.TH "TESTING/MATGEN/slatme.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME TESTING/MATGEN/slatme.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBslatme\fP (n, dist, iseed, d, mode, cond, dmax, ei, rsign, upper, sim, ds, modes, conds, kl, ku, anorm, a, lda, work, info)" .br .RI "\fBSLATME\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine slatme (integer n, character dist, integer, dimension( 4 ) iseed, real, dimension( * ) d, integer mode, real cond, real dmax, character, dimension( * ) ei, character rsign, character upper, character sim, real, dimension( * ) ds, integer modes, real conds, integer kl, integer ku, real anorm, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work, integer info)" .PP \fBSLATME\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SLATME generates random non-symmetric square matrices with !> specified eigenvalues for testing LAPACK programs\&. !> !> SLATME operates by applying the following sequence of !> operations: !> !> 1\&. Set the diagonal to D, where D may be input or !> computed according to MODE, COND, DMAX, and RSIGN !> as described below\&. !> !> 2\&. If complex conjugate pairs are desired (MODE=0 and EI(1)='R', !> or MODE=5), certain pairs of adjacent elements of D are !> interpreted as the real and complex parts of a complex !> conjugate pair; A thus becomes block diagonal, with 1x1 !> and 2x2 blocks\&. !> !> 3\&. If UPPER='T', the upper triangle of A is set to random values !> out of distribution DIST\&. !> !> 4\&. If SIM='T', A is multiplied on the left by a random matrix !> X, whose singular values are specified by DS, MODES, and !> CONDS, and on the right by X inverse\&. !> !> 5\&. If KL < N-1, the lower bandwidth is reduced to KL using !> Householder transformations\&. If KU < N-1, the upper !> bandwidth is reduced to KU\&. !> !> 6\&. If ANORM is not negative, the matrix is scaled to have !> maximum-element-norm ANORM\&. !> !> (Note: since the matrix cannot be reduced beyond Hessenberg form, !> no packing options are available\&.) !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf !> N is INTEGER !> The number of columns (or rows) of A\&. Not modified\&. !> .fi .PP .br \fIDIST\fP .PP .nf !> DIST is CHARACTER*1 !> On entry, DIST specifies the type of distribution to be used !> to generate the random eigen-/singular values, and for the !> upper triangle (see UPPER)\&. !> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) !> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) !> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) !> Not modified\&. !> .fi .PP .br \fIISEED\fP .PP .nf !> 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 SLATME !> to continue the same random number sequence\&. !> Changed on exit\&. !> .fi .PP .br \fID\fP .PP .nf !> D is REAL array, dimension ( N ) !> This array is used to specify the eigenvalues of A\&. If !> MODE=0, then D is assumed to contain the eigenvalues (but !> see the description of EI), otherwise they will be !> computed according to MODE, COND, DMAX, and RSIGN and !> placed in D\&. !> Modified if MODE is nonzero\&. !> .fi .PP .br \fIMODE\fP .PP .nf !> MODE is INTEGER !> On entry this describes how the eigenvalues are to !> be specified: !> MODE = 0 means use D (with EI) 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\&. Each odd-even pair !> of elements will be either used as two real !> eigenvalues or as the real and imaginary part !> of a complex conjugate pair of eigenvalues; !> the choice of which is done is random, with !> 50-50 probability, for each pair\&. !> 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 between 1 and 4, D has entries ranging !> from 1 to 1/COND, if between -1 and -4, D has entries !> ranging from 1/COND to 1, !> Not modified\&. !> .fi .PP .br \fICOND\fP .PP .nf !> COND is REAL !> On entry, this is used as described under MODE above\&. !> If used, it must be >= 1\&. Not modified\&. !> .fi .PP .br \fIDMAX\fP .PP .nf !> 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)))\&. 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\&. !> .fi .PP .br \fIEI\fP .PP .nf !> EI is CHARACTER*1 array, dimension ( N ) !> If MODE is 0, and EI(1) is not ' ' (space character), !> this array specifies which elements of D (on input) are !> real eigenvalues and which are the real and imaginary parts !> of a complex conjugate pair of eigenvalues\&. The elements !> of EI may then only have the values 'R' and 'I'\&. If !> EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is !> CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex !> conjugate thereof\&. If EI(j)=EI(j+1)='R', then the j-th !> eigenvalue is D(j) (i\&.e\&., real)\&. EI(1) may not be 'I', !> nor may two adjacent elements of EI both have the value 'I'\&. !> If MODE is not 0, then EI is ignored\&. If MODE is 0 and !> EI(1)=' ', then the eigenvalues will all be real\&. !> Not modified\&. !> .fi .PP .br \fIRSIGN\fP .PP .nf !> RSIGN is CHARACTER*1 !> If MODE is not 0, 6, or -6, and RSIGN='T', then the !> elements of D, as computed according to MODE and COND, will !> be multiplied by a random sign (+1 or -1)\&. If RSIGN='F', !> they will not be\&. RSIGN may only have the values 'T' or !> 'F'\&. !> Not modified\&. !> .fi .PP .br \fIUPPER\fP .PP .nf !> UPPER is CHARACTER*1 !> If UPPER='T', then the elements of A above the diagonal !> (and above the 2x2 diagonal blocks, if A has complex !> eigenvalues) will be set to random numbers out of DIST\&. !> If UPPER='F', they will not\&. UPPER may only have the !> values 'T' or 'F'\&. !> Not modified\&. !> .fi .PP .br \fISIM\fP .PP .nf !> SIM is CHARACTER*1 !> If SIM='T', then A will be operated on by a , i\&.e\&., multiplied on the left by a matrix X and !> on the right by X inverse\&. X = U S V, where U and V are !> random unitary matrices and S is a (diagonal) matrix of !> singular values specified by DS, MODES, and CONDS\&. If !> SIM='F', then A will not be transformed\&. !> Not modified\&. !> .fi .PP .br \fIDS\fP .PP .nf !> DS is REAL array, dimension ( N ) !> This array is used to specify the singular values of X, !> in the same way that D specifies the eigenvalues of A\&. !> If MODE=0, the DS contains the singular values, which !> may not be zero\&. !> Modified if MODE is nonzero\&. !> .fi .PP .br \fIMODES\fP .PP .nf !> MODES is INTEGER !> .fi .PP .br \fICONDS\fP .PP .nf !> CONDS is REAL !> Same as MODE and COND, but for specifying the diagonal !> of S\&. MODES=-6 and +6 are not allowed (since they would !> result in randomly ill-conditioned eigenvalues\&.) !> .fi .PP .br \fIKL\fP .PP .nf !> KL is INTEGER !> This specifies the lower bandwidth of the matrix\&. KL=1 !> specifies upper Hessenberg form\&. If KL is at least N-1, !> then A will have full lower bandwidth\&. KL must be at !> least 1\&. !> Not modified\&. !> .fi .PP .br \fIKU\fP .PP .nf !> KU is INTEGER !> This specifies the upper bandwidth of the matrix\&. KU=1 !> specifies lower Hessenberg form\&. If KU is at least N-1, !> then A will have full upper bandwidth; if KU and KL !> are both at least N-1, then A will be dense\&. Only one of !> KU and KL may be less than N-1\&. KU must be at least 1\&. !> Not modified\&. !> .fi .PP .br \fIANORM\fP .PP .nf !> ANORM is REAL !> If ANORM is not negative, then A will be scaled by a non- !> negative real number to make the maximum-element-norm of A !> to be ANORM\&. !> Not modified\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension ( LDA, N ) !> On exit A is the desired test matrix\&. !> Modified\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> LDA specifies the first dimension of A as declared in the !> calling program\&. LDA must be at least N\&. !> Not modified\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension ( 3*N ) !> Workspace\&. !> Modified\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> Error code\&. On exit, INFO will be set to one of the !> following values: !> 0 => normal return !> -1 => N negative !> -2 => DIST illegal string !> -5 => MODE not in range -6 to 6 !> -6 => COND less than 1\&.0, and MODE neither -6, 0 nor 6 !> -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or !> two adjacent elements of EI are 'I'\&. !> -9 => RSIGN is not 'T' or 'F' !> -10 => UPPER is not 'T' or 'F' !> -11 => SIM is not 'T' or 'F' !> -12 => MODES=0 and DS has a zero singular value\&. !> -13 => MODES is not in the range -5 to 5\&. !> -14 => MODES is nonzero and CONDS is less than 1\&. !> -15 => KL is less than 1\&. !> -16 => KU is less than 1, or KL and KU are both less than !> N-1\&. !> -19 => LDA is less than N\&. !> 1 => Error return from SLATM1 (computing D) !> 2 => Cannot scale to DMAX (max\&. eigenvalue is 0) !> 3 => Error return from SLATM1 (computing DS) !> 4 => Error return from SLARGE !> 5 => Zero singular value from SLATM1\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB327\fP of file \fBslatme\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.