537 lines
17 KiB
FortranFixed
537 lines
17 KiB
FortranFixed
SUBROUTINE CLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI, RSIGN,
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$ UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A,
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$ LDA, WORK, INFO )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER DIST, EI, RSIGN, SIM, UPPER
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INTEGER INFO, KL, KU, LDA, MODE, MODES, N
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REAL ANORM, COND, CONDS
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COMPLEX DMAX
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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REAL DS( * )
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COMPLEX A( LDA, * ), D( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CLATME generates random non-symmetric square matrices with
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* specified eigenvalues for testing LAPACK programs.
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*
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* CLATME operates by applying the following sequence of
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* operations:
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*
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* 1. Set the diagonal to D, where D may be input or
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* computed according to MODE, COND, DMAX, and RSIGN
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* as described below.
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*
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* 2. If UPPER='T', the upper triangle of A is set to random values
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* out of distribution DIST.
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*
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* 3. If SIM='T', A is multiplied on the left by a random matrix
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* X, whose singular values are specified by DS, MODES, and
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* CONDS, and on the right by X inverse.
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*
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* 4. If KL < N-1, the lower bandwidth is reduced to KL using
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* Householder transformations. If KU < N-1, the upper
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* bandwidth is reduced to KU.
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*
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* 5. If ANORM is not negative, the matrix is scaled to have
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* maximum-element-norm ANORM.
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*
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* (Note: since the matrix cannot be reduced beyond Hessenberg form,
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* no packing options are available.)
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*
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* Arguments
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* =========
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*
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* N - INTEGER
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* The number of columns (or rows) of A. Not modified.
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*
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* DIST - CHARACTER*1
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* On entry, DIST specifies the type of distribution to be used
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* to generate the random eigen-/singular values, and on the
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* upper triangle (see UPPER).
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* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform )
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* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
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* 'N' => NORMAL( 0, 1 ) ( 'N' for normal )
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* 'D' => uniform on the complex disc |z| < 1.
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* Not modified.
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*
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* ISEED - INTEGER array, dimension ( 4 )
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* On entry ISEED specifies the seed of the random number
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* generator. They should lie between 0 and 4095 inclusive,
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* and ISEED(4) should be odd. The random number generator
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* uses a linear congruential sequence limited to small
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* integers, and so should produce machine independent
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* random numbers. The values of ISEED are changed on
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* exit, and can be used in the next call to CLATME
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* to continue the same random number sequence.
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* Changed on exit.
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*
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* D - COMPLEX array, dimension ( N )
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* This array is used to specify the eigenvalues of A. If
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* MODE=0, then D is assumed to contain the eigenvalues
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* otherwise they will be computed according to MODE, COND,
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* DMAX, and RSIGN and placed in D.
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* Modified if MODE is nonzero.
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*
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* MODE - INTEGER
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* On entry this describes how the eigenvalues are to
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* be specified:
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* MODE = 0 means use D as input
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* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
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* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
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* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
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* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
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* MODE = 5 sets D to random numbers in the range
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* ( 1/COND , 1 ) such that their logarithms
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* are uniformly distributed.
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* MODE = 6 set D to random numbers from same distribution
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* as the rest of the matrix.
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* MODE < 0 has the same meaning as ABS(MODE), except that
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* the order of the elements of D is reversed.
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* Thus if MODE is between 1 and 4, D has entries ranging
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* from 1 to 1/COND, if between -1 and -4, D has entries
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* ranging from 1/COND to 1,
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* Not modified.
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*
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* COND - REAL
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* On entry, this is used as described under MODE above.
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* If used, it must be >= 1. Not modified.
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*
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* DMAX - COMPLEX
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* If MODE is neither -6, 0 nor 6, the contents of D, as
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* computed according to MODE and COND, will be scaled by
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* DMAX / max(abs(D(i))). Note that DMAX need not be
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* positive or real: if DMAX is negative or complex (or zero),
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* D will be scaled by a negative or complex number (or zero).
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* If RSIGN='F' then the largest (absolute) eigenvalue will be
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* equal to DMAX.
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* Not modified.
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*
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* EI - CHARACTER*1 (ignored)
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* Not modified.
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*
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* RSIGN - CHARACTER*1
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* If MODE is not 0, 6, or -6, and RSIGN='T', then the
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* elements of D, as computed according to MODE and COND, will
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* be multiplied by a random complex number from the unit
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* circle |z| = 1. If RSIGN='F', they will not be. RSIGN may
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* only have the values 'T' or 'F'.
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* Not modified.
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*
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* UPPER - CHARACTER*1
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* If UPPER='T', then the elements of A above the diagonal
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* will be set to random numbers out of DIST. If UPPER='F',
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* they will not. UPPER may only have the values 'T' or 'F'.
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* Not modified.
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*
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* SIM - CHARACTER*1
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* If SIM='T', then A will be operated on by a "similarity
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* transform", i.e., multiplied on the left by a matrix X and
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* on the right by X inverse. X = U S V, where U and V are
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* random unitary matrices and S is a (diagonal) matrix of
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* singular values specified by DS, MODES, and CONDS. If
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* SIM='F', then A will not be transformed.
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* Not modified.
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*
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* DS - REAL array, dimension ( N )
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* This array is used to specify the singular values of X,
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* in the same way that D specifies the eigenvalues of A.
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* If MODE=0, the DS contains the singular values, which
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* may not be zero.
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* Modified if MODE is nonzero.
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*
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* MODES - INTEGER
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* CONDS - REAL
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* Similar to MODE and COND, but for specifying the diagonal
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* of S. MODES=-6 and +6 are not allowed (since they would
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* result in randomly ill-conditioned eigenvalues.)
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*
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* KL - INTEGER
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* This specifies the lower bandwidth of the matrix. KL=1
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* specifies upper Hessenberg form. If KL is at least N-1,
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* then A will have full lower bandwidth.
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* Not modified.
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*
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* KU - INTEGER
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* This specifies the upper bandwidth of the matrix. KU=1
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* specifies lower Hessenberg form. If KU is at least N-1,
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* then A will have full upper bandwidth; if KU and KL
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* are both at least N-1, then A will be dense. Only one of
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* KU and KL may be less than N-1.
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* Not modified.
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*
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* ANORM - REAL
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* If ANORM is not negative, then A will be scaled by a non-
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* negative real number to make the maximum-element-norm of A
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* to be ANORM.
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* Not modified.
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*
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* A - COMPLEX array, dimension ( LDA, N )
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* On exit A is the desired test matrix.
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* Modified.
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*
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* LDA - INTEGER
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* LDA specifies the first dimension of A as declared in the
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* calling program. LDA must be at least M.
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* Not modified.
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*
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* WORK - COMPLEX array, dimension ( 3*N )
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* Workspace.
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* Modified.
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*
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* INFO - INTEGER
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* Error code. On exit, INFO will be set to one of the
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* following values:
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* 0 => normal return
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* -1 => N negative
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* -2 => DIST illegal string
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* -5 => MODE not in range -6 to 6
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* -6 => COND less than 1.0, and MODE neither -6, 0 nor 6
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* -9 => RSIGN is not 'T' or 'F'
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* -10 => UPPER is not 'T' or 'F'
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* -11 => SIM is not 'T' or 'F'
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* -12 => MODES=0 and DS has a zero singular value.
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* -13 => MODES is not in the range -5 to 5.
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* -14 => MODES is nonzero and CONDS is less than 1.
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* -15 => KL is less than 1.
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* -16 => KU is less than 1, or KL and KU are both less than
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* N-1.
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* -19 => LDA is less than M.
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* 1 => Error return from CLATM1 (computing D)
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* 2 => Cannot scale to DMAX (max. eigenvalue is 0)
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* 3 => Error return from SLATM1 (computing DS)
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* 4 => Error return from CLARGE
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* 5 => Zero singular value from SLATM1.
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO
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PARAMETER ( ZERO = 0.0E+0 )
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REAL ONE
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PARAMETER ( ONE = 1.0E+0 )
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COMPLEX CZERO
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PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) )
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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL BADS
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INTEGER I, IC, ICOLS, IDIST, IINFO, IR, IROWS, IRSIGN,
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$ ISIM, IUPPER, J, JC, JCR
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REAL RALPHA, TEMP
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COMPLEX ALPHA, TAU, XNORMS
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* ..
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* .. Local Arrays ..
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REAL TEMPA( 1 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL CLANGE
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COMPLEX CLARND
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EXTERNAL LSAME, CLANGE, CLARND
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* ..
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* .. External Subroutines ..
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EXTERNAL CCOPY, CGEMV, CGERC, CLACGV, CLARFG, CLARGE,
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$ CLARNV, CLATM1, CLASET, CSCAL, CSSCAL, SLATM1,
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$ XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, CONJG, MAX, MOD
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* ..
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* .. Executable Statements ..
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*
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* 1) Decode and Test the input parameters.
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* Initialize flags & seed.
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*
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INFO = 0
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Decode DIST
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*
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IF( LSAME( DIST, 'U' ) ) THEN
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IDIST = 1
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ELSE IF( LSAME( DIST, 'S' ) ) THEN
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IDIST = 2
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ELSE IF( LSAME( DIST, 'N' ) ) THEN
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IDIST = 3
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ELSE IF( LSAME( DIST, 'D' ) ) THEN
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IDIST = 4
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ELSE
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IDIST = -1
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END IF
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*
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* Decode RSIGN
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*
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IF( LSAME( RSIGN, 'T' ) ) THEN
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IRSIGN = 1
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ELSE IF( LSAME( RSIGN, 'F' ) ) THEN
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IRSIGN = 0
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ELSE
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IRSIGN = -1
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END IF
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*
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* Decode UPPER
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*
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IF( LSAME( UPPER, 'T' ) ) THEN
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IUPPER = 1
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ELSE IF( LSAME( UPPER, 'F' ) ) THEN
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IUPPER = 0
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ELSE
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IUPPER = -1
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END IF
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*
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* Decode SIM
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*
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IF( LSAME( SIM, 'T' ) ) THEN
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ISIM = 1
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ELSE IF( LSAME( SIM, 'F' ) ) THEN
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ISIM = 0
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ELSE
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ISIM = -1
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END IF
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*
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* Check DS, if MODES=0 and ISIM=1
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*
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BADS = .FALSE.
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IF( MODES.EQ.0 .AND. ISIM.EQ.1 ) THEN
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DO 10 J = 1, N
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IF( DS( J ).EQ.ZERO )
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$ BADS = .TRUE.
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10 CONTINUE
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END IF
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*
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* Set INFO if an error
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*
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( IDIST.EQ.-1 ) THEN
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INFO = -2
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ELSE IF( ABS( MODE ).GT.6 ) THEN
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INFO = -5
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ELSE IF( ( MODE.NE.0 .AND. ABS( MODE ).NE.6 ) .AND. COND.LT.ONE )
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$ THEN
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INFO = -6
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ELSE IF( IRSIGN.EQ.-1 ) THEN
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INFO = -9
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ELSE IF( IUPPER.EQ.-1 ) THEN
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INFO = -10
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ELSE IF( ISIM.EQ.-1 ) THEN
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INFO = -11
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ELSE IF( BADS ) THEN
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INFO = -12
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ELSE IF( ISIM.EQ.1 .AND. ABS( MODES ).GT.5 ) THEN
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INFO = -13
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ELSE IF( ISIM.EQ.1 .AND. MODES.NE.0 .AND. CONDS.LT.ONE ) THEN
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INFO = -14
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ELSE IF( KL.LT.1 ) THEN
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INFO = -15
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ELSE IF( KU.LT.1 .OR. ( KU.LT.N-1 .AND. KL.LT.N-1 ) ) THEN
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INFO = -16
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -19
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CLATME', -INFO )
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RETURN
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END IF
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*
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* Initialize random number generator
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*
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DO 20 I = 1, 4
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ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 )
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20 CONTINUE
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*
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IF( MOD( ISEED( 4 ), 2 ).NE.1 )
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$ ISEED( 4 ) = ISEED( 4 ) + 1
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*
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* 2) Set up diagonal of A
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*
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* Compute D according to COND and MODE
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*
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CALL CLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, IINFO )
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IF( IINFO.NE.0 ) THEN
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INFO = 1
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RETURN
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END IF
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IF( MODE.NE.0 .AND. ABS( MODE ).NE.6 ) THEN
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*
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* Scale by DMAX
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*
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TEMP = ABS( D( 1 ) )
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DO 30 I = 2, N
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TEMP = MAX( TEMP, ABS( D( I ) ) )
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30 CONTINUE
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*
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IF( TEMP.GT.ZERO ) THEN
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ALPHA = DMAX / TEMP
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ELSE
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INFO = 2
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RETURN
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END IF
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*
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CALL CSCAL( N, ALPHA, D, 1 )
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*
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END IF
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*
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CALL CLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
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CALL CCOPY( N, D, 1, A, LDA+1 )
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*
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* 3) If UPPER='T', set upper triangle of A to random numbers.
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*
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IF( IUPPER.NE.0 ) THEN
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DO 40 JC = 2, N
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CALL CLARNV( IDIST, ISEED, JC-1, A( 1, JC ) )
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40 CONTINUE
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END IF
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*
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* 4) If SIM='T', apply similarity transformation.
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*
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* -1
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* Transform is X A X , where X = U S V, thus
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*
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* it is U S V A V' (1/S) U'
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*
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IF( ISIM.NE.0 ) THEN
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*
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* Compute S (singular values of the eigenvector matrix)
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* according to CONDS and MODES
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*
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CALL SLATM1( MODES, CONDS, 0, 0, ISEED, DS, N, IINFO )
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IF( IINFO.NE.0 ) THEN
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INFO = 3
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RETURN
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END IF
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*
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* Multiply by V and V'
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*
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CALL CLARGE( N, A, LDA, ISEED, WORK, IINFO )
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IF( IINFO.NE.0 ) THEN
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INFO = 4
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RETURN
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END IF
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*
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* Multiply by S and (1/S)
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*
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DO 50 J = 1, N
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CALL CSSCAL( N, DS( J ), A( J, 1 ), LDA )
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IF( DS( J ).NE.ZERO ) THEN
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CALL CSSCAL( N, ONE / DS( J ), A( 1, J ), 1 )
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ELSE
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INFO = 5
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RETURN
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END IF
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50 CONTINUE
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*
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* Multiply by U and U'
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*
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CALL CLARGE( N, A, LDA, ISEED, WORK, IINFO )
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IF( IINFO.NE.0 ) THEN
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INFO = 4
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RETURN
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END IF
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END IF
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*
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* 5) Reduce the bandwidth.
