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931 lines
32 KiB
931 lines
32 KiB
*> \brief \b CDRVSX
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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 CDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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* NIUNIT, NOUNIT, A, LDA, H, HT, W, WT, WTMP, VS,
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* LDVS, VS1, RESULT, WORK, LWORK, RWORK, BWORK,
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* INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
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* $ NTYPES
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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL BWORK( * ), DOTYPE( * )
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* INTEGER ISEED( 4 ), NN( * )
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* REAL RESULT( 17 ), RWORK( * )
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* COMPLEX A( LDA, * ), H( LDA, * ), HT( LDA, * ),
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* $ VS( LDVS, * ), VS1( LDVS, * ), W( * ),
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* $ WORK( * ), WT( * ), WTMP( * )
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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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*> CDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
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*> expert driver CGEESX.
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*>
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*> CDRVSX 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 CDRVSX 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, 15
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*> tests will be performed:
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*>
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*> (1) 0 if T is in Schur form, 1/ulp otherwise
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*> (no sorting of eigenvalues)
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*>
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*> (2) | A - VS T VS' | / ( n |A| ulp )
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*>
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*> Here VS is the matrix of Schur eigenvectors, and T is in Schur
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*> form (no sorting of eigenvalues).
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*>
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*> (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
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*>
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*> (4) 0 if W are eigenvalues of T
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*> 1/ulp otherwise
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*> (no sorting of eigenvalues)
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*>
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*> (5) 0 if T(with VS) = T(without VS),
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*> 1/ulp otherwise
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*> (no sorting of eigenvalues)
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*>
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*> (6) 0 if eigenvalues(with VS) = eigenvalues(without VS),
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*> 1/ulp otherwise
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*> (no sorting of eigenvalues)
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*>
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*> (7) 0 if T is in Schur form, 1/ulp otherwise
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*> (with sorting of eigenvalues)
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*>
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*> (8) | A - VS T VS' | / ( n |A| ulp )
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*>
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*> Here VS is the matrix of Schur eigenvectors, and T is in Schur
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*> form (with sorting of eigenvalues).
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*>
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*> (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
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*>
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*> (10) 0 if W are eigenvalues of T
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*> 1/ulp otherwise
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*> If workspace sufficient, also compare W with and
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*> without reciprocal condition numbers
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*> (with sorting of eigenvalues)
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*>
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*> (11) 0 if T(with VS) = