL+IOFFST, ICOL ), $ ILDA, TEMP, EXTRA ) IF( ILTEMP ) THEN CALL SLARTG( A( IR+1-ISKEW*( ICOL+1 )+IOFFST, $ ICOL+1 ), TEMP, C, S, DUMMY ) IROW = MAX( 1, JCH-JKL-JKU ) IL = IR + 2 - IROW EXTRA = ZERO CALL SLAROT( .FALSE., JCH.GT.JKL+JKU, $ .TRUE., $ IL, C, -S, A( IROW-ISKEW*ICOL+ $ IOFFST, ICOL ), ILDA, EXTRA, $ TEMP ) IC = ICOL IR = IROW END IF 60 CONTINUE 70 CONTINUE 80 CONTINUE * ELSE * * Bottom-Up -- Start at the bottom right. * JKL = 0 DO 110 JKU = 1, UUB * * Transform from bandwidth JKL, JKU-1 to JKL, JKU * * First row actually rotated is M * First column actually rotated is MIN( M+JKU, N ) * IENDCH = MIN( M, N+JKL ) - 1 DO 100 JC = MIN( M+JKU, N ) - 1, 1 - JKL, -1 EXTRA = ZERO ANGLE = TWOPI*SLARND( 1, ISEED ) C = COS( ANGLE ) S = SIN( ANGLE ) IROW = MAX( 1, JC-JKU+1 ) IF( JC.GT.0 ) THEN IL = MIN( M, JC+JKL+1 ) + 1 - IROW CALL SLAROT( .FALSE., .FALSE., JC+JKL.LT.M, $ IL, $ C, S, A( IROW-ISKEW*JC+IOFFST, $ JC ), ILDA, DUMMY, EXTRA ) END IF * * Chase "EXTRA" back down * IC = JC DO 90 JCH = JC + JKL, IENDCH, JKL + JKU ILEXTR = IC.GT.0 IF( ILEXTR ) THEN CALL SLARTG( A( JCH-ISKEW*IC+IOFFST, IC ), $ EXTRA, C, S, DUMMY ) END IF IC = MAX( 1, IC ) ICOL = MIN( N-1, JCH+JKU ) ILTEMP = JCH + JKU.LT.N TEMP = ZERO CALL SLAROT( .TRUE., ILEXTR, ILTEMP, $ ICOL+2-IC, $ C, S, A( JCH-ISKEW*IC+IOFFST, IC ), $ ILDA, EXTRA, TEMP ) IF( ILTEMP ) THEN CALL SLARTG( A( JCH-ISKEW*ICOL+IOFFST, $ ICOL ), TEMP, C, S, DUMMY ) IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH EXTRA = ZERO CALL SLAROT( .FALSE., .TRUE., $ JCH+JKL+JKU.LE.IENDCH, IL, C, S, $ A( JCH-ISKEW*ICOL+IOFFST, $ ICOL ), ILDA, TEMP, EXTRA ) IC = ICOL END IF 90 CONTINUE 100 CONTINUE 110 CONTINUE * JKU = UUB DO 140 JKL = 1, LLB * * Transform from bandwidth JKL-1, JKU to JKL, JKU * * First row actually rotated is MIN( N+JKL, M ) * First column actually rotated is N * IENDCH = MIN( N, M+JKU ) - 1 DO 130 JR = MIN( N+JKL, M ) - 1, 1 - JKU, -1 EXTRA = ZERO ANGLE = TWOPI*SLARND( 1, ISEED ) C = COS( ANGLE ) S = SIN( ANGLE ) ICOL = MAX( 1, JR-JKL+1 ) IF( JR.GT.0 ) THEN IL = MIN( N, JR+JKU+1 ) + 1 - ICOL CALL SLAROT( .TRUE., .FALSE., JR+JKU.LT.N, $ IL, $ C, S, A( JR-ISKEW*ICOL+IOFFST, $ ICOL ), ILDA, DUMMY, EXTRA ) END IF * * Chase "EXTRA" back down * IR = JR DO 120 JCH = JR + JKU, IENDCH, JKL + JKU ILEXTR = IR.GT.0 IF( ILEXTR ) THEN CALL SLARTG( A( IR-ISKEW*JCH+IOFFST, JCH ), $ EXTRA, C, S, DUMMY ) END IF IR = MAX( 1, IR ) IROW = MIN( M-1, JCH+JKL ) ILTEMP = JCH + JKL.LT.M TEMP = ZERO CALL SLAROT( .FALSE., ILEXTR, ILTEMP, $ IROW+2-IR, $ C, S, A( IR-ISKEW*JCH+IOFFST, $ JCH ), ILDA, EXTRA, TEMP ) IF( ILTEMP ) THEN CALL SLARTG( A( IROW-ISKEW*JCH+IOFFST, JCH ), $ TEMP, C, S, DUMMY ) IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH EXTRA = ZERO CALL SLAROT( .TRUE., .TRUE., $ JCH+JKL+JKU.LE.IENDCH, IL, C, S, $ A( IROW-ISKEW*JCH+IOFFST, JCH ), $ ILDA, TEMP, EXTRA ) IR = IROW END IF 120 CONTINUE 130 CONTINUE 140 CONTINUE END IF * ELSE * * Symmetric -- A = U D U' * IPACKG = IPACK IOFFG = IOFFST * IF( TOPDWN ) THEN * * Top-Down -- Generate Upper triangle only * IF( IPACK.GE.5 ) THEN IPACKG = 6 IOFFG = UUB + 1 ELSE IPACKG = 1 END IF CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFG, 1 ), ILDA+1 ) * DO 170 K = 1, UUB DO 160 JC = 1, N - 1 IROW = MAX( 1, JC-K ) IL = MIN( JC+1, K+2 ) EXTRA = ZERO TEMP = A( JC-ISKEW*( JC+1 )+IOFFG, JC+1 ) ANGLE = TWOPI*SLARND( 1, ISEED ) C = COS( ANGLE ) S = SIN( ANGLE ) CALL SLAROT( .FALSE., JC.GT.K, .TRUE., IL, C, S, $ A( IROW-ISKEW*JC+IOFFG, JC ), ILDA, $ EXTRA, TEMP ) CALL SLAROT( .TRUE., .TRUE., .FALSE., $ MIN( K, N-JC )+1, C, S, $ A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA, $ TEMP, DUMMY ) * * Chase EXTRA back up the matrix * ICOL = JC DO 150 JCH = JC - K, 1, -K CALL SLARTG( A( JCH+1-ISKEW*( ICOL+1 )+IOFFG, $ ICOL+1 ), EXTRA, C, S, DUMMY ) TEMP = A( JCH-ISKEW*( JCH+1 )+IOFFG, JCH+1 ) CALL SLAROT( .TRUE., .TRUE., .TRUE., K+2, C, $ -S, $ A( ( 1-ISKEW )*JCH+IOFFG, JCH ), $ ILDA, TEMP, EXTRA ) IROW = MAX( 1, JCH-K ) IL = MIN( JCH+1, K+2 ) EXTRA = ZERO CALL SLAROT( .FALSE., JCH.GT.K, .TRUE., IL, $ C, $ -S, A( IROW-ISKEW*JCH+IOFFG, JCH ), $ ILDA, EXTRA, TEMP ) ICOL = JCH 150 CONTINUE 160 CONTINUE 170 CONTINUE * * If we need lower triangle, copy from upper. Note that * the order of copying is chosen to work for 'q' -> 'b' * IF( IPACK.NE.IPACKG .AND. IPACK.NE.3 ) THEN DO 190 JC = 1, N IROW = IOFFST - ISKEW*JC DO 180 JR = JC, MIN( N, JC+UUB ) A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR ) 180 CONTINUE 190 CONTINUE IF( IPACK.EQ.5 ) THEN DO 210 JC = N - UUB + 1, N DO 200 JR = N + 2 - JC, UUB + 1 A( JR, JC ) = ZERO 200 CONTINUE 210 CONTINUE END IF IF( IPACKG.EQ.6 ) THEN IPACKG = IPACK ELSE IPACKG = 0 END IF END IF ELSE * * Bottom-Up -- Generate Lower triangle only * IF( IPACK.GE.5 ) THEN IPACKG = 5 IF( IPACK.EQ.6 ) $ IOFFG = 1 ELSE IPACKG = 2 END IF CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFG, 1 ), ILDA+1 ) * DO 240 K = 1, UUB DO 230 JC = N - 1, 1, -1 IL = MIN( N+1-JC, K+2 ) EXTRA = ZERO TEMP = A( 1+( 1-ISKEW )*JC+IOFFG, JC ) ANGLE = TWOPI*SLARND( 1, ISEED ) C = COS( ANGLE ) S = -SIN( ANGLE ) CALL SLAROT( .FALSE., .TRUE., N-JC.GT.K, IL, C, $ S, $ A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA, $ TEMP, EXTRA ) ICOL = MAX( 1, JC-K+1 ) CALL SLAROT( .TRUE., .FALSE., .TRUE., JC+2-ICOL, $ C, $ S, A( JC-ISKEW*ICOL+IOFFG, ICOL ), $ ILDA, DUMMY, TEMP ) * * Chase EXTRA back down the matrix * ICOL = JC DO 220 JCH = JC + K, N - 1, K CALL SLARTG( A( JCH-ISKEW*ICOL+IOFFG, ICOL ), $ EXTRA, C, S, DUMMY ) TEMP = A( 1+( 1-ISKEW )*JCH+IOFFG, JCH ) CALL SLAROT( .TRUE., .TRUE., .TRUE., K+2, C, $ S, $ A( JCH-ISKEW*ICOL+IOFFG, ICOL ), $ ILDA, EXTRA, TEMP ) IL = MIN( N+1-JCH, K+2 ) EXTRA = ZERO CALL SLAROT( .FALSE., .TRUE., N-JCH.GT.K, IL, $ C, $ S, A( ( 1-ISKEW )*JCH+IOFFG, JCH ), $ ILDA, TEMP, EXTRA ) ICOL = JCH 220 CONTINUE 230 CONTINUE 240 CONTINUE * * If we need upper triangle, copy from lower. Note that * the order of copying is chosen to work for 'b' -> 'q' * IF( IPACK.NE.IPACKG .AND. IPACK.NE.4 ) THEN DO 260 JC = N, 1, -1 IROW = IOFFST - ISKEW*JC DO 250 JR = JC, MAX( 1, JC-UUB ), -1 A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR ) 250 CONTINUE 260 CONTINUE IF( IPACK.EQ.6 ) THEN DO 280 JC = 1, UUB DO 270 JR = 1, UUB + 1 - JC A( JR, JC ) = ZERO 270 CONTINUE 280 CONTINUE END IF IF( IPACKG.EQ.5 ) THEN IPACKG = IPACK ELSE IPACKG = 0 END IF END IF END IF END IF * ELSE * * 4) Generate Banded Matrix by first * Rotating by random Unitary matrices, * then reducing the bandwidth using Householder * transformations. * * Note: we should get here only if LDA .ge. N * IF( ISYM.EQ.1 ) THEN * * Non-symmetric -- A = U D V * CALL SLAGGE( MR, NC, LLB, UUB, D, A, LDA, ISEED, WORK, $ IINFO ) ELSE * * Symmetric -- A = U D U' * CALL SLAGSY( M, LLB, D, A, LDA, ISEED, WORK, IINFO ) * END IF IF( IINFO.NE.0 ) THEN INFO = 3 RETURN END IF END IF * * 5) Pack the matrix * IF( IPACK.NE.IPACKG ) THEN IF( IPACK.EQ.1 ) THEN * * 'U' -- Upper triangular, not packed * DO 300 J = 1, M DO 290 I = J + 1, M A( I, J ) = ZERO 290 CONTINUE 300 CONTINUE * ELSE IF( IPACK.EQ.2 ) THEN * * 'L' -- Lower triangular, not packed * DO 320 J = 2, M DO 310 I = 1, J - 1 A( I, J ) = ZERO 310 CONTINUE 320 CONTINUE * ELSE IF( IPACK.EQ.3 ) THEN * * 'C' -- Upper triangle packed Columnwise. * ICOL = 1 IROW = 0 DO 340 J = 1, M DO 330 I = 1, J IROW = IROW + 1 IF( IROW.GT.LDA ) THEN IROW = 1 ICOL = ICOL + 1 END IF A( IROW, ICOL ) = A( I, J ) 330 CONTINUE 340 CONTINUE * ELSE IF( IPACK.EQ.4 ) THEN * * 'R' -- Lower triangle packed Columnwise. * ICOL = 1 IROW = 0 DO 360 J = 1, M DO 350 I = J, M IROW = IROW + 1 IF( IROW.GT.LDA ) THEN IROW = 1 ICOL = ICOL + 1 END IF A( IROW, ICOL ) = A( I, J ) 350 CONTINUE 360 CONTINUE * ELSE IF( IPACK.GE.5 ) THEN * * 'B' -- The lower triangle is packed as a band matrix. * 'Q' -- The upper triangle is packed as a band matrix. * 'Z' -- The whole matrix is packed as a band matrix. * IF( IPACK.EQ.5 ) $ UUB = 0 IF( IPACK.EQ.6 ) $ LLB = 0 * DO 380 J = 1, UUB DO 370 I = MIN( J+LLB, M ), 1, -1 A( I-J+UUB+1, J ) = A( I, J ) 370 CONTINUE 380 CONTINUE * DO 400 J = UUB + 2, N DO 390 I = J - UUB, MIN( J+LLB, M ) A( I-J+UUB+1, J ) = A( I, J ) 390 CONTINUE 400 CONTINUE END IF * * If packed, zero out extraneous elements. * * Symmetric/Triangular Packed -- * zero out everything after A(IROW,ICOL) * IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN DO 420 JC = ICOL, M DO 410 JR = IROW + 1, LDA A( JR, JC ) = ZERO 410 CONTINUE IROW = 0 420 CONTINUE * ELSE IF( IPACK.GE.5 ) THEN * * Packed Band -- * 1st row is now in A( UUB+2-j, j), zero above it * m-th row is now in A( M+UUB-j,j), zero below it * last non-zero diagonal is now in A( UUB+LLB+1,j ), * zero below it, too. * IR1 = UUB + LLB + 2 IR2 = UUB + M + 2 DO 450 JC = 1, N DO 430 JR = 1, UUB + 1 - JC A( JR, JC ) = ZERO 430 CONTINUE DO 440 JR = MAX( 1, MIN( IR1, IR2-JC ) ), LDA A( JR, JC ) = ZERO 440 CONTINUE 450 CONTINUE END IF END IF * RETURN * * End of SLATMS * END