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*
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IF( KL.LT.N-1 ) THEN
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*
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* Reduce bandwidth -- kill column
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*
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DO 60 JCR = KL + 1, N - 1
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IC = JCR - KL
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IROWS = N + 1 - JCR
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ICOLS = N + KL - JCR
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*
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CALL CCOPY( IROWS, A( JCR, IC ), 1, WORK, 1 )
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XNORMS = WORK( 1 )
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CALL CLARFG( IROWS, XNORMS, WORK( 2 ), 1, TAU )
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TAU = CONJG( TAU )
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WORK( 1 ) = CONE
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ALPHA = CLARND( 5, ISEED )
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*
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CALL CGEMV( 'C', IROWS, ICOLS, CONE, A( JCR, IC+1 ), LDA,
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$ WORK, 1, CZERO, WORK( IROWS+1 ), 1 )
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CALL CGERC( IROWS, ICOLS, -TAU, WORK, 1, WORK( IROWS+1 ), 1,
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$ A( JCR, IC+1 ), LDA )
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*
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CALL CGEMV( 'N', N, IROWS, CONE, A( 1, JCR ), LDA, WORK, 1,
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$ CZERO, WORK( IROWS+1 ), 1 )
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CALL CGERC( N, IROWS, -CONJG( TAU ), WORK( IROWS+1 ), 1,
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$ WORK, 1, A( 1, JCR ), LDA )
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*
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A( JCR, IC ) = XNORMS
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CALL CLASET( 'Full', IROWS-1, 1, CZERO, CZERO,
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$ A( JCR+1, IC ), LDA )
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*
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CALL CSCAL( ICOLS+1, ALPHA, A( JCR, IC ), LDA )
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CALL CSCAL( N, CONJG( ALPHA ), A( 1, JCR ), 1 )
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60 CONTINUE
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ELSE IF( KU.LT.N-1 ) THEN
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*
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* Reduce upper bandwidth -- kill a row at a time.
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*
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|
DO 70 JCR = KU + 1, N - 1
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|
IR = JCR - KU
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|
IROWS = N + KU - JCR
|
|
ICOLS = N + 1 - JCR
|
|
*
|
|
CALL CCOPY( ICOLS, A( IR, JCR ), LDA, WORK, 1 )
|
|
XNORMS = WORK( 1 )
|
|
CALL CLARFG( ICOLS, XNORMS, WORK( 2 ), 1, TAU )
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|
TAU = CONJG( TAU )
|
|
WORK( 1 ) = CONE
|
|
CALL CLACGV( ICOLS-1, WORK( 2 ), 1 )
|
|
ALPHA = CLARND( 5, ISEED )
|
|
*
|
|
CALL CGEMV( 'N', IROWS, ICOLS, CONE, A( IR+1, JCR ), LDA,
|
|
$ WORK, 1, CZERO, WORK( ICOLS+1 ), 1 )
|
|
CALL CGERC( IROWS, ICOLS, -TAU, WORK( ICOLS+1 ), 1, WORK, 1,
|
|
$ A( IR+1, JCR ), LDA )
|
|
*
|
|
CALL CGEMV( 'C', ICOLS, N, CONE, A( JCR, 1 ), LDA, WORK, 1,
|
|
$ CZERO, WORK( ICOLS+1 ), 1 )
|
|
CALL CGERC( ICOLS, N, -CONJG( TAU ), WORK, 1,
|
|
$ WORK( ICOLS+1 ), 1, A( JCR, 1 ), LDA )
|
|
*
|
|
A( IR, JCR ) = XNORMS
|
|
CALL CLASET( 'Full', 1, ICOLS-1, CZERO, CZERO,
|
|
$ A( IR, JCR+1 ), LDA )
|
|
*
|
|
CALL CSCAL( IROWS+1, ALPHA, A( IR, JCR ), 1 )
|
|
CALL CSCAL( N, CONJG( ALPHA ), A( JCR, 1 ), LDA )
|
|
70 CONTINUE
|
|
END IF
|
|
*
|
|
* Scale the matrix to have norm ANORM
|
|
*
|
|
IF( ANORM.GE.ZERO ) THEN
|
|
TEMP = CLANGE( 'M', N, N, A, LDA, TEMPA )
|
|
IF( TEMP.GT.ZERO ) THEN
|
|
RALPHA = ANORM / TEMP
|
|
DO 80 J = 1, N
|
|
CALL CSSCAL( N, RALPHA, A( 1, J ), 1 )
|
|
80 CONTINUE
|
|
END IF
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CLATME
|
|
*
|
|
END
|