1021 lines
35 KiB
Fortran
1021 lines
35 KiB
Fortran
*> \brief \b DDRVVX
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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* NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1,
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* VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1,
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* RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1,
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* RESULT, WORK, NWORK, IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
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* $ NSIZES, NTYPES, NWORK
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* DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER ISEED( 4 ), IWORK( * ), NN( * )
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* DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
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* $ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
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* $ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
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* $ RESULT( 11 ), SCALE( * ), SCALE1( * ),
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* $ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
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* $ WI1( * ), WORK( * ), WR( * ), WR1( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DDRVVX checks the nonsymmetric eigenvalue problem expert driver
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*> DGEEVX.
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*>
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*> DDRVVX uses both test matrices generated randomly depending on
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*> data supplied in the calling sequence, as well as on data
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*> read from an input file and including precomputed condition
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*> numbers to which it compares the ones it computes.
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*>
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*> When DDRVVX is called, a number of matrix "sizes" ("n's") and a
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*> number of matrix "types" are specified in the calling sequence.
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*> For each size ("n") and each type of matrix, one matrix will be
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*> generated and used to test the nonsymmetric eigenroutines. For
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*> each matrix, 9 tests will be performed:
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*>
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*> (1) | A * VR - VR * W | / ( n |A| ulp )
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*>
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*> Here VR is the matrix of unit right eigenvectors.
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*> W is a block diagonal matrix, with a 1x1 block for each
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*> real eigenvalue and a 2x2 block for each complex conjugate
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*> pair. If eigenvalues j and j+1 are a complex conjugate pair,
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*> so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
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*> 2 x 2 block corresponding to the pair will be:
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*>
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*> ( wr wi )
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*> ( -wi wr )
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*>
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*> Such a block multiplying an n x 2 matrix ( ur ui ) on the
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*> right will be the same as multiplying ur + i*ui by wr + i*wi.
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*>
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*> (2) | A**H * VL - VL * W**H | / ( n |A| ulp )
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*>
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*> Here VL is the matrix of unit left eigenvectors, A**H is the
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*> conjugate transpose of A, and W is as above.
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*>
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*> (3) | |VR(i)| - 1 | / ulp and largest component real
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*>
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*> VR(i) denotes the i-th column of VR.
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*>
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*> (4) | |VL(i)| - 1 | / ulp and largest component real
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*>
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*> VL(i) denotes the i-th column of VL.
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*>
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*> (5) W(full) = W(partial)
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*>
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*> W(full) denotes the eigenvalues computed when VR, VL, RCONDV
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*> and RCONDE are also computed, and W(partial) denotes the
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*> eigenvalues computed when only some of VR, VL, RCONDV, and
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*> RCONDE are computed.
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*>
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*> (6) VR(full) = VR(partial)
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*>
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*> VR(full) denotes the right eigenvectors computed when VL, RCONDV
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*> and RCONDE are computed, and VR(partial) denotes the result
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*> when only some of VL and RCONDV are computed.
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*>
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*> (7) VL(full) = VL(partial)
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*>
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*> VL(full) denotes the left eigenvectors computed when VR, RCONDV
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*> and RCONDE are computed, and VL(partial) denotes the result
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*> when only some of VR and RCONDV are computed.
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*>
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*> (8) 0 if SCALE, ILO, IHI, ABNRM (full) =
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*> SCALE, ILO, IHI, ABNRM (partial)
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*> 1/ulp otherwise
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*>
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*> SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
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*> (full) is when VR, VL, RCONDE and RCONDV are also computed, and
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*> (partial) is when some are not computed.
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*>
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*> (9) RCONDV(full) = RCONDV(partial)
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*>
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*> RCONDV(full) denotes the reciprocal condition numbers of the
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*> right eigenvectors computed when VR, VL and RCONDE are also
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*> computed. RCONDV(partial) denotes the reciprocal condition
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*> numbers when only some of VR, VL and RCONDE are computed.
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*>
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*> The "sizes" are specified by an array NN(1:NSIZES); the value of
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*> each element NN(j) specifies one size.
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*> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
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*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
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*> Currently, the list of possible types is:
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*>
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*> (1) The zero matrix.
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*> (2) The identity matrix.
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*> (3) A (transposed) Jordan block, with 1's on the diagonal.
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*>
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*> (4) A diagonal matrix with evenly spaced entries
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*> 1, ..., ULP and random signs.
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*> (ULP = (first number larger than 1) - 1 )
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*> (5) A diagonal matrix with geometrically spaced entries
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*> 1, ..., ULP and random signs.
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*> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
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*> and random signs.
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*>
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*> (7) Same as (4), but multiplied by a constant near
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*> the overflow threshold
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*> (8) Same as (4), but multiplied by a constant near
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*> the underflow threshold
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*>
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*> (9) A matrix of the form U' T U, where U is orthogonal and
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*> T has evenly spaced entries 1, ..., ULP with random signs
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*> on the diagonal and random O(1) entries in the upper
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*> triangle.
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*>
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*> (10) A matrix of the form U' T U, where U is orthogonal and
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*> T has geometrically spaced entries 1, ..., ULP with random
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*> signs on the diagonal and random O(1) entries in the upper
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*> triangle.
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*>
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*> (11) A matrix of the form U' T U, where U is orthogonal and
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*> T has "clustered" entries 1, ULP,..., ULP with random
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*> signs on the diagonal and random O(1) entries in the upper
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*> triangle.
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*>
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*> (12) A matrix of the form U' T U, where U is orthogonal and
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*> T has real or complex conjugate paired eigenvalues randomly
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*> chosen from ( ULP, 1 ) and random O(1) entries in the upper
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*> triangle.
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*>
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*> (13) A matrix of the form X' T X, where X has condition
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*> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
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*> with random signs on the diagonal and random O(1) entries
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*> in the upper triangle.
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*>
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*> (14) A matrix of the form X' T X, where X has condition
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*> SQRT( ULP ) and T has geometrically spaced entries
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*> 1, ..., ULP with random signs on the diagonal and random
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*> O(1) entries in the upper triangle.
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*>
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*> (15) A matrix of the form X' T X, where X has condition
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*> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
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*> with random signs on the diagonal and random O(1) entries
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*> in the upper triangle.
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*>
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*> (16) A matrix of the form X' T X, where X has condition
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*> SQRT( ULP ) and T has real or complex conjugate paired
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*> eigenvalues randomly chosen from ( ULP, 1 ) and random
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*> O(1) entries in the upper triangle.
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*>
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*> (17) Same as (16), but multiplied by a constant
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*> near the overflow threshold
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*> (18) Same as (16), but multiplied by a constant
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*> near the underflow threshold
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*>
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*> (19) Nonsymmetric matrix with random entries chosen from (-1,1).
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*> If N is at least 4, all entries in first two rows and last
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*> row, and first column and last two columns are zero.
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*> (20) Same as (19), but multiplied by a constant
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*> near the overflow threshold
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*> (21) Same as (19), but multiplied by a constant
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*> near the underflow threshold
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*>
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*> In addition, an input file will be read from logical unit number
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*> NIUNIT. The file contains matrices along with precomputed
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*> eigenvalues and reciprocal condition numbers for the eigenvalues
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*> and right eigenvectors. For these matrices, in addition to tests
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*> (1) to (9) we will compute the following two tests:
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*>
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*> (10) |RCONDV - RCDVIN| / cond(RCONDV)
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*>
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*> RCONDV is the reciprocal right eigenvector condition number
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*> computed by DGEEVX and RCDVIN (the precomputed true value)
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*> is supplied as input. cond(RCONDV) is the condition number of
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*> RCONDV, and takes errors in computing RCONDV into account, so
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*> that the resulting quantity should be O(ULP). cond(RCONDV) is
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*> essentially given by norm(A)/RCONDE.
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*>
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*> (11) |RCONDE - RCDEIN| / cond(RCONDE)
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*>
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*> RCONDE is the reciprocal eigenvalue condition number
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*> computed by DGEEVX and RCDEIN (the precomputed true value)
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*> is supplied as input. cond(RCONDE) is the condition number
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*> of RCONDE, and takes errors in computing RCONDE into account,
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*> so that the resulting quantity should be O(ULP). cond(RCONDE)
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*> is essentially given by norm(A)/RCONDV.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NSIZES
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*> \verbatim
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*> NSIZES is INTEGER
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*> The number of sizes of matrices to use. NSIZES must be at
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*> least zero. If it is zero, no randomly generated matrices
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*> are tested, but any test matrices read from NIUNIT will be
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*> tested.
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*> \endverbatim
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*>
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*> \param[in] NN
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*> \verbatim
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*> NN is INTEGER array, dimension (NSIZES)
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*> An array containing the sizes to be used for the matrices.
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*> Zero values will be skipped. The values must be at least
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*> zero.
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*> \endverbatim
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*>
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*> \param[in] NTYPES
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*> \verbatim
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*> NTYPES is INTEGER
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*> The number of elements in DOTYPE. NTYPES must be at least
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*> zero. If it is zero, no randomly generated test matrices
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*> are tested, but and test matrices read from NIUNIT will be
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*> tested. If it is MAXTYP+1 and NSIZES is 1, then an
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*> additional type, MAXTYP+1 is defined, which is to use
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*> whatever matrix is in A. This is only useful if
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*> DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
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*> \endverbatim
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*>
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*> \param[in] DOTYPE
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*> \verbatim
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*> DOTYPE is LOGICAL array, dimension (NTYPES)
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*> If DOTYPE(j) is .TRUE., then for each size in NN a
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*> matrix of that size and of type j will be generated.
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*> If NTYPES is smaller than the maximum number of types
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*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
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*> MAXTYP will not be generated. If NTYPES is larger
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*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
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*> will be ignored.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry ISEED specifies the seed of the random number
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*> generator. The array elements should be between 0 and 4095;
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*> if not they will be reduced mod 4096. Also, ISEED(4) must
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*> be odd. The random number generator uses a linear
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*> congruential sequence limited to small integers, and so
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*> should produce machine independent random numbers. The
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*> values of ISEED are changed on exit, and can be used in the
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*> next call to DDRVVX to continue the same random number
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*> sequence.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is DOUBLE PRECISION
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*> A test will count as "failed" if the "error", computed as
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*> described above, exceeds THRESH. Note that the error
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*> is scaled to be O(1), so THRESH should be a reasonably
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*> small multiple of 1, e.g., 10 or 100. In particular,
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*> it should not depend on the precision (single vs. double)
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*> or the size of the matrix. It must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] NIUNIT
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*> \verbatim
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*> NIUNIT is INTEGER
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*> The FORTRAN unit number for reading in the data file of
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*> problems to solve.
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*> \endverbatim
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*>
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*> \param[in] NOUNIT
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*> \verbatim
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*> NOUNIT is INTEGER
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*> The FORTRAN unit number for printing out error messages
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*> (e.g., if a routine returns INFO not equal to 0.)
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension
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*> (LDA, max(NN,12))
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*> Used to hold the matrix whose eigenvalues are to be
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*> computed. On exit, A contains the last matrix actually used.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the arrays A and H.
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*> LDA >= max(NN,12), since 12 is the dimension of the largest
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*> matrix in the precomputed input file.
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*> \endverbatim
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*>
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*> \param[out] H
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*> \verbatim
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*> H is DOUBLE PRECISION array, dimension
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*> (LDA, max(NN,12))
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*> Another copy of the test matrix A, modified by DGEEVX.
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*> \endverbatim
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*>
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*> \param[out] WR
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*> \verbatim
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*> WR is DOUBLE PRECISION array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] WI
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*> \verbatim
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*> WI is DOUBLE PRECISION array, dimension (max(NN))
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*>
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*> The real and imaginary parts of the eigenvalues of A.
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*> On exit, WR + WI*i are the eigenvalues of the matrix in A.
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*> \endverbatim
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*>
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*> \param[out] WR1
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*> \verbatim
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*> WR1 is DOUBLE PRECISION array, dimension (max(NN,12))
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*> \endverbatim
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*>
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*> \param[out] WI1
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*> \verbatim
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*> WI1 is DOUBLE PRECISION array, dimension (max(NN,12))
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*>
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*> Like WR, WI, these arrays contain the eigenvalues of A,
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*> but those computed when DGEEVX only computes a partial
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*> eigendecomposition, i.e. not the eigenvalues and left
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*> and right eigenvectors.
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*> \endverbatim
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*>
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*> \param[out] VL
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*> \verbatim
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*> VL is DOUBLE PRECISION array, dimension
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*> (LDVL, max(NN,12))
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*> VL holds the computed left eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDVL
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*> \verbatim
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*> LDVL is INTEGER
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*> Leading dimension of VL. Must be at least max(1,max(NN,12)).
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*> \endverbatim
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*>
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*> \param[out] VR
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*> \verbatim
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*> VR is DOUBLE PRECISION array, dimension
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*> (LDVR, max(NN,12))
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*> VR holds the computed right eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDVR
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*> \verbatim
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*> LDVR is INTEGER
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*> Leading dimension of VR. Must be at least max(1,max(NN,12)).
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*> \endverbatim
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*>
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*> \param[out] LRE
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*> \verbatim
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*> LRE is DOUBLE PRECISION array, dimension
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*> (LDLRE, max(NN,12))
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*> LRE holds the computed right or left eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDLRE
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*> \verbatim
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*> LDLRE is INTEGER
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*> Leading dimension of LRE. Must be at least max(1,max(NN,12))
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*> \endverbatim
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*>
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*> \param[out] RCONDV
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*> \verbatim
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*> RCONDV is DOUBLE PRECISION array, dimension (N)
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*> RCONDV holds the computed reciprocal condition numbers
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*> for eigenvectors.
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*> \endverbatim
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*>
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*> \param[out] RCNDV1
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*> \verbatim
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*> RCNDV1 is DOUBLE PRECISION array, dimension (N)
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*> RCNDV1 holds more computed reciprocal condition numbers
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*> for eigenvectors.
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*> \endverbatim
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*>
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*> \param[out] RCDVIN
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*> \verbatim
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*> RCDVIN is DOUBLE PRECISION array, dimension (N)
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*> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
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*> condition numbers for eigenvectors to be compared with
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*> RCONDV.
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*> \endverbatim
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*>
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*> \param[out] RCONDE
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*> \verbatim
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*> RCONDE is DOUBLE PRECISION array, dimension (N)
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*> RCONDE holds the computed reciprocal condition numbers
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*> for eigenvalues.
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*> \endverbatim
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*>
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*> \param[out] RCNDE1
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*> \verbatim
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*> RCNDE1 is DOUBLE PRECISION array, dimension (N)
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*> RCNDE1 holds more computed reciprocal condition numbers
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*> for eigenvalues.
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*> \endverbatim
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*>
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*> \param[out] RCDEIN
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*> \verbatim
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*> RCDEIN is DOUBLE PRECISION array, dimension (N)
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*> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
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*> condition numbers for eigenvalues to be compared with
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*> RCONDE.
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*> \endverbatim
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*>
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*> \param[out] SCALE
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*> \verbatim
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*> SCALE is DOUBLE PRECISION array, dimension (N)
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*> Holds information describing balancing of matrix.
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*> \endverbatim
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*>
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*> \param[out] SCALE1
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*> \verbatim
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*> SCALE1 is DOUBLE PRECISION array, dimension (N)
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*> Holds information describing balancing of matrix.
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is DOUBLE PRECISION array, dimension (11)
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*> The values computed by the seven tests described above.
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*> The values are currently limited to 1/ulp, to avoid overflow.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (NWORK)
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*> \endverbatim
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*>
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*> \param[in] NWORK
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*> \verbatim
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*> NWORK is INTEGER
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*> The number of entries in WORK. This must be at least
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*> max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
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*> max( 360 ,6*NN(j)+2*NN(j)**2) for all j.
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (2*max(NN,12))
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] INFO
|
|
*> \verbatim
|
|
*> INFO is INTEGER
|
|
*> If 0, then successful exit.
|
|
*> If <0, then input paramter -INFO is incorrect.
|
|
*> If >0, DLATMR, SLATMS, SLATME or DGET23 returned an error
|
|
*> code, and INFO is its absolute value.
|
|
*>
|
|
*>-----------------------------------------------------------------------
|
|
*>
|
|
*> Some Local Variables and Parameters:
|
|
*> ---- ----- --------- --- ----------
|
|
*>
|
|
*> ZERO, ONE Real 0 and 1.
|
|
*> MAXTYP The number of types defined.
|
|
*> NMAX Largest value in NN or 12.
|
|
*> NERRS The number of tests which have exceeded THRESH
|
|
*> COND, CONDS,
|
|
*> IMODE Values to be passed to the matrix generators.
|
|
*> ANORM Norm of A; passed to matrix generators.
|
|
*>
|
|
*> OVFL, UNFL Overflow and underflow thresholds.
|
|
*> ULP, ULPINV Finest relative precision and its inverse.
|
|
*> RTULP, RTULPI Square roots of the previous 4 values.
|
|
*>
|
|
*> The following four arrays decode JTYPE:
|
|
*> KTYPE(j) The general type (1-10) for type "j".
|
|
*> KMODE(j) The MODE value to be passed to the matrix
|
|
*> generator for type "j".
|
|
*> KMAGN(j) The order of magnitude ( O(1),
|
|
*> O(overflow^(1/2) ), O(underflow^(1/2) )
|
|
*> KCONDS(j) Selectw whether CONDS is to be 1 or
|
|
*> 1/sqrt(ulp). (0 means irrelevant.)
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date November 2011
|
|
*
|
|
*> \ingroup double_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
|
|
$ NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1,
|
|
$ VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1,
|
|
$ RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1,
|
|
$ RESULT, WORK, NWORK, IWORK, INFO )
|
|
*
|
|
* -- LAPACK test routine (version 3.4.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
|
|
$ NSIZES, NTYPES, NWORK
|
|
DOUBLE PRECISION THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
LOGICAL DOTYPE( * )
|
|
INTEGER ISEED( 4 ), IWORK( * ), NN( * )
|
|
DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
|
|
$ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
|
|
$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
|
|
$ RESULT( 11 ), SCALE( * ), SCALE1( * ),
|
|
$ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
|
|
$ WI1( * ), WORK( * ), WR( * ), WR1( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
|
|
INTEGER MAXTYP
|
|
PARAMETER ( MAXTYP = 21 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL BADNN
|
|
CHARACTER BALANC
|
|
CHARACTER*3 PATH
|
|
INTEGER I, IBAL, IINFO, IMODE, ITYPE, IWK, J, JCOL,
|
|
$ JSIZE, JTYPE, MTYPES, N, NERRS, NFAIL, NMAX,
|
|
$ NNWORK, NTEST, NTESTF, NTESTT
|
|
DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP,
|
|
$ ULPINV, UNFL
|
|
* ..
|
|
* .. Local Arrays ..
|
|
CHARACTER ADUMMA( 1 ), BAL( 4 )
|
|
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
|
|
$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
|
|
$ KTYPE( MAXTYP )
|
|
* ..
|
|
* .. External Functions ..
|
|
DOUBLE PRECISION DLAMCH
|
|
EXTERNAL DLAMCH
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DGET23, DLABAD, DLASET, DLASUM, DLATME, DLATMR,
|
|
$ DLATMS, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, MAX, MIN, SQRT
|
|
* ..
|
|
* .. Data statements ..
|
|
DATA KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
|
|
DATA KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
|
|
$ 3, 1, 2, 3 /
|
|
DATA KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
|
|
$ 1, 5, 5, 5, 4, 3, 1 /
|
|
DATA KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 /
|
|
DATA BAL / 'N', 'P', 'S', 'B' /
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
PATH( 1: 1 ) = 'Double precision'
|
|
PATH( 2: 3 ) = 'VX'
|
|
*
|
|
* Check for errors
|
|
*
|
|
NTESTT = 0
|
|
NTESTF = 0
|
|
INFO = 0
|
|
*
|
|
* Important constants
|
|
*
|
|
BADNN = .FALSE.
|
|
*
|
|
* 12 is the largest dimension in the input file of precomputed
|
|
* problems
|
|
*
|
|
NMAX = 12
|
|
DO 10 J = 1, NSIZES
|
|
NMAX = MAX( NMAX, NN( J ) )
|
|
IF( NN( J ).LT.0 )
|
|
$ BADNN = .TRUE.
|
|
10 CONTINUE
|
|
*
|
|
* Check for errors
|
|
*
|
|
IF( NSIZES.LT.0 ) THEN
|
|
INFO = -1
|
|
ELSE IF( BADNN ) THEN
|
|
INFO = -2
|
|
ELSE IF( NTYPES.LT.0 ) THEN
|
|
INFO = -3
|
|
ELSE IF( THRESH.LT.ZERO ) THEN
|
|
INFO = -6
|
|
ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
|
|
INFO = -10
|
|
ELSE IF( LDVL.LT.1 .OR. LDVL.LT.NMAX ) THEN
|
|
INFO = -17
|
|
ELSE IF( LDVR.LT.1 .OR. LDVR.LT.NMAX ) THEN
|
|
INFO = -19
|
|
ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.NMAX ) THEN
|
|
INFO = -21
|
|
ELSE IF( 6*NMAX+2*NMAX**2.GT.NWORK ) THEN
|
|
INFO = -32
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'DDRVVX', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* If nothing to do check on NIUNIT
|
|
*
|
|
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
|
|
$ GO TO 160
|
|
*
|
|
* More Important constants
|
|
*
|
|
UNFL = DLAMCH( 'Safe minimum' )
|
|
OVFL = ONE / UNFL
|
|
CALL DLABAD( UNFL, OVFL )
|
|
ULP = DLAMCH( 'Precision' )
|
|
ULPINV = ONE / ULP
|
|
RTULP = SQRT( ULP )
|
|
RTULPI = ONE / RTULP
|
|
*
|
|
* Loop over sizes, types
|
|
*
|
|
NERRS = 0
|
|
*
|
|
DO 150 JSIZE = 1, NSIZES
|
|
N = NN( JSIZE )
|
|
IF( NSIZES.NE.1 ) THEN
|
|
MTYPES = MIN( MAXTYP, NTYPES )
|
|
ELSE
|
|
MTYPES = MIN( MAXTYP+1, NTYPES )
|
|
END IF
|
|
*
|
|
DO 140 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 140
|
|
*
|
|
* Save ISEED in case of an error.
|
|
*
|
|
DO 20 J = 1, 4
|
|
IOLDSD( J ) = ISEED( J )
|
|
20 CONTINUE
|
|
*
|
|
* Compute "A"
|
|
*
|
|
* Control parameters:
|
|
*
|
|
* KMAGN KCONDS KMODE KTYPE
|
|
* =1 O(1) 1 clustered 1 zero
|
|
* =2 large large clustered 2 identity
|
|
* =3 small exponential Jordan
|
|
* =4 arithmetic diagonal, (w/ eigenvalues)
|
|
* =5 random log symmetric, w/ eigenvalues
|
|
* =6 random general, w/ eigenvalues
|
|
* =7 random diagonal
|
|
* =8 random symmetric
|
|
* =9 random general
|
|
* =10 random triangular
|
|
*
|
|
IF( MTYPES.GT.MAXTYP )
|
|
$ GO TO 90
|
|
*
|
|
ITYPE = KTYPE( JTYPE )
|
|
IMODE = KMODE( JTYPE )
|
|
*
|
|
* Compute norm
|
|
*
|
|
GO TO ( 30, 40, 50 )KMAGN( JTYPE )
|
|
*
|
|
30 CONTINUE
|
|
ANORM = ONE
|
|
GO TO 60
|
|
*
|
|
40 CONTINUE
|
|
ANORM = OVFL*ULP
|
|
GO TO 60
|
|
*
|
|
50 CONTINUE
|
|
ANORM = UNFL*ULPINV
|
|
GO TO 60
|
|
*
|
|
60 CONTINUE
|
|
*
|
|
CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
|
|
IINFO = 0
|
|
COND = ULPINV
|
|
*
|
|
* Special Matrices -- Identity & Jordan block
|
|
*
|
|
* Zero
|
|
*
|
|
IF( ITYPE.EQ.1 ) THEN
|
|
IINFO = 0
|
|
*
|
|
ELSE IF( ITYPE.EQ.2 ) THEN
|
|
*
|
|
* Identity
|
|
*
|
|
DO 70 JCOL = 1, N
|
|
A( JCOL, JCOL ) = ANORM
|
|
70 CONTINUE
|
|
*
|
|
ELSE IF( ITYPE.EQ.3 ) THEN
|
|
*
|
|
* Jordan Block
|
|
*
|
|
DO 80 JCOL = 1, N
|
|
A( JCOL, JCOL ) = ANORM
|
|
IF( JCOL.GT.1 )
|
|
$ A( JCOL, JCOL-1 ) = ONE
|
|
80 CONTINUE
|
|
*
|
|
ELSE IF( ITYPE.EQ.4 ) THEN
|
|
*
|
|
* Diagonal Matrix, [Eigen]values Specified
|
|
*
|
|
CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
|
|
$ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
|
|
$ IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.5 ) THEN
|
|
*
|
|
* Symmetric, eigenvalues specified
|
|
*
|
|
CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
|
|
$ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
|
|
$ IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.6 ) THEN
|
|
*
|
|
* General, eigenvalues specified
|
|
*
|
|
IF( KCONDS( JTYPE ).EQ.1 ) THEN
|
|
CONDS = ONE
|
|
ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN
|
|
CONDS = RTULPI
|
|
ELSE
|
|
CONDS = ZERO
|
|
END IF
|
|
*
|
|
ADUMMA( 1 ) = ' '
|
|
CALL DLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE,
|
|
$ ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4,
|
|
$ CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ),
|
|
$ IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.7 ) THEN
|
|
*
|
|
* Diagonal, random eigenvalues
|
|
*
|
|
CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.8 ) THEN
|
|
*
|
|
* Symmetric, random eigenvalues
|
|
*
|
|
CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.9 ) THEN
|
|
*
|
|
* General, random eigenvalues
|
|
*
|
|
CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
|
IF( N.GE.4 ) THEN
|
|
CALL DLASET( 'Full', 2, N, ZERO, ZERO, A, LDA )
|
|
CALL DLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ),
|
|
$ LDA )
|
|
CALL DLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ),
|
|
$ LDA )
|
|
CALL DLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ),
|
|
$ LDA )
|
|
END IF
|
|
*
|
|
ELSE IF( ITYPE.EQ.10 ) THEN
|
|
*
|
|
* Triangular, random eigenvalues
|
|
*
|
|
CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
|
*
|
|
ELSE
|
|
*
|
|
IINFO = 1
|
|
END IF
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9992 )'Generator', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
90 CONTINUE
|
|
*
|
|
* Test for minimal and generous workspace
|
|
*
|
|
DO 130 IWK = 1, 3
|
|
IF( IWK.EQ.1 ) THEN
|
|
NNWORK = 3*N
|
|
ELSE IF( IWK.EQ.2 ) THEN
|
|
NNWORK = 6*N + N**2
|
|
ELSE
|
|
NNWORK = 6*N + 2*N**2
|
|
END IF
|
|
NNWORK = MAX( NNWORK, 1 )
|
|
*
|
|
* Test for all balancing options
|
|
*
|
|
DO 120 IBAL = 1, 4
|
|
BALANC = BAL( IBAL )
|
|
*
|
|
* Perform tests
|
|
*
|
|
CALL DGET23( .FALSE., BALANC, JTYPE, THRESH, IOLDSD,
|
|
$ NOUNIT, N, A, LDA, H, WR, WI, WR1, WI1,
|
|
$ VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV,
|
|
$ RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN,
|
|
$ SCALE, SCALE1, RESULT, WORK, NNWORK,
|
|
$ IWORK, INFO )
|
|
*
|
|
* Check for RESULT(j) > THRESH
|
|
*
|
|
NTEST = 0
|
|
NFAIL = 0
|
|
DO 100 J = 1, 9
|
|
IF( RESULT( J ).GE.ZERO )
|
|
$ NTEST = NTEST + 1
|
|
IF( RESULT( J ).GE.THRESH )
|
|
$ NFAIL = NFAIL + 1
|
|
100 CONTINUE
|
|
*
|
|
IF( NFAIL.GT.0 )
|
|
$ NTESTF = NTESTF + 1
|
|
IF( NTESTF.EQ.1 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )PATH
|
|
WRITE( NOUNIT, FMT = 9998 )
|
|
WRITE( NOUNIT, FMT = 9997 )
|
|
WRITE( NOUNIT, FMT = 9996 )
|
|
WRITE( NOUNIT, FMT = 9995 )THRESH
|
|
NTESTF = 2
|
|
END IF
|
|
*
|
|
DO 110 J = 1, 9
|
|
IF( RESULT( J ).GE.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9994 )BALANC, N, IWK,
|
|
$ IOLDSD, JTYPE, J, RESULT( J )
|
|
END IF
|
|
110 CONTINUE
|
|
*
|
|
NERRS = NERRS + NFAIL
|
|
NTESTT = NTESTT + NTEST
|
|
*
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
140 CONTINUE
|
|
150 CONTINUE
|
|
*
|
|
160 CONTINUE
|
|
*
|
|
* Read in data from file to check accuracy of condition estimation.
|
|
* Assume input eigenvalues are sorted lexicographically (increasing
|
|
* by real part, then decreasing by imaginary part)
|
|
*
|
|
JTYPE = 0
|
|
170 CONTINUE
|
|
READ( NIUNIT, FMT = *, END = 220 )N
|
|
*
|
|
* Read input data until N=0
|
|
*
|
|
IF( N.EQ.0 )
|
|
$ GO TO 220
|
|
JTYPE = JTYPE + 1
|
|
ISEED( 1 ) = JTYPE
|
|
DO 180 I = 1, N
|
|
READ( NIUNIT, FMT = * )( A( I, J ), J = 1, N )
|
|
180 CONTINUE
|
|
DO 190 I = 1, N
|
|
READ( NIUNIT, FMT = * )WR1( I ), WI1( I ), RCDEIN( I ),
|
|
$ RCDVIN( I )
|
|
190 CONTINUE
|
|
CALL DGET23( .TRUE., 'N', 22, THRESH, ISEED, NOUNIT, N, A, LDA, H,
|
|
$ WR, WI, WR1, WI1, VL, LDVL, VR, LDVR, LRE, LDLRE,
|
|
$ RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN,
|
|
$ SCALE, SCALE1, RESULT, WORK, 6*N+2*N**2, IWORK,
|
|
$ INFO )
|
|
*
|
|
* Check for RESULT(j) > THRESH
|
|
*
|
|
NTEST = 0
|
|
NFAIL = 0
|
|
DO 200 J = 1, 11
|
|
IF( RESULT( J ).GE.ZERO )
|
|
$ NTEST = NTEST + 1
|
|
IF( RESULT( J ).GE.THRESH )
|
|
$ NFAIL = NFAIL + 1
|
|
200 CONTINUE
|
|
*
|
|
IF( NFAIL.GT.0 )
|
|
$ NTESTF = NTESTF + 1
|
|
IF( NTESTF.EQ.1 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )PATH
|
|
WRITE( NOUNIT, FMT = 9998 )
|
|
WRITE( NOUNIT, FMT = 9997 )
|
|
WRITE( NOUNIT, FMT = 9996 )
|
|
WRITE( NOUNIT, FMT = 9995 )THRESH
|
|
NTESTF = 2
|
|
END IF
|
|
*
|
|
DO 210 J = 1, 11
|
|
IF( RESULT( J ).GE.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9993 )N, JTYPE, J, RESULT( J )
|
|
END IF
|
|
210 CONTINUE
|
|
*
|
|
NERRS = NERRS + NFAIL
|
|
NTESTT = NTESTT + NTEST
|
|
GO TO 170
|
|
220 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL DLASUM( PATH, NOUNIT, NERRS, NTESTT )
|
|
*
|
|
9999 FORMAT( / 1X, A3, ' -- Real Eigenvalue-Eigenvector Decomposition',
|
|
$ ' Expert Driver', /
|
|
$ ' Matrix types (see DDRVVX for details): ' )
|
|
*
|
|
9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
|
|
$ ' ', ' 5=Diagonal: geometr. spaced entries.',
|
|
$ / ' 2=Identity matrix. ', ' 6=Diagona',
|
|
$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
|
|
$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
|
|
$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
|
|
$ 'mall, evenly spaced.' )
|
|
9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
|
|
$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
|
|
$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
|
|
$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
|
|
$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
|
|
$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
|
|
$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
|
|
$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
|
|
$ ' complx ' )
|
|
9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
|
|
$ 'with small random entries.', / ' 20=Matrix with large ran',
|
|
$ 'dom entries. ', ' 22=Matrix read from input file', / )
|
|
9995 FORMAT( ' Tests performed with test threshold =', F8.2,
|
|
$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
|
|
$ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
|
|
$ / ' 3 = | |VR(i)| - 1 | / ulp ',
|
|
$ / ' 4 = | |VL(i)| - 1 | / ulp ',
|
|
$ / ' 5 = 0 if W same no matter if VR or VL computed,',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 6 = 0 if VR same no matter what else computed,',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 7 = 0 if VL same no matter what else computed,',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 8 = 0 if RCONDV same no matter what else computed,',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
|
|
$ ' computed, 1/ulp otherwise',
|
|
$ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
|
|
$ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
|
|
9994 FORMAT( ' BALANC=''', A1, ''',N=', I4, ',IWK=', I1, ', seed=',
|
|
$ 4( I4, ',' ), ' type ', I2, ', test(', I2, ')=', G10.3 )
|
|
9993 FORMAT( ' N=', I5, ', input example =', I3, ', test(', I2, ')=',
|
|
$ G10.3 )
|
|
9992 FORMAT( ' DDRVVX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of DDRVVX
|
|
*
|
|
END
|