numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
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| lapack/TESTING/MATGEN/slatmr.f | 43147B | -rw-r--r-- |
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*> \brief \b SLATMR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SLATMR( 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 ) * * .. Scalar Arguments .. * CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM * INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N * REAL ANORM, COND, CONDL, CONDR, DMAX, SPARSE * .. * .. Array Arguments .. * INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * ) * REAL A( LDA, * ), D( * ), DL( * ), DR( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLATMR generates random matrices of various types for testing *> LAPACK programs. *> *> SLATMR 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 SLATMR differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> *> If two calls to SLATMR 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> Number of rows of A. Not modified. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> 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 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. *> \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 SLATMR *> to continue the same random number sequence. *> Changed on exit. *> \endverbatim *> *> \param[in] SYM *> \verbatim *> SYM is CHARACTER*1 *> If SYM='S' or 'H', generated matrix is symmetric. *> If SYM='N', generated matrix is nonsymmetric. *> Not modified. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is REAL 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. *> \endverbatim *> *> \param[in] MODE *> \verbatim *> MODE is 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. *> \endverbatim *> *> \param[in] COND *> \verbatim *> COND is REAL *> On entry, used as described under MODE above. *> If used, it must be >= 1. Not modified. *> \endverbatim *> *> \param[in] DMAX *> \verbatim *> DMAX is REAL *> 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). *> \endverbatim *> *> \param[in] RSIGN *> \verbatim *> RSIGN is 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. *> \endverbatim *> *> \param[in] GRADE *> \verbatim *> GRADE is 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. *> \endverbatim *> *> \param[in,out] DL *> \verbatim *> DL is REAL 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. *> \endverbatim *> *> \param[in] MODEL *> \verbatim *> MODEL is INTEGER *> This specifies how the diagonal array DL is to be computed, *> just as MODE specifies how D is to be computed. *> Not modified. *> \endverbatim *> *> \param[in] CONDL *> \verbatim *> CONDL is REAL *> When MODEL is not zero, this specifies the condition number *> of the computed DL. Not modified. *> \endverbatim *> *> \param[in,out] DR *> \verbatim *> DR is REAL 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. *> \endverbatim *> *> \param[in] MODER *> \verbatim *> MODER is INTEGER *> This specifies how the diagonal array DR is to be computed, *> just as MODE specifies how D is to be computed. *> Not modified. *> \endverbatim *> *> \param[in] CONDR *> \verbatim *> CONDR is REAL *> When MODER is not zero, this specifies the condition number *> of the computed DR. Not modified. *> \endverbatim *> *> \param[in] PIVTNG *> \verbatim *> PIVTNG is 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 SLATMR 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. *> \endverbatim *> *> \param[in] IPIVOT *> \verbatim *> IPIVOT is 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, SLATMR *> 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. *> \endverbatim *> *> \param[in] KL *> \verbatim *> KL is 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. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is 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. *> \endverbatim *> *> \param[in] SPARSE *> \verbatim *> SPARSE is REAL *> 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. *> \endverbatim *> *> \param[in] ANORM *> \verbatim *> ANORM is REAL *> 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. *> \endverbatim *> *> \param[in] PACK *> \verbatim *> PACK is 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 SLATMR 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. 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. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is 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, M-1 ) *> Not modified. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension ( N or M) *> Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is 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 SLATM1 (computing D) *> 2 => Cannot scale diagonal to DMAX (max. entry is 0) *> 3 => Error return from SLATM1 (computing DL) *> 4 => Error return from SLATM1 (computing DR) *> 5 => ANORM is positive, but matrix constructed prior to *> attempting to scale it to have norm ANORM, is zero *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup real_matgen * * ===================================================================== SUBROUTINE SLATMR( 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 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, GRADE, PACK, PIVTNG, RSIGN, SYM INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N REAL ANORM, COND, CONDL, CONDR, DMAX, SPARSE * .. * .. Array Arguments .. INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * ) REAL A( LDA, * ), D( * ), DL( * ), DR( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) REAL ONE PARAMETER ( ONE = 1.0E0 ) * .. * .. 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 REAL ALPHA, ONORM, TEMP * .. * .. Local Arrays .. REAL TEMPA( 1 ) * .. * .. External Functions .. LOGICAL LSAME REAL SLANGB, SLANGE, SLANSB, $ SLANSP, SLANSY, SLATM2, $ SLATM3 EXTERNAL LSAME, SLANGB, SLANGE, $ SLANSB, SLANSP, SLANSY, $ SLATM2, SLATM3 * .. * .. External Subroutines .. EXTERNAL SLATM1, SSCAL, 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( 'SLATMR', -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 SLATM1( 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 SLATM1( 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 SLATM1( 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 SLATM3 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 = SLATM3( 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 = SLATM3( 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 = SLATM3( 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 = SLATM3( 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 = SLATM3( 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 = SLATM3( 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 = SLATM3( 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 = SLATM3( 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 = SLATM3( 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 = SLATM3( 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 SLATM2 * IF( IPACK.EQ.0 ) THEN IF( ISYM.EQ.0 ) THEN DO 300 J = 1, N DO 290 I = 1, J A( I, J ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 ) = SLATM2( 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 = SLANGE( 'M', M, N, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.1 ) THEN ONORM = SLANSY( 'M', 'U', N, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.2 ) THEN ONORM = SLANSY( 'M', 'L', N, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.3 ) THEN ONORM = SLANSP( 'M', 'U', N, A, TEMPA ) ELSE IF( IPACK.EQ.4 ) THEN ONORM = SLANSP( 'M', 'L', N, A, TEMPA ) ELSE IF( IPACK.EQ.5 ) THEN ONORM = SLANSB( 'M', 'L', N, KLL, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.6 ) THEN ONORM = SLANSB( 'M', 'U', N, KUU, A, LDA, TEMPA ) ELSE IF( IPACK.EQ.7 ) THEN ONORM = SLANGB( '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 SSCAL( M, ONE / ONORM, A( 1, J ), 1 ) CALL SSCAL( M, ANORM, A( 1, J ), 1 ) 510 CONTINUE * ELSE IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN * CALL SSCAL( N*( N+1 ) / 2, ONE / ONORM, A, 1 ) CALL SSCAL( N*( N+1 ) / 2, ANORM, A, 1 ) * ELSE IF( IPACK.GE.5 ) THEN * DO 520 J = 1, N CALL SSCAL( KLL+KUU+1, ONE / ONORM, A( 1, J ), 1 ) CALL SSCAL( 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 SSCAL( M, ANORM / ONORM, A( 1, J ), 1 ) 530 CONTINUE * ELSE IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN * CALL SSCAL( N*( N+1 ) / 2, ANORM / ONORM, A, 1 ) * ELSE IF( IPACK.GE.5 ) THEN * DO 540 J = 1, N CALL SSCAL( KLL+KUU+1, ANORM / ONORM, A( 1, J ), 1 ) 540 CONTINUE END IF * END IF * END IF * * End of SLATMR * END