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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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| subroutine clatme | ( | integer | n, |
| character | dist, | ||
| integer, dimension( 4 ) | iseed, | ||
| complex, dimension( * ) | d, | ||
| integer | mode, | ||
| real | cond, | ||
| complex | dmax, | ||
| character | rsign, | ||
| character | upper, | ||
| character | sim, | ||
| real, dimension( * ) | ds, | ||
| integer | modes, | ||
| real | conds, | ||
| integer | kl, | ||
| integer | ku, | ||
| real | anorm, | ||
| complex, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| complex, dimension( * ) | work, | ||
| integer | info ) |
CLATME
!> !> CLATME generates random non-symmetric square matrices with !> specified eigenvalues for testing LAPACK programs. !> !> CLATME 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 UPPER='T', the upper triangle of A is set to random values !> out of distribution DIST. !> !> 3. 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. !> !> 4. 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. !> !> 5. 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.) !>
| [in] | N | !> N is INTEGER !> The number of columns (or rows) of A. Not modified. !> |
| [in] | DIST | !> DIST is CHARACTER*1 !> On entry, DIST specifies the type of distribution to be used !> to generate the random eigen-/singular values, and on 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 ) !> 'D' => uniform on the complex disc |z| < 1. !> Not modified. !> |
| [in,out] | ISEED | !> 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 CLATME !> to continue the same random number sequence. !> Changed on exit. !> |
| [in,out] | D | !> D is COMPLEX array, dimension ( N ) !> This array is used to specify the eigenvalues of A. If !> MODE=0, then D is assumed to contain the eigenvalues !> otherwise they will be computed according to MODE, COND, !> DMAX, and RSIGN and placed in D. !> Modified if MODE is nonzero. !> |
| [in] | MODE | !> MODE is INTEGER !> On entry this describes how the eigenvalues are to !> be specified: !> MODE = 0 means use D as input !> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND !> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND !> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) !> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) !> MODE = 5 sets D to random numbers in the range !> ( 1/COND , 1 ) such that their logarithms !> are uniformly distributed. !> MODE = 6 set D to random numbers from same distribution !> as the rest of the matrix. !> MODE < 0 has the same meaning as ABS(MODE), except that !> the order of the elements of D is reversed. !> Thus if MODE is 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. !> |
| [in] | COND | !> COND is REAL !> On entry, this is used as described under MODE above. !> If used, it must be >= 1. Not modified. !> |
| [in] | DMAX | !> DMAX is COMPLEX !> 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 or real: if DMAX is negative or complex (or zero), !> D will be scaled by a negative or complex number (or zero). !> If RSIGN='F' then the largest (absolute) eigenvalue will be !> equal to DMAX. !> Not modified. !> |
| [in] | RSIGN | !> 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 complex number from the unit !> circle |z| = 1. If RSIGN='F', they will not be. RSIGN may !> only have the values 'T' or 'F'. !> Not modified. !> |
| [in] | UPPER | !> UPPER is CHARACTER*1 !> If UPPER='T', then the elements of A above the diagonal !> 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. !> |
| [in] | SIM | !> 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. !> |
| [in,out] | DS | !> 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. !> |
| [in] | MODES | !> MODES is INTEGER !> |
| [in] | CONDS | !> CONDS is REAL !> Similar to 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.) !> |
| [in] | KL | !> 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. !> Not modified. !> |
| [in] | KU | !> 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. !> Not modified. !> |
| [in] | ANORM | !> 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. !> |
| [out] | A | !> A is COMPLEX array, dimension ( LDA, N ) !> On exit A is the desired test matrix. !> Modified. !> |
| [in] | LDA | !> LDA is INTEGER !> LDA specifies the first dimension of A as declared in the !> calling program. LDA must be at least M. !> Not modified. !> |
| [out] | WORK | !> WORK is COMPLEX array, dimension ( 3*N ) !> Workspace. !> Modified. !> |
| [out] | INFO | !> 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 !> -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 M. !> 1 => Error return from CLATM1 (computing D) !> 2 => Cannot scale to DMAX (max. eigenvalue is 0) !> 3 => Error return from SLATM1 (computing DS) !> 4 => Error return from CLARGE !> 5 => Zero singular value from SLATM1. !> |
Definition at line 296 of file clatme.f.
1.11.0