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SUBROUTINE DLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
$ RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, $ CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, $ PACK, A, LDA, IWORK, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * June 2010 * * .. Scalar Arguments .. CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N DOUBLE PRECISION ANORM, COND, CONDL, CONDR, DMAX, SPARSE * .. * .. Array Arguments .. INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * ) DOUBLE PRECISION A( LDA, * ), D( * ), DL( * ), DR( * ) * .. * * Purpose * ======= * * DLATMR generates random matrices of various types for testing * LAPACK programs. * * DLATMR operates by applying the following sequence of * operations: * * Generate a matrix A with random entries of distribution DIST * which is symmetric if SYM='S', and nonsymmetric * if SYM='N'. * * Set the diagonal to D, where D may be input or * computed according to MODE, COND, DMAX and RSIGN * as described below. * * Grade the matrix, if desired, from the left and/or right * as specified by GRADE. The inputs DL, MODEL, CONDL, DR, * MODER and CONDR also determine the grading as described * below. * * Permute, if desired, the rows and/or columns as specified by * PIVTNG and IPIVOT. * * Set random entries to zero, if desired, to get a random sparse * matrix as specified by SPARSE. * * Make A a band matrix, if desired, by zeroing out the matrix * outside a band of lower bandwidth KL and upper bandwidth KU. * * Scale A, if desired, to have maximum entry ANORM. * * 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 * square upper triangular) * store the lower half columnwise (if symmetric or * square lower triangular) * same as upper half rowwise if symmetric * store the lower triangle in banded format (if symmetric) * store the upper triangle in banded format (if symmetric) * store the entire matrix in banded format * * Note: If two calls to DLATMR differ only in the PACK parameter, * they will generate mathematically equivalent matrices. * * If two calls to DLATMR both have full bandwidth (KL = M-1 * and KU = N-1), and differ only in the PIVTNG and PACK * parameters, then the matrices generated will differ only * in the order of the rows and/or columns, and otherwise * contain the same data. This consistency cannot be and * is not maintained with less than full bandwidth. * * Arguments * ========= * * M (input) INTEGER * Number of rows of A. Not modified. * * N (input) INTEGER * Number of columns of A. Not modified. * * DIST (input) CHARACTER*1 * On entry, DIST specifies the type of distribution to be used * to generate a random matrix . * '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 DLATMR * to continue the same random number sequence. * Changed on exit. * * SYM (input) CHARACTER*1 * If SYM='S' or 'H', generated matrix is symmetric. * If SYM='N', generated matrix is nonsymmetric. * Not modified. * * D (input/output) DOUBLE PRECISION array, dimension (min(M,N)) * On entry this array specifies the diagonal entries * of the diagonal of A. D may either be specified * on entry, or set according to MODE and COND as described * below. May be changed on exit if MODE is nonzero. * * MODE (input) INTEGER * On entry describes how D is to be used: * 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, * Not modified. * * COND (input) DOUBLE PRECISION * On entry, used as described under MODE above. * If used, it must be >= 1. Not modified. * * DMAX (input) DOUBLE PRECISION * If MODE neither -6, 0 nor 6, the diagonal is scaled by * DMAX / max(abs(D(i))), so that maximum absolute entry * of diagonal is abs(DMAX). If DMAX is negative (or zero), * diagonal will be scaled by a negative number (or zero). * * RSIGN (input) CHARACTER*1 * If MODE neither -6, 0 nor 6, specifies sign of diagonal * as follows: * 'T' => diagonal entries are multiplied by 1 or -1 * with probability .5 * 'F' => diagonal unchanged * Not modified. * * GRADE (input) CHARACTER*1 * Specifies grading of matrix as follows: * 'N' => no grading * 'L' => matrix premultiplied by diag( DL ) * (only if matrix nonsymmetric) * 'R' => matrix postmultiplied by diag( DR ) * (only if matrix nonsymmetric) * 'B' => matrix premultiplied by diag( DL ) and * postmultiplied by diag( DR ) * (only if matrix nonsymmetric) * 'S' or 'H' => matrix premultiplied by diag( DL ) and * postmultiplied by diag( DL ) * ('S' for symmetric, or 'H' for Hermitian) * 'E' => matrix premultiplied by diag( DL ) and * postmultiplied by inv( diag( DL ) ) * ( 'E' for eigenvalue invariance) * (only if matrix nonsymmetric) * Note: if GRADE='E', then M must equal N. * Not modified. * * DL (input/output) DOUBLE PRECISION array, dimension (M) * If MODEL=0, then on entry this array specifies the diagonal * entries of a diagonal matrix used as described under GRADE * above. If MODEL is not zero, then DL will be set according * to MODEL and CONDL, analogous to the way D is set according * to MODE and COND (except there is no DMAX parameter for DL). * If GRADE='E', then DL cannot have zero entries. * Not referenced if GRADE = 'N' or 'R'. Changed on exit. * * MODEL (input) INTEGER * This specifies how the diagonal array DL is to be computed, * just as MODE specifies how D is to be computed. * Not modified. * * CONDL (input) DOUBLE PRECISION * When MODEL is not zero, this specifies the condition number * of the computed DL. Not modified. * * DR (input/output) DOUBLE PRECISION array, dimension (N) * If MODER=0, then on entry this array specifies the diagonal * entries of a diagonal matrix used as described under GRADE * above. If MODER is not zero, then DR will be set according * to MODER and CONDR, analogous to the way D is set according * to MODE and COND (except there is no DMAX parameter for DR). * Not referenced if GRADE = 'N', 'L', 'H', 'S' or 'E'. * Changed on exit. * * MODER (input) INTEGER * This specifies how the diagonal array DR is to be computed, * just as MODE specifies how D is to be computed. * Not modified. * * CONDR (input) DOUBLE PRECISION * When MODER is not zero, this specifies the condition number * of the computed DR. Not modified. * * PIVTNG (input) CHARACTER*1 * On entry specifies pivoting permutations as follows: * 'N' or ' ' => none. * 'L' => left or row pivoting (matrix must be nonsymmetric). * 'R' => right or column pivoting (matrix must be * nonsymmetric). * 'B' or 'F' => both or full pivoting, i.e., on both sides. * In this case, M must equal N * * If two calls to DLATMR both have full bandwidth (KL = M-1 * and KU = N-1), and differ only in the PIVTNG and PACK * parameters, then the matrices generated will differ only * in the order of the rows and/or columns, and otherwise * contain the same data. This consistency cannot be * maintained with less than full bandwidth. * * IPIVOT (input) INTEGER array, dimension (N or M) * This array specifies the permutation used. After the * basic matrix is generated, the rows, columns, or both * are permuted. If, say, row pivoting is selected, DLATMR * starts with the *last* row and interchanges the M-th and * IPIVOT(M)-th rows, then moves to the next-to-last row, * interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, * and so on. In terms of "2-cycles", the permutation is * (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) * where the rightmost cycle is applied first. This is the * *inverse* of the effect of pivoting in LINPACK. The idea * is that factoring (with pivoting) an identity matrix * which has been inverse-pivoted in this way should * result in a pivot vector identical to IPIVOT. * Not referenced if PIVTNG = 'N'. Not modified. * * SPARSE (input) DOUBLE PRECISION * On entry specifies the sparsity of the matrix if a sparse * matrix is to be generated. SPARSE should lie between * 0 and 1. To generate a sparse matrix, for each matrix entry * a uniform ( 0, 1 ) random number x is generated and * compared to SPARSE; if x is larger the matrix entry * is unchanged and if x is smaller the entry is set * to zero. Thus on the average a fraction SPARSE of the * entries will be set to zero. * Not modified. * * KL (input) INTEGER * On entry specifies the lower bandwidth of the matrix. For * example, KL=0 implies upper triangular, KL=1 implies upper * Hessenberg, and KL at least M-1 implies the matrix is not * banded. Must equal KU if matrix is symmetric. * Not modified. * * KU (input) INTEGER * On entry specifies the upper bandwidth of the matrix. For * example, KU=0 implies lower triangular, KU=1 implies lower * Hessenberg, and KU at least N-1 implies the matrix is not * banded. Must equal KL if matrix is symmetric. * Not modified. * * ANORM (input) DOUBLE PRECISION * On entry specifies maximum entry of output matrix * (output matrix will by multiplied by a constant so that * its largest absolute entry equal ANORM) * if ANORM is nonnegative. If ANORM is negative no scaling * is done. Not modified. * * PACK (input) CHARACTER*1 * On entry 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 matrix symmetric or square upper triangular) * 'R' => store the lower triangle columnwise * (only if matrix symmetric or square lower triangular) * (same as upper half rowwise if symmetric) * 'B' => store the lower triangle in band storage scheme * (only if matrix symmetric) * 'Q' => store the upper triangle in band storage scheme * (only if matrix symmetric) * '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 DLATMR differ only in the PACK parameter, * they will generate mathematically equivalent matrices. * Not modified. * * A (output) DOUBLE PRECISION array, dimension (LDA,N) * On exit A is the desired test matrix. Only those * entries of A which are significant on output * will be referenced (even if A is in packed or band * storage format). The 'unoccupied corners' of A in * band format will be zeroed out. * * LDA (input) INTEGER * on entry LDA specifies the first dimension of A as * declared in the calling program. * If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). * If PACK='C' or 'R', LDA must be at least 1. * If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) * If PACK='Z', LDA must be at least KUU+KLL+1, where * KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) * Not modified. * * IWORK (workspace) INTEGER array, dimension ( N or M) * Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. * * INFO (output) INTEGER * Error parameter on exit: * 0 => normal return * -1 => M negative or unequal to N and SYM='S' or 'H' * -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 => MODE neither -6, 0 nor 6 and RSIGN illegal string * -11 => GRADE illegal string, or GRADE='E' and * M not equal to N, or GRADE='L', 'R', 'B' or 'E' and * SYM = 'S' or 'H' * -12 => GRADE = 'E' and DL contains zero * -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', * 'S' or 'E' * -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', * and MODEL neither -6, 0 nor 6 * -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' * -17 => CONDR less than 1.0, GRADE='R' or 'B', and * MODER neither -6, 0 nor 6 * -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and * M not equal to N, or PIVTNG='L' or 'R' and SYM='S' * or 'H' * -19 => IPIVOT contains out of range number and * PIVTNG not equal to 'N' * -20 => KL negative * -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL * -22 => SPARSE not in range 0. to 1. * -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' * and SYM='N', or PACK='C' and SYM='N' and either KL * not equal to 0 or N not equal to M, or PACK='R' and * SYM='N', and either KU not equal to 0 or N not equal * to M * -26 => LDA too small * 1 => Error return from DLATM1 (computing D) * 2 => Cannot scale diagonal to DMAX (max. entry is 0) * 3 => Error return from DLATM1 (computing DL) * 4 => Error return from DLATM1 (computing DR) * 5 => ANORM is positive, but matrix constructed prior to * attempting to scale it to have norm ANORM, is zero * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) * .. * .. Local Scalars .. LOGICAL BADPVT, DZERO, FULBND INTEGER I, IDIST, IGRADE, IISUB, IPACK, IPVTNG, IRSIGN, $ ISUB, ISYM, J, JJSUB, JSUB, K, KLL, KUU, MNMIN, $ MNSUB, MXSUB, NPVTS DOUBLE PRECISION ALPHA, ONORM, TEMP * .. * .. Local Arrays .. DOUBLE PRECISION TEMPA( 1 ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLANGB, DLANGE, DLANSB, DLANSP, DLANSY, DLATM2, $ DLATM3 EXTERNAL LSAME, DLANGB, DLANGE, DLANSB, DLANSP, DLANSY, $ DLATM2, DLATM3 * .. * .. External Subroutines .. EXTERNAL DLATM1, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, MOD * .. * .. 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, 'S' ) ) THEN ISYM = 0 ELSE IF( LSAME( SYM, 'N' ) ) THEN ISYM = 1 ELSE IF( LSAME( SYM, 'H' ) ) THEN ISYM = 0 ELSE ISYM = -1 END IF * * Decode RSIGN * IF( LSAME( RSIGN, 'F' ) ) THEN IRSIGN = 0 ELSE IF( LSAME( RSIGN, 'T' ) ) THEN IRSIGN = 1 ELSE IRSIGN = -1 END IF * * Decode PIVTNG * IF( LSAME( PIVTNG, 'N' ) ) THEN IPVTNG = 0 ELSE IF( LSAME( PIVTNG, ' ' ) ) THEN IPVTNG = 0 ELSE IF( LSAME( PIVTNG, 'L' ) ) THEN IPVTNG = 1 NPVTS = M ELSE IF( LSAME( PIVTNG, 'R' ) ) THEN IPVTNG = 2 NPVTS = N ELSE IF( LSAME( PIVTNG, 'B' ) ) THEN IPVTNG = 3 NPVTS = MIN( N, M ) ELSE IF( LSAME( PIVTNG, 'F' ) ) THEN IPVTNG = 3 NPVTS = MIN( N, M ) ELSE IPVTNG = -1 END IF * * Decode GRADE * IF( LSAME( GRADE, 'N' ) ) THEN IGRADE = 0 ELSE IF( LSAME( GRADE, 'L' ) ) THEN IGRADE = 1 ELSE IF( LSAME( GRADE, 'R' ) ) THEN IGRADE = 2 ELSE IF( LSAME( GRADE, 'B' ) ) THEN IGRADE = 3 ELSE IF( LSAME( GRADE, 'E' ) ) THEN IGRADE = 4 ELSE IF( LSAME( GRADE, 'H' ) .OR. LSAME( GRADE, 'S' ) ) THEN IGRADE = 5 ELSE IGRADE = -1 END IF * * Decode PACK * IF( LSAME( PACK, 'N' ) ) THEN IPACK = 0 ELSE IF( LSAME( PACK, 'U' ) ) THEN IPACK = 1 ELSE IF( LSAME( PACK, 'L' ) ) THEN IPACK = 2 ELSE IF( LSAME( PACK, 'C' ) ) THEN IPACK = 3 ELSE IF( LSAME( PACK, 'R' ) ) THEN IPACK = 4 ELSE IF( LSAME( PACK, 'B' ) ) THEN IPACK = 5 ELSE IF( LSAME( PACK, 'Q' ) ) THEN IPACK = 6 ELSE IF( LSAME( PACK, 'Z' ) ) THEN IPACK = 7 ELSE IPACK = -1 END IF * * Set certain internal parameters * MNMIN = MIN( M, N ) KLL = MIN( KL, M-1 ) KUU = MIN( KU, N-1 ) * * If inv(DL) is used, check to see if DL has a zero entry. * DZERO = .FALSE. IF( IGRADE.EQ.4 .AND. MODEL.EQ.0 ) THEN DO 10 I = 1, M IF( DL( I ).EQ.ZERO ) $ DZERO = .TRUE. 10 CONTINUE END IF * * Check values in IPIVOT * BADPVT = .FALSE. IF( IPVTNG.GT.0 ) THEN DO 20 J = 1, NPVTS IF( IPIVOT( J ).LE.0 .OR. IPIVOT( J ).GT.NPVTS ) $ BADPVT = .TRUE. 20 CONTINUE END IF * * Set INFO if an error * IF( M.LT.0 ) THEN INFO = -1 ELSE IF( M.NE.N .AND. ISYM.EQ.0 ) 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( MODE.LT.-6 .OR. MODE.GT.6 ) THEN INFO = -7 ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND. $ COND.LT.ONE ) THEN INFO = -8 ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND. $ IRSIGN.EQ.-1 ) THEN INFO = -10 ELSE IF( IGRADE.EQ.-1 .OR. ( IGRADE.EQ.4 .AND. M.NE.N ) .OR. $ ( ( IGRADE.GE.1 .AND. IGRADE.LE.4 ) .AND. ISYM.EQ.0 ) ) $ THEN INFO = -11 ELSE IF( IGRADE.EQ.4 .AND. DZERO ) THEN INFO = -12 ELSE IF( ( IGRADE.EQ.1 .OR. IGRADE.EQ.3 .OR. IGRADE.EQ.4 .OR. $ IGRADE.EQ.5 ) .AND. ( MODEL.LT.-6 .OR. MODEL.GT.6 ) ) $ THEN INFO = -13 ELSE IF( ( IGRADE.EQ.1 .OR. IGRADE.EQ.3 .OR. IGRADE.EQ.4 .OR. $ IGRADE.EQ.5 ) .AND. ( MODEL.NE.-6 .AND. MODEL.NE.0 .AND. $ MODEL.NE.6 ) .AND. CONDL.LT.ONE ) THEN INFO = -14 ELSE IF( ( IGRADE.EQ.2 .OR. IGRADE.EQ.3 ) .AND. $ ( MODER.LT.-6 .OR. MODER.GT.6 ) ) THEN INFO = -16 ELSE IF( ( IGRADE.EQ.2 .OR. IGRADE.EQ.3 ) .AND. $ ( MODER.NE.-6 .AND. MODER.NE.0 .AND. MODER.NE.6 ) .AND. $ CONDR.LT.ONE ) THEN INFO = -17 ELSE IF( IPVTNG.EQ.-1 .OR. ( IPVTNG.EQ.3 .AND. M.NE.N ) .OR. $ ( ( IPVTNG.EQ.1 .OR. IPVTNG.EQ.2 ) .AND. ISYM.EQ.0 ) ) $ THEN INFO = -18 ELSE IF( IPVTNG.NE.0 .AND. BADPVT ) THEN INFO = -19 ELSE IF( KL.LT.0 ) THEN INFO = -20 ELSE IF( KU.LT.0 .OR. ( ISYM.EQ.0 .AND. KL.NE.KU ) ) THEN INFO = -21 ELSE IF( SPARSE.LT.ZERO .OR. SPARSE.GT.ONE ) THEN INFO = -22 ELSE IF( IPACK.EQ.-1 .OR. ( ( IPACK.EQ.1 .OR. IPACK.EQ.2 .OR. $ IPACK.EQ.5 .OR. IPACK.EQ.6 ) .AND. ISYM.EQ.1 ) .OR. $ ( IPACK.EQ.3 .AND. ISYM.EQ.1 .AND. ( KL.NE.0 .OR. M.NE. $ N ) ) .OR. ( IPACK.EQ.4 .AND. ISYM.EQ.1 .AND. ( KU.NE. $ 0 .OR. M.NE.N ) ) ) THEN INFO = -24 ELSE IF( ( ( IPACK.EQ.0 .OR. IPACK.EQ.1 .OR. IPACK.EQ.2 ) .AND. $ LDA.LT.MAX( 1, M ) ) .OR. ( ( IPACK.EQ.3 .OR. IPACK.EQ. $ 4 ) .AND. LDA.LT.1 ) .OR. ( ( IPACK.EQ.5 .OR. IPACK.EQ. $ 6 ) .AND. LDA.LT.KUU+1 ) .OR. $ ( IPACK.EQ.7 .AND. LDA.LT.KLL+KUU+1 ) ) THEN INFO = -26 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLATMR', -INFO ) RETURN END IF * * Decide if we can pivot consistently * FULBND = .FALSE. IF( KUU.EQ.N-1 .AND. KLL.EQ.M-1 ) $ FULBND = .TRUE. * * Initialize random number generator * DO 30 I = 1, 4 ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 ) 30 CONTINUE * ISEED( 4 ) = 2*( ISEED( 4 ) / 2 ) + 1 * * 2) Set up D, DL, and DR, if indicated. * * Compute D according to COND and MODE * CALL DLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, MNMIN, INFO ) IF( INFO.NE.0 ) THEN INFO = 1 RETURN END IF IF( MODE.NE.0 .AND. MODE.NE.-6 .AND. MODE.NE.6 ) THEN * * Scale by DMAX * TEMP = ABS( D( 1 ) ) DO 40 I = 2, MNMIN TEMP = MAX( TEMP, ABS( D( I ) ) ) 40 CONTINUE IF( TEMP.EQ.ZERO .AND. DMAX.NE.ZERO ) THEN INFO = 2 RETURN END IF IF( TEMP.NE.ZERO ) THEN ALPHA = DMAX / TEMP ELSE ALPHA = ONE END IF DO 50 I = 1, MNMIN D( I ) = ALPHA*D( I ) 50 CONTINUE * END IF * * Compute DL if grading set * IF( IGRADE.EQ.1 .OR. IGRADE.EQ.3 .OR. IGRADE.EQ.4 .OR. IGRADE.EQ. $ 5 ) THEN CALL DLATM1( MODEL, CONDL, 0, IDIST, ISEED, DL, M, INFO ) IF( INFO.NE.0 ) THEN INFO = 3 RETURN END IF END IF * * Compute DR if grading set * IF( IGRADE.EQ.2 .OR. IGRADE.EQ.3 ) THEN CALL DLATM1( MODER, CONDR, 0, IDIST, ISEED, DR, N, INFO ) IF( INFO.NE.0 ) THEN INFO = 4 RETURN END IF END IF * * 3) Generate IWORK if pivoting * IF( IPVTNG.GT.0 ) THEN DO 60 I = 1, NPVTS IWORK( I ) = I 60 CONTINUE IF( FULBND ) THEN DO 70 I = 1, NPVTS K = IPIVOT( I ) J = IWORK( I ) IWORK( I ) = IWORK( K ) IWORK( K ) = J 70 CONTINUE ELSE DO 80 I = NPVTS, 1, -1 K = IPIVOT( I ) J = IWORK( I ) IWORK( I ) = IWORK( K ) IWORK( K ) = J 80 CONTINUE END IF END IF * * 4) Generate matrices for each kind of PACKing * Always sweep matrix columnwise (if symmetric, upper * half only) so that matrix generated does not depend * on PACK * IF( FULBND ) THEN * * Use DLATM3 so matrices generated with differing PIVOTing only * differ only in the order of their rows and/or columns. * IF( IPACK.EQ.0 ) THEN IF( ISYM.EQ.0 ) THEN DO 100 J = 1, N DO 90 I = 1, J TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) A( ISUB, JSUB ) = TEMP A( JSUB, ISUB ) = TEMP 90 CONTINUE 100 CONTINUE ELSE IF( ISYM.EQ.1 ) THEN DO 120 J = 1, N DO 110 I = 1, M TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) A( ISUB, JSUB ) = TEMP 110 CONTINUE 120 CONTINUE END IF * ELSE IF( IPACK.EQ.1 ) THEN * DO 140 J = 1, N DO 130 I = 1, J TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) MNSUB = MIN( ISUB, JSUB ) MXSUB = MAX( ISUB, JSUB ) A( MNSUB, MXSUB ) = TEMP IF( MNSUB.NE.MXSUB ) $ A( MXSUB, MNSUB ) = ZERO 130 CONTINUE 140 CONTINUE * ELSE IF( IPACK.EQ.2 ) THEN * DO 160 J = 1, N DO 150 I = 1, J TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) MNSUB = MIN( ISUB, JSUB ) MXSUB = MAX( ISUB, JSUB ) A( MXSUB, MNSUB ) = TEMP IF( MNSUB.NE.MXSUB ) $ A( MNSUB, MXSUB ) = ZERO 150 CONTINUE 160 CONTINUE * ELSE IF( IPACK.EQ.3 ) THEN * DO 180 J = 1, N DO 170 I = 1, J TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) * * Compute K = location of (ISUB,JSUB) entry in packed * array * MNSUB = MIN( ISUB, JSUB ) MXSUB = MAX( ISUB, JSUB ) K = MXSUB*( MXSUB-1 ) / 2 + MNSUB * * Convert K to (IISUB,JJSUB) location * JJSUB = ( K-1 ) / LDA + 1 IISUB = K - LDA*( JJSUB-1 ) * A( IISUB, JJSUB ) = TEMP 170 CONTINUE 180 CONTINUE * ELSE IF( IPACK.EQ.4 ) THEN * DO 200 J = 1, N DO 190 I = 1, J TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) * * Compute K = location of (I,J) entry in packed array * MNSUB = MIN( ISUB, JSUB ) MXSUB = MAX( ISUB, JSUB ) IF( MNSUB.EQ.1 ) THEN K = MXSUB ELSE K = N*( N+1 ) / 2 - ( N-MNSUB+1 )*( N-MNSUB+2 ) / $ 2 + MXSUB - MNSUB + 1 END IF * * Convert K to (IISUB,JJSUB) location * JJSUB = ( K-1 ) / LDA + 1 IISUB = K - LDA*( JJSUB-1 ) * A( IISUB, JJSUB ) = TEMP 190 CONTINUE 200 CONTINUE * ELSE IF( IPACK.EQ.5 ) THEN * DO 220 J = 1, N DO 210 I = J - KUU, J IF( I.LT.1 ) THEN A( J-I+1, I+N ) = ZERO ELSE TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) MNSUB = MIN( ISUB, JSUB ) MXSUB = MAX( ISUB, JSUB ) A( MXSUB-MNSUB+1, MNSUB ) = TEMP END IF 210 CONTINUE 220 CONTINUE * ELSE IF( IPACK.EQ.6 ) THEN * DO 240 J = 1, N DO 230 I = J - KUU, J TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) MNSUB = MIN( ISUB, JSUB ) MXSUB = MAX( ISUB, JSUB ) A( MNSUB-MXSUB+KUU+1, MXSUB ) = TEMP 230 CONTINUE 240 CONTINUE * ELSE IF( IPACK.EQ.7 ) THEN * IF( ISYM.EQ.0 ) THEN DO 260 J = 1, N DO 250 I = J - KUU, J TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) MNSUB = MIN( ISUB, JSUB ) MXSUB = MAX( ISUB, JSUB ) A( MNSUB-MXSUB+KUU+1, MXSUB ) = TEMP IF( I.LT.1 ) $ A( J-I+1+KUU, I+N ) = ZERO IF( I.GE.1 .AND. MNSUB.NE.MXSUB ) $ A( MXSUB-MNSUB+1+KUU, MNSUB ) = TEMP 250 CONTINUE 260 CONTINUE ELSE IF( ISYM.EQ.1 ) THEN DO 280 J = 1, N DO 270 I = J - KUU, J + KLL TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) A( ISUB-JSUB+KUU+1, JSUB ) = TEMP 270 CONTINUE 280 CONTINUE END IF * END IF * ELSE * * Use DLATM2 * IF( IPACK.EQ.0 ) THEN IF( ISYM.EQ.0 ) THEN DO 300 J = 1, N DO 290 I = 1, J A( I, J ) = DLATM2( M, N, I, J, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) A( J, I ) = A( I, J ) 290 CONTINUE 300 CONTINUE ELSE IF( ISYM.EQ.1 ) THEN DO 320 J = 1, N DO 310 I = 1, M A( I, J ) = DLATM2( M, N, I, J, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) 310 CONTINUE 320 CONTINUE END IF * ELSE IF( IPACK.EQ.1 ) THEN * DO 340 J = 1, N DO 330 I = 1, J A( I, J ) = DLATM2( M, N, I, J, KL, KU, IDIST, ISEED, $ D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) IF( I.NE.J ) $ A( J, I ) = ZERO 330 CONTINUE 340 CONTINUE * ELSE IF( IPACK.EQ.2 ) THEN * DO 360 J = 1, N DO 350 I = 1, J A( J, I ) = DLATM2( M, N, I, J, KL, KU, IDIST, ISEED, $ D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) IF( I.NE.J ) $ A( I, J ) = ZERO 350 CONTINUE 360 CONTINUE * ELSE IF( IPACK.EQ.3 ) THEN * ISUB = 0 JSUB = 1 DO 380 J = 1, N DO 370 I = 1, J ISUB = ISUB + 1 IF( ISUB.GT.LDA ) THEN ISUB = 1 JSUB = JSUB + 1 END IF A( ISUB, JSUB ) = DLATM2( M, N, I, J, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) 370 CONTINUE 380 CONTINUE * ELSE IF( IPACK.EQ.4 ) THEN * IF( ISYM.EQ.0 ) THEN DO 400 J = 1, N DO 390 I = 1, J * * Compute K = location of (I,J) entry in packed array * IF( I.EQ.1 ) THEN K = J ELSE K = N*( N+1 ) / 2 - ( N-I+1 )*( N-I+2 ) / 2 + $ J - I + 1 END IF * * Convert K to (ISUB,JSUB) location * JSUB = ( K-1 ) / LDA + 1 ISUB = K - LDA*( JSUB-1 ) * A( ISUB, JSUB ) = DLATM2( M, N, I, J, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, $ IPVTNG, IWORK, SPARSE ) 390 CONTINUE 400 CONTINUE ELSE ISUB = 0 JSUB = 1 DO 420 J = 1, N DO 410 I = J, M ISUB = ISUB + 1 IF( ISUB.GT.LDA ) THEN ISUB = 1 JSUB = JSUB + 1 END IF A( ISUB, JSUB ) = DLATM2( M, N, I, J, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, $ IPVTNG, IWORK, SPARSE ) 410 CONTINUE 420 CONTINUE END IF * ELSE IF( IPACK.EQ.5 ) THEN * DO 440 J = 1, N DO 430 I = J - KUU, J IF( I.LT.1 ) THEN A( J-I+1, I+N ) = ZERO ELSE A( J-I+1, I ) = DLATM2( M, N, I, J, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) END IF 430 CONTINUE 440 CONTINUE * ELSE IF( IPACK.EQ.6 ) THEN * DO 460 J = 1, N DO 450 I = J - KUU, J A( I-J+KUU+1, J ) = DLATM2( M, N, I, J, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, $ IWORK, SPARSE ) 450 CONTINUE 460 CONTINUE * ELSE IF( IPACK.EQ.7 ) THEN * IF( ISYM.EQ.0 ) THEN DO 480 J = 1, N DO 470 I = J - KUU, J A( I-J+KUU+1, J ) = DLATM2( M, N, I, J, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, $ DR, IPVTNG, IWORK, SPARSE ) IF( I.LT.1 ) $ A( J-I+1+KUU, I+N ) = ZERO IF( I.GE.1 .AND. I.NE.J ) $ A( J-I+1+KUU, I ) = A( I-J+KUU+1, J ) 470 CONTINUE 480 CONTINUE ELSE IF( ISYM.EQ.1 ) THEN DO 500 J = 1, N DO 490 I = J - KUU, J + KLL A( I-J+KUU+1, J ) = DLATM2( M, N, I, J, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, $ DR, IPVTNG, IWORK, SPARSE ) 490 CONTINUE 500 CONTINUE END IF * END IF * END IF * * 5) Scaling the norm * IF( IPACK.EQ.0 ) THEN ONORM = DLANGE( 'M', M, N, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.1 ) THEN ONORM = DLANSY( 'M', 'U', N, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.2 ) THEN ONORM = DLANSY( 'M', 'L', N, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.3 ) THEN ONORM = DLANSP( 'M', 'U', N, A, TEMPA ) ELSE IF( IPACK.EQ.4 ) THEN ONORM = DLANSP( 'M', 'L', N, A, TEMPA ) ELSE IF( IPACK.EQ.5 ) THEN ONORM = DLANSB( 'M', 'L', N, KLL, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.6 ) THEN ONORM = DLANSB( 'M', 'U', N, KUU, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.7 ) THEN ONORM = DLANGB( 'M', N, KLL, KUU, A, LDA, TEMPA ) END IF * IF( ANORM.GE.ZERO ) THEN * IF( ANORM.GT.ZERO .AND. ONORM.EQ.ZERO ) THEN * * Desired scaling impossible * INFO = 5 RETURN * ELSE IF( ( ANORM.GT.ONE .AND. ONORM.LT.ONE ) .OR. $ ( ANORM.LT.ONE .AND. ONORM.GT.ONE ) ) THEN * * Scale carefully to avoid over / underflow * IF( IPACK.LE.2 ) THEN DO 510 J = 1, N CALL DSCAL( M, ONE / ONORM, A( 1, J ), 1 ) CALL DSCAL( M, ANORM, A( 1, J ), 1 ) 510 CONTINUE * ELSE IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN * CALL DSCAL( N*( N+1 ) / 2, ONE / ONORM, A, 1 ) CALL DSCAL( N*( N+1 ) / 2, ANORM, A, 1 ) * ELSE IF( IPACK.GE.5 ) THEN * DO 520 J = 1, N CALL DSCAL( KLL+KUU+1, ONE / ONORM, A( 1, J ), 1 ) CALL DSCAL( KLL+KUU+1, ANORM, A( 1, J ), 1 ) 520 CONTINUE * END IF * ELSE * * Scale straightforwardly * IF( IPACK.LE.2 ) THEN DO 530 J = 1, N CALL DSCAL( M, ANORM / ONORM, A( 1, J ), 1 ) 530 CONTINUE * ELSE IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN * CALL DSCAL( N*( N+1 ) / 2, ANORM / ONORM, A, 1 ) * ELSE IF( IPACK.GE.5 ) THEN * DO 540 J = 1, N CALL DSCAL( KLL+KUU+1, ANORM / ONORM, A( 1, J ), 1 ) 540 CONTINUE END IF * END IF * END IF * * End of DLATMR * END |