981 lines
34 KiB
Fortran
981 lines
34 KiB
Fortran
*> \brief \b DDRVEV
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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 DDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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* NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL,
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* VR, LDVR, LRE, LDLRE, RESULT, WORK, NWORK,
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* IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NOUNIT, NSIZES,
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* $ 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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* $ RESULT( 7 ), VL( LDVL, * ), VR( LDVR, * ),
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* $ WI( * ), 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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*> DDRVEV checks the nonsymmetric eigenvalue problem driver DGEEV.
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*>
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*> When DDRVEV is called, a number of matrix "sizes" ("n's") and a
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*> number of matrix "types" are specified. For each size ("n")
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*> and each type of matrix, one matrix will be generated and used
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*> to test the nonsymmetric eigenroutines. For each matrix, 7
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*> 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 whether 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 whether 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 both VR and VL
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*> are also computed, and W(partial) denotes the eigenvalues
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*> computed when only W, only W and VR, or only W and VL are
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*> 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 both VR
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*> and VL are computed, and VR(partial) denotes the result
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*> when only VR is 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 both VR
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*> and VL are also computed, and VL(partial) denotes the result
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*> when only VL is 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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*> \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. If it is zero,
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*> DDRVEV does nothing. It must be at least zero.
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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. If it is zero, DDRVEV
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*> does nothing. It must be at least zero. If it is MAXTYP+1
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*> and NSIZES is 1, then an additional type, MAXTYP+1 is
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*> defined, which is to use whatever matrix is in A. This
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*> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
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*> 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 DDRVEV 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] 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 (LDA, max(NN))
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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 A, and H. LDA must be at
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*> least 1 and at least max(NN).
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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 (LDA, max(NN))
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*> Another copy of the test matrix A, modified by DGEEV.
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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))
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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))
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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 DGEEV 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 (LDVL, max(NN))
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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)).
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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 (LDVR, max(NN))
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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)).
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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 (LDLRE,max(NN))
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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)).
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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 (7)
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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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*> 5*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 (max(NN))
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> If 0, then everything ran OK.
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*> -1: NSIZES < 0
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*> -2: Some NN(j) < 0
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*> -3: NTYPES < 0
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*> -6: THRESH < 0
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*> -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
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*> -16: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ).
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*> -18: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ).
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*> -20: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ).
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*> -23: NWORK too small.
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*> If DLATMR, SLATMS, SLATME or DGEEV returns an error code,
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*> the absolute value of it is returned.
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*>
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*>-----------------------------------------------------------------------
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*>
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*> Some Local Variables and Parameters:
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*> ---- ----- --------- --- ----------
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*>
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*> ZERO, ONE Real 0 and 1.
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*> MAXTYP The number of types defined.
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*> NMAX Largest value in NN.
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*> NERRS The number of tests which have exceeded THRESH
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*> COND, CONDS,
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*> IMODE Values to be passed to the matrix generators.
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*> ANORM Norm of A; passed to matrix generators.
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*>
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*> OVFL, UNFL Overflow and underflow thresholds.
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*> ULP, ULPINV Finest relative precision and its inverse.
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*> RTULP, RTULPI Square roots of the previous 4 values.
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*>
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*> The following four arrays decode JTYPE:
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*> KTYPE(j) The general type (1-10) for type "j".
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*> KMODE(j) The MODE value to be passed to the matrix
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*> generator for type "j".
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*> KMAGN(j) The order of magnitude ( O(1),
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*> O(overflow^(1/2) ), O(underflow^(1/2) )
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*> KCONDS(j) Selectw whether CONDS is to be 1 or
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*> 1/sqrt(ulp). (0 means irrelevant.)
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup double_eig
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*
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* =====================================================================
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SUBROUTINE DDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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$ NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL,
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$ VR, LDVR, LRE, LDLRE, RESULT, WORK, NWORK,
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$ IWORK, INFO )
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*
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* -- LAPACK test routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NOUNIT, NSIZES,
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$ 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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$ RESULT( 7 ), VL( LDVL, * ), VR( LDVR, * ),
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$ WI( * ), WI1( * ), WORK( * ), WR( * ), WR1( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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DOUBLE PRECISION TWO
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PARAMETER ( TWO = 2.0D0 )
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INTEGER MAXTYP
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PARAMETER ( MAXTYP = 21 )
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* ..
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* .. Local Scalars ..
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LOGICAL BADNN
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CHARACTER*3 PATH
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INTEGER IINFO, IMODE, ITYPE, IWK, J, JCOL, JJ, JSIZE,
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$ JTYPE, MTYPES, N, NERRS, NFAIL, NMAX, NNWORK,
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$ NTEST, NTESTF, NTESTT
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DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TNRM,
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$ ULP, ULPINV, UNFL, VMX, VRMX, VTST
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* ..
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* .. Local Arrays ..
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CHARACTER ADUMMA( 1 )
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INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
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$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
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$ KTYPE( MAXTYP )
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DOUBLE PRECISION DUM( 1 ), RES( 2 )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2
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EXTERNAL DLAMCH, DLAPY2, DNRM2
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* ..
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* .. External Subroutines ..
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EXTERNAL DGEEV, DGET22, DLABAD, DLACPY, DLASET, DLASUM,
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$ DLATME, DLATMR, DLATMS, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, SQRT
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* ..
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* .. Data statements ..
|
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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 /
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
PATH( 1: 1 ) = 'Double precision'
|
|
PATH( 2: 3 ) = 'EV'
|
|
*
|
|
* Check for errors
|
|
*
|
|
NTESTT = 0
|
|
NTESTF = 0
|
|
INFO = 0
|
|
*
|
|
* Important constants
|
|
*
|
|
BADNN = .FALSE.
|
|
NMAX = 0
|
|
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( NOUNIT.LE.0 ) THEN
|
|
INFO = -7
|
|
ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
|
|
INFO = -9
|
|
ELSE IF( LDVL.LT.1 .OR. LDVL.LT.NMAX ) THEN
|
|
INFO = -16
|
|
ELSE IF( LDVR.LT.1 .OR. LDVR.LT.NMAX ) THEN
|
|
INFO = -18
|
|
ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.NMAX ) THEN
|
|
INFO = -20
|
|
ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN
|
|
INFO = -23
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'DDRVEV', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if nothing to do
|
|
*
|
|
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
* 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 270 JSIZE = 1, NSIZES
|
|
N = NN( JSIZE )
|
|
IF( NSIZES.NE.1 ) THEN
|
|
MTYPES = MIN( MAXTYP, NTYPES )
|
|
ELSE
|
|
MTYPES = MIN( MAXTYP+1, NTYPES )
|
|
END IF
|
|
*
|
|
DO 260 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 260
|
|
*
|
|
* 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 = 9993 )'Generator', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
90 CONTINUE
|
|
*
|
|
* Test for minimal and generous workspace
|
|
*
|
|
DO 250 IWK = 1, 2
|
|
IF( IWK.EQ.1 ) THEN
|
|
NNWORK = 4*N
|
|
ELSE
|
|
NNWORK = 5*N + 2*N**2
|
|
END IF
|
|
NNWORK = MAX( NNWORK, 1 )
|
|
*
|
|
* Initialize RESULT
|
|
*
|
|
DO 100 J = 1, 7
|
|
RESULT( J ) = -ONE
|
|
100 CONTINUE
|
|
*
|
|
* Compute eigenvalues and eigenvectors, and test them
|
|
*
|
|
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL DGEEV( 'V', 'V', N, H, LDA, WR, WI, VL, LDVL, VR,
|
|
$ LDVR, WORK, NNWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
WRITE( NOUNIT, FMT = 9993 )'DGEEV1', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Do Test (1)
|
|
*
|
|
CALL DGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, WR, WI,
|
|
$ WORK, RES )
|
|
RESULT( 1 ) = RES( 1 )
|
|
*
|
|
* Do Test (2)
|
|
*
|
|
CALL DGET22( 'T', 'N', 'T', N, A, LDA, VL, LDVL, WR, WI,
|
|
$ WORK, RES )
|
|
RESULT( 2 ) = RES( 1 )
|
|
*
|
|
* Do Test (3)
|
|
*
|
|
DO 120 J = 1, N
|
|
TNRM = ONE
|
|
IF( WI( J ).EQ.ZERO ) THEN
|
|
TNRM = DNRM2( N, VR( 1, J ), 1 )
|
|
ELSE IF( WI( J ).GT.ZERO ) THEN
|
|
TNRM = DLAPY2( DNRM2( N, VR( 1, J ), 1 ),
|
|
$ DNRM2( N, VR( 1, J+1 ), 1 ) )
|
|
END IF
|
|
RESULT( 3 ) = MAX( RESULT( 3 ),
|
|
$ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) )
|
|
IF( WI( J ).GT.ZERO ) THEN
|
|
VMX = ZERO
|
|
VRMX = ZERO
|
|
DO 110 JJ = 1, N
|
|
VTST = DLAPY2( VR( JJ, J ), VR( JJ, J+1 ) )
|
|
IF( VTST.GT.VMX )
|
|
$ VMX = VTST
|
|
IF( VR( JJ, J+1 ).EQ.ZERO .AND.
|
|
$ ABS( VR( JJ, J ) ).GT.VRMX )
|
|
$ VRMX = ABS( VR( JJ, J ) )
|
|
110 CONTINUE
|
|
IF( VRMX / VMX.LT.ONE-TWO*ULP )
|
|
$ RESULT( 3 ) = ULPINV
|
|
END IF
|
|
120 CONTINUE
|
|
*
|
|
* Do Test (4)
|
|
*
|
|
DO 140 J = 1, N
|
|
TNRM = ONE
|
|
IF( WI( J ).EQ.ZERO ) THEN
|
|
TNRM = DNRM2( N, VL( 1, J ), 1 )
|
|
ELSE IF( WI( J ).GT.ZERO ) THEN
|
|
TNRM = DLAPY2( DNRM2( N, VL( 1, J ), 1 ),
|
|
$ DNRM2( N, VL( 1, J+1 ), 1 ) )
|
|
END IF
|
|
RESULT( 4 ) = MAX( RESULT( 4 ),
|
|
$ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) )
|
|
IF( WI( J ).GT.ZERO ) THEN
|
|
VMX = ZERO
|
|
VRMX = ZERO
|
|
DO 130 JJ = 1, N
|
|
VTST = DLAPY2( VL( JJ, J ), VL( JJ, J+1 ) )
|
|
IF( VTST.GT.VMX )
|
|
$ VMX = VTST
|
|
IF( VL( JJ, J+1 ).EQ.ZERO .AND.
|
|
$ ABS( VL( JJ, J ) ).GT.VRMX )
|
|
$ VRMX = ABS( VL( JJ, J ) )
|
|
130 CONTINUE
|
|
IF( VRMX / VMX.LT.ONE-TWO*ULP )
|
|
$ RESULT( 4 ) = ULPINV
|
|
END IF
|
|
140 CONTINUE
|
|
*
|
|
* Compute eigenvalues only, and test them
|
|
*
|
|
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL DGEEV( 'N', 'N', N, H, LDA, WR1, WI1, DUM, 1, DUM,
|
|
$ 1, WORK, NNWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
WRITE( NOUNIT, FMT = 9993 )'DGEEV2', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Do Test (5)
|
|
*
|
|
DO 150 J = 1, N
|
|
IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
|
|
$ RESULT( 5 ) = ULPINV
|
|
150 CONTINUE
|
|
*
|
|
* Compute eigenvalues and right eigenvectors, and test them
|
|
*
|
|
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL DGEEV( 'N', 'V', N, H, LDA, WR1, WI1, DUM, 1, LRE,
|
|
$ LDLRE, WORK, NNWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
WRITE( NOUNIT, FMT = 9993 )'DGEEV3', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Do Test (5) again
|
|
*
|
|
DO 160 J = 1, N
|
|
IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
|
|
$ RESULT( 5 ) = ULPINV
|
|
160 CONTINUE
|
|
*
|
|
* Do Test (6)
|
|
*
|
|
DO 180 J = 1, N
|
|
DO 170 JJ = 1, N
|
|
IF( VR( J, JJ ).NE.LRE( J, JJ ) )
|
|
$ RESULT( 6 ) = ULPINV
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
*
|
|
* Compute eigenvalues and left eigenvectors, and test them
|
|
*
|
|
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL DGEEV( 'V', 'N', N, H, LDA, WR1, WI1, LRE, LDLRE,
|
|
$ DUM, 1, WORK, NNWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
WRITE( NOUNIT, FMT = 9993 )'DGEEV4', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Do Test (5) again
|
|
*
|
|
DO 190 J = 1, N
|
|
IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
|
|
$ RESULT( 5 ) = ULPINV
|
|
190 CONTINUE
|
|
*
|
|
* Do Test (7)
|
|
*
|
|
DO 210 J = 1, N
|
|
DO 200 JJ = 1, N
|
|
IF( VL( J, JJ ).NE.LRE( J, JJ ) )
|
|
$ RESULT( 7 ) = ULPINV
|
|
200 CONTINUE
|
|
210 CONTINUE
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
220 CONTINUE
|
|
*
|
|
NTEST = 0
|
|
NFAIL = 0
|
|
DO 230 J = 1, 7
|
|
IF( RESULT( J ).GE.ZERO )
|
|
$ NTEST = NTEST + 1
|
|
IF( RESULT( J ).GE.THRESH )
|
|
$ NFAIL = NFAIL + 1
|
|
230 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 240 J = 1, 7
|
|
IF( RESULT( J ).GE.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9994 )N, IWK, IOLDSD, JTYPE,
|
|
$ J, RESULT( J )
|
|
END IF
|
|
240 CONTINUE
|
|
*
|
|
NERRS = NERRS + NFAIL
|
|
NTESTT = NTESTT + NTEST
|
|
*
|
|
250 CONTINUE
|
|
260 CONTINUE
|
|
270 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL DLASUM( PATH, NOUNIT, NERRS, NTESTT )
|
|
*
|
|
9999 FORMAT( / 1X, A3, ' -- Real Eigenvalue-Eigenvector Decomposition',
|
|
$ ' Driver', / ' Matrix types (see DDRVEV 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 ', 6X, ' ',
|
|
$ ' 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. ', / )
|
|
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 if VL computed,',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 7 = 0 if VL same no matter if VR computed,',
|
|
$ ' 1/ulp otherwise', / )
|
|
9994 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ),
|
|
$ ' type ', I2, ', test(', I2, ')=', G10.3 )
|
|
9993 FORMAT( ' DDRVEV: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of DDRVEV
|
|
*
|
|
END
|