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SUBROUTINE ZLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
$ RANK, KL, KU, PACK, A, LDA, WORK, INFO ) * * -- LAPACK test routine (version 3.1) -- * Craig Lucas, University of Manchester / NAG Ltd. * October, 2008 * * .. Scalar Arguments .. DOUBLE PRECISION COND, DMAX INTEGER INFO, KL, KU, LDA, M, MODE, N, RANK CHARACTER DIST, PACK, SYM * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), WORK( * ) DOUBLE PRECISION D( * ) INTEGER ISEED( 4 ) * .. * * Purpose * ======= * * ZLATMT generates random matrices with specified singular values * (or hermitian with specified eigenvalues) * for testing LAPACK programs. * * ZLATMT 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 hermitian or 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 hermitian or 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 hermitian) * zero out lower half (if hermitian) * store the upper half columnwise (if hermitian or upper * triangular) * store the lower half columnwise (if hermitian or lower * triangular) * store the lower triangle in banded format (if hermitian or * lower triangular) * store the upper triangle in banded format (if hermitian 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. * * Arguments * ========= * * M (input) INTEGER * The number of rows of A. Not modified. * * N (input) INTEGER * The number of columns of A. N must equal M if the matrix * is symmetric or hermitian (i.e., if SYM is not 'N') * Not modified. * * DIST (input) 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. * * ISEED (input/output) 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 ZLATMT * to continue the same random number sequence. * Changed on exit. * * SYM (input) CHARACTER*1 * If SYM='H', the generated matrix is hermitian, with * eigenvalues specified by D, COND, MODE, and DMAX; they * may be positive, negative, or zero. * If SYM='P', the generated matrix is hermitian, 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. * If SYM='S', the generated matrix is (complex) symmetric, * with singular values specified by D, COND, MODE, and * DMAX; they will not be negative. * Not modified. * * D (input/output) DOUBLE PRECISION 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. * * MODE (input) 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:RANK)=1.0/COND * MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND * MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-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='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. * * COND (input) DOUBLE PRECISION * On entry, this is used as described under MODE above. * If used, it must be >= 1. Not modified. * * DMAX (input) DOUBLE PRECISION * 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. * * RANK (input) INTEGER * The rank of matrix to be generated for modes 1,2,3 only. * D( RANK+1:N ) = 0. * Not modified. * * KL (input) 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 or hermitian. * Not modified. * * KU (input) 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 or hermitian. * Not modified. * * PACK (input) CHARACTER*1 * This specifies packing of matrix as follows: * 'N' => no packing * 'U' => zero out all subdiagonal entries (if symmetric * or hermitian) * 'L' => zero out all superdiagonal entries (if symmetric * or hermitian) * 'C' => store the upper triangle columnwise (only if the * matrix is symmetric, hermitian, or upper triangular) * 'R' => store the lower triangle columnwise (only if the * matrix is symmetric, hermitian, or lower triangular) * 'B' => store the lower triangle in band storage scheme * (only if the matrix is symmetric, hermitian, or * lower triangular) * 'Q' => store the upper triangle in band storage scheme * (only if the matrix is symmetric, hermitian, 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, HB, or TB - use 'B' or 'Q' * PP, SP, HB, or TP - use 'C' or 'R' * * If two calls to ZLATMT differ only in the PACK parameter, * they will generate mathematically equivalent matrices. * Not modified. * * A (input/output) COMPLEX*16 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. * * LDA (input) 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. * * WORK (workspace) COMPLEX*16 array, dimension ( 3*MAX( N, M ) ) * Workspace. * Modified. * * INFO (output) 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 is not 'N' and KU is 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 DLATM7 * 2 => Cannot scale to DMAX (max. sing. value is 0) * 3 => Error return from ZLAGGE, ZLAGHE or ZLAGSY * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) COMPLEX*16 CZERO PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) ) DOUBLE PRECISION TWOPI PARAMETER ( TWOPI = 6.2831853071795864769252867663D+0 ) * .. * .. Local Scalars .. COMPLEX*16 C, CT, DUMMY, EXTRA, S, ST, ZTEMP DOUBLE PRECISION ALPHA, ANGLE, REALC, TEMP 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 LOGICAL CSYM, GIVENS, ILEXTR, ILTEMP, TOPDWN * .. * .. External Functions .. COMPLEX*16 ZLARND DOUBLE PRECISION DLARND LOGICAL LSAME EXTERNAL ZLARND, DLARND, LSAME * .. * .. External Subroutines .. EXTERNAL DLATM7, DSCAL, XERBLA, ZLAGGE, ZLAGHE, $ ZLAGSY, ZLAROT, ZLARTG, ZLASET * .. * .. Intrinsic Functions .. INTRINSIC ABS, COS, DBLE, DCMPLX, DCONJG, MAX, MIN, MOD, $ 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 CSYM = .FALSE. ELSE IF( LSAME( SYM, 'P' ) ) THEN ISYM = 2 IRSIGN = 0 CSYM = .FALSE. ELSE IF( LSAME( SYM, 'S' ) ) THEN ISYM = 2 IRSIGN = 0 CSYM = .TRUE. ELSE IF( LSAME( SYM, 'H' ) ) THEN ISYM = 2 IRSIGN = 1 CSYM = .FALSE. 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( DBLE( LLB+UUB ).LT.0.3D0*DBLE( 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( 'ZLATMT', -INFO ) RETURN END IF * * Initialize random number generator * DO 100 I = 1, 4 ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 ) 100 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 DLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, MNMIN, RANK, $ 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( RANK ) ) ) 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 110 I = 2, RANK TEMP = MAX( TEMP, ABS( D( I ) ) ) 110 CONTINUE * IF( TEMP.GT.ZERO ) THEN ALPHA = DMAX / TEMP ELSE INFO = 2 RETURN END IF * CALL DSCAL( RANK, ALPHA, D, 1 ) * END IF * CALL ZLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA ) * * 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, HE, SY, GB, HB, 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 * * Diagonal Matrix -- We are done, unless it * is to be stored HP/SP/PP/TP (PACK='R' or 'C') * IF( LLB.EQ.0 .AND. UUB.EQ.0 ) THEN DO 120 J = 1, MNMIN A( ( 1-ISKEW )*J+IOFFST, J ) = DCMPLX( D( J ) ) 120 CONTINUE * 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 * DO 130 J = 1, MNMIN A( ( 1-ISKEW )*J+IOFFST, J ) = DCMPLX( D( J ) ) 130 CONTINUE * IF( TOPDWN ) THEN JKL = 0 DO 160 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 150 JR = 1, MIN( M+JKU, N ) + JKL - 1 EXTRA = CZERO ANGLE = TWOPI*DLARND( 1, ISEED ) C = COS( ANGLE )*ZLARND( 5, ISEED ) S = SIN( ANGLE )*ZLARND( 5, ISEED ) ICOL = MAX( 1, JR-JKL ) IF( JR.LT.M ) THEN IL = MIN( N, JR+JKU ) + 1 - ICOL CALL ZLAROT( .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 140 JCH = JR - JKL, 1, -JKL - JKU IF( IR.LT.M ) THEN CALL ZLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST, $ IC+1 ), EXTRA, REALC, S, DUMMY ) DUMMY = DLARND( 5, ISEED ) C = DCONJG( REALC*DUMMY ) S = DCONJG( -S*DUMMY ) END IF IROW = MAX( 1, JCH-JKU ) IL = IR + 2 - IROW ZTEMP = CZERO ILTEMP = JCH.GT.JKU CALL ZLAROT( .FALSE., ILTEMP, .TRUE., IL, C, S, $ A( IROW-ISKEW*IC+IOFFST, IC ), $ ILDA, ZTEMP, EXTRA ) IF( ILTEMP ) THEN CALL ZLARTG( A( IROW+1-ISKEW*( IC+1 )+IOFFST, $ IC+1 ), ZTEMP, REALC, S, DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = DCONJG( REALC*DUMMY ) S = DCONJG( -S*DUMMY ) * ICOL = MAX( 1, JCH-JKU-JKL ) IL = IC + 2 - ICOL EXTRA = CZERO CALL ZLAROT( .TRUE., JCH.GT.JKU+JKL, .TRUE., $ IL, C, S, A( IROW-ISKEW*ICOL+ $ IOFFST, ICOL ), ILDA, EXTRA, $ ZTEMP ) IC = ICOL IR = IROW END IF 140 CONTINUE 150 CONTINUE 160 CONTINUE * JKU = UUB DO 190 JKL = 1, LLB * * Transform from bandwidth JKL-1, JKU to JKL, JKU * DO 180 JC = 1, MIN( N+JKL, M ) + JKU - 1 EXTRA = CZERO ANGLE = TWOPI*DLARND( 1, ISEED ) C = COS( ANGLE )*ZLARND( 5, ISEED ) S = SIN( ANGLE )*ZLARND( 5, ISEED ) IROW = MAX( 1, JC-JKU ) IF( JC.LT.N ) THEN IL = MIN( M, JC+JKL ) + 1 - IROW CALL ZLAROT( .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 170 JCH = JC - JKU, 1, -JKL - JKU IF( IC.LT.N ) THEN CALL ZLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST, $ IC+1 ), EXTRA, REALC, S, DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = DCONJG( REALC*DUMMY ) S = DCONJG( -S*DUMMY ) END IF ICOL = MAX( 1, JCH-JKL ) IL = IC + 2 - ICOL ZTEMP = CZERO ILTEMP = JCH.GT.JKL CALL ZLAROT( .TRUE., ILTEMP, .TRUE., IL, C, S, $ A( IR-ISKEW*ICOL+IOFFST, ICOL ), $ ILDA, ZTEMP, EXTRA ) IF( ILTEMP ) THEN CALL ZLARTG( A( IR+1-ISKEW*( ICOL+1 )+IOFFST, $ ICOL+1 ), ZTEMP, REALC, S, $ DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = DCONJG( REALC*DUMMY ) S = DCONJG( -S*DUMMY ) IROW = MAX( 1, JCH-JKL-JKU ) IL = IR + 2 - IROW EXTRA = CZERO CALL ZLAROT( .FALSE., JCH.GT.JKL+JKU, .TRUE., $ IL, C, S, A( IROW-ISKEW*ICOL+ $ IOFFST, ICOL ), ILDA, EXTRA, $ ZTEMP ) IC = ICOL IR = IROW END IF 170 CONTINUE 180 CONTINUE 190 CONTINUE * ELSE * * Bottom-Up -- Start at the bottom right. * JKL = 0 DO 220 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 210 JC = MIN( M+JKU, N ) - 1, 1 - JKL, -1 EXTRA = CZERO ANGLE = TWOPI*DLARND( 1, ISEED ) C = COS( ANGLE )*ZLARND( 5, ISEED ) S = SIN( ANGLE )*ZLARND( 5, ISEED ) IROW = MAX( 1, JC-JKU+1 ) IF( JC.GT.0 ) THEN IL = MIN( M, JC+JKL+1 ) + 1 - IROW CALL ZLAROT( .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 200 JCH = JC + JKL, IENDCH, JKL + JKU ILEXTR = IC.GT.0 IF( ILEXTR ) THEN CALL ZLARTG( A( JCH-ISKEW*IC+IOFFST, IC ), $ EXTRA, REALC, S, DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = REALC*DUMMY S = S*DUMMY END IF IC = MAX( 1, IC ) ICOL = MIN( N-1, JCH+JKU ) ILTEMP = JCH + JKU.LT.N ZTEMP = CZERO CALL ZLAROT( .TRUE., ILEXTR, ILTEMP, ICOL+2-IC, $ C, S, A( JCH-ISKEW*IC+IOFFST, IC ), $ ILDA, EXTRA, ZTEMP ) IF( ILTEMP ) THEN CALL ZLARTG( A( JCH-ISKEW*ICOL+IOFFST, $ ICOL ), ZTEMP, REALC, S, DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = REALC*DUMMY S = S*DUMMY IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH EXTRA = CZERO CALL ZLAROT( .FALSE., .TRUE., $ JCH+JKL+JKU.LE.IENDCH, IL, C, S, $ A( JCH-ISKEW*ICOL+IOFFST, $ ICOL ), ILDA, ZTEMP, EXTRA ) IC = ICOL END IF 200 CONTINUE 210 CONTINUE 220 CONTINUE * JKU = UUB DO 250 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 240 JR = MIN( N+JKL, M ) - 1, 1 - JKU, -1 EXTRA = CZERO ANGLE = TWOPI*DLARND( 1, ISEED ) C = COS( ANGLE )*ZLARND( 5, ISEED ) S = SIN( ANGLE )*ZLARND( 5, ISEED ) ICOL = MAX( 1, JR-JKL+1 ) IF( JR.GT.0 ) THEN IL = MIN( N, JR+JKU+1 ) + 1 - ICOL CALL ZLAROT( .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 230 JCH = JR + JKU, IENDCH, JKL + JKU ILEXTR = IR.GT.0 IF( ILEXTR ) THEN CALL ZLARTG( A( IR-ISKEW*JCH+IOFFST, JCH ), $ EXTRA, REALC, S, DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = REALC*DUMMY S = S*DUMMY END IF IR = MAX( 1, IR ) IROW = MIN( M-1, JCH+JKL ) ILTEMP = JCH + JKL.LT.M ZTEMP = CZERO CALL ZLAROT( .FALSE., ILEXTR, ILTEMP, IROW+2-IR, $ C, S, A( IR-ISKEW*JCH+IOFFST, $ JCH ), ILDA, EXTRA, ZTEMP ) IF( ILTEMP ) THEN CALL ZLARTG( A( IROW-ISKEW*JCH+IOFFST, JCH ), $ ZTEMP, REALC, S, DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = REALC*DUMMY S = S*DUMMY IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH EXTRA = CZERO CALL ZLAROT( .TRUE., .TRUE., $ JCH+JKL+JKU.LE.IENDCH, IL, C, S, $ A( IROW-ISKEW*JCH+IOFFST, JCH ), $ ILDA, ZTEMP, EXTRA ) IR = IROW END IF 230 CONTINUE 240 CONTINUE 250 CONTINUE * END IF * ELSE * * Symmetric -- A = U D U' * Hermitian -- 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 * DO 260 J = 1, MNMIN A( ( 1-ISKEW )*J+IOFFG, J ) = DCMPLX( D( J ) ) 260 CONTINUE * DO 290 K = 1, UUB DO 280 JC = 1, N - 1 IROW = MAX( 1, JC-K ) IL = MIN( JC+1, K+2 ) EXTRA = CZERO ZTEMP = A( JC-ISKEW*( JC+1 )+IOFFG, JC+1 ) ANGLE = TWOPI*DLARND( 1, ISEED ) C = COS( ANGLE )*ZLARND( 5, ISEED ) S = SIN( ANGLE )*ZLARND( 5, ISEED ) IF( CSYM ) THEN CT = C ST = S ELSE ZTEMP = DCONJG( ZTEMP ) CT = DCONJG( C ) ST = DCONJG( S ) END IF CALL ZLAROT( .FALSE., JC.GT.K, .TRUE., IL, C, S, $ A( IROW-ISKEW*JC+IOFFG, JC ), ILDA, $ EXTRA, ZTEMP ) CALL ZLAROT( .TRUE., .TRUE., .FALSE., $ MIN( K, N-JC )+1, CT, ST, $ A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA, $ ZTEMP, DUMMY ) * * Chase EXTRA back up the matrix * ICOL = JC DO 270 JCH = JC - K, 1, -K CALL ZLARTG( A( JCH+1-ISKEW*( ICOL+1 )+IOFFG, $ ICOL+1 ), EXTRA, REALC, S, DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = DCONJG( REALC*DUMMY ) S = DCONJG( -S*DUMMY ) ZTEMP = A( JCH-ISKEW*( JCH+1 )+IOFFG, JCH+1 ) IF( CSYM ) THEN CT = C ST = S ELSE ZTEMP = DCONJG( ZTEMP ) CT = DCONJG( C ) ST = DCONJG( S ) END IF CALL ZLAROT( .TRUE., .TRUE., .TRUE., K+2, C, S, $ A( ( 1-ISKEW )*JCH+IOFFG, JCH ), $ ILDA, ZTEMP, EXTRA ) IROW = MAX( 1, JCH-K ) IL = MIN( JCH+1, K+2 ) EXTRA = CZERO CALL ZLAROT( .FALSE., JCH.GT.K, .TRUE., IL, CT, $ ST, A( IROW-ISKEW*JCH+IOFFG, JCH ), $ ILDA, EXTRA, ZTEMP ) ICOL = JCH 270 CONTINUE 280 CONTINUE 290 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 320 JC = 1, N IROW = IOFFST - ISKEW*JC IF( CSYM ) THEN DO 300 JR = JC, MIN( N, JC+UUB ) A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR ) 300 CONTINUE ELSE DO 310 JR = JC, MIN( N, JC+UUB ) A( JR+IROW, JC ) = DCONJG( A( JC-ISKEW*JR+ $ IOFFG, JR ) ) 310 CONTINUE END IF 320 CONTINUE IF( IPACK.EQ.5 ) THEN DO 340 JC = N - UUB + 1, N DO 330 JR = N + 2 - JC, UUB + 1 A( JR, JC ) = CZERO 330 CONTINUE 340 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 * DO 350 J = 1, MNMIN A( ( 1-ISKEW )*J+IOFFG, J ) = DCMPLX( D( J ) ) 350 CONTINUE * DO 380 K = 1, UUB DO 370 JC = N - 1, 1, -1 IL = MIN( N+1-JC, K+2 ) EXTRA = CZERO ZTEMP = A( 1+( 1-ISKEW )*JC+IOFFG, JC ) ANGLE = TWOPI*DLARND( 1, ISEED ) C = COS( ANGLE )*ZLARND( 5, ISEED ) S = SIN( ANGLE )*ZLARND( 5, ISEED ) IF( CSYM ) THEN CT = C ST = S ELSE ZTEMP = DCONJG( ZTEMP ) CT = DCONJG( C ) ST = DCONJG( S ) END IF CALL ZLAROT( .FALSE., .TRUE., N-JC.GT.K, IL, C, S, $ A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA, $ ZTEMP, EXTRA ) ICOL = MAX( 1, JC-K+1 ) CALL ZLAROT( .TRUE., .FALSE., .TRUE., JC+2-ICOL, $ CT, ST, A( JC-ISKEW*ICOL+IOFFG, $ ICOL ), ILDA, DUMMY, ZTEMP ) * * Chase EXTRA back down the matrix * ICOL = JC DO 360 JCH = JC + K, N - 1, K CALL ZLARTG( A( JCH-ISKEW*ICOL+IOFFG, ICOL ), $ EXTRA, REALC, S, DUMMY ) DUMMY = ZLARND( 5, ISEED ) C = REALC*DUMMY S = S*DUMMY ZTEMP = A( 1+( 1-ISKEW )*JCH+IOFFG, JCH ) IF( CSYM ) THEN CT = C ST = S ELSE ZTEMP = DCONJG( ZTEMP ) CT = DCONJG( C ) ST = DCONJG( S ) END IF CALL ZLAROT( .TRUE., .TRUE., .TRUE., K+2, C, S, $ A( JCH-ISKEW*ICOL+IOFFG, ICOL ), $ ILDA, EXTRA, ZTEMP ) IL = MIN( N+1-JCH, K+2 ) EXTRA = CZERO CALL ZLAROT( .FALSE., .TRUE., N-JCH.GT.K, IL, $ CT, ST, A( ( 1-ISKEW )*JCH+IOFFG, $ JCH ), ILDA, ZTEMP, EXTRA ) ICOL = JCH 360 CONTINUE 370 CONTINUE 380 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 410 JC = N, 1, -1 IROW = IOFFST - ISKEW*JC IF( CSYM ) THEN DO 390 JR = JC, MAX( 1, JC-UUB ), -1 A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR ) 390 CONTINUE ELSE DO 400 JR = JC, MAX( 1, JC-UUB ), -1 A( JR+IROW, JC ) = DCONJG( A( JC-ISKEW*JR+ $ IOFFG, JR ) ) 400 CONTINUE END IF 410 CONTINUE IF( IPACK.EQ.6 ) THEN DO 430 JC = 1, UUB DO 420 JR = 1, UUB + 1 - JC A( JR, JC ) = CZERO 420 CONTINUE 430 CONTINUE END IF IF( IPACKG.EQ.5 ) THEN IPACKG = IPACK ELSE IPACKG = 0 END IF END IF END IF * * Ensure that the diagonal is real if Hermitian * IF( .NOT.CSYM ) THEN DO 440 JC = 1, N IROW = IOFFST + ( 1-ISKEW )*JC A( IROW, JC ) = DCMPLX( DBLE( A( IROW, JC ) ) ) 440 CONTINUE 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 ZLAGGE( MR, NC, LLB, UUB, D, A, LDA, ISEED, WORK, $ IINFO ) ELSE * * Symmetric -- A = U D U' or * Hermitian -- A = U D U* * IF( CSYM ) THEN CALL ZLAGSY( M, LLB, D, A, LDA, ISEED, WORK, IINFO ) ELSE CALL ZLAGHE( M, LLB, D, A, LDA, ISEED, WORK, IINFO ) END IF 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 460 J = 1, M DO 450 I = J + 1, M A( I, J ) = CZERO 450 CONTINUE 460 CONTINUE * ELSE IF( IPACK.EQ.2 ) THEN * * 'L' -- Lower triangular, not packed * DO 480 J = 2, M DO 470 I = 1, J - 1 A( I, J ) = CZERO 470 CONTINUE 480 CONTINUE * ELSE IF( IPACK.EQ.3 ) THEN * * 'C' -- Upper triangle packed Columnwise. * ICOL = 1 IROW = 0 DO 500 J = 1, M DO 490 I = 1, J IROW = IROW + 1 IF( IROW.GT.LDA ) THEN IROW = 1 ICOL = ICOL + 1 END IF A( IROW, ICOL ) = A( I, J ) 490 CONTINUE 500 CONTINUE * ELSE IF( IPACK.EQ.4 ) THEN * * 'R' -- Lower triangle packed Columnwise. * ICOL = 1 IROW = 0 DO 520 J = 1, M DO 510 I = J, M IROW = IROW + 1 IF( IROW.GT.LDA ) THEN IROW = 1 ICOL = ICOL + 1 END IF A( IROW, ICOL ) = A( I, J ) 510 CONTINUE 520 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 540 J = 1, UUB DO 530 I = MIN( J+LLB, M ), 1, -1 A( I-J+UUB+1, J ) = A( I, J ) 530 CONTINUE 540 CONTINUE * DO 560 J = UUB + 2, N DO 550 I = J - UUB, MIN( J+LLB, M ) A( I-J+UUB+1, J ) = A( I, J ) 550 CONTINUE 560 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 580 JC = ICOL, M DO 570 JR = IROW + 1, LDA A( JR, JC ) = CZERO 570 CONTINUE IROW = 0 580 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 610 JC = 1, N DO 590 JR = 1, UUB + 1 - JC A( JR, JC ) = CZERO 590 CONTINUE DO 600 JR = MAX( 1, MIN( IR1, IR2-JC ) ), LDA A( JR, JC ) = CZERO 600 CONTINUE 610 CONTINUE END IF END IF * RETURN * * End of ZLATMT * END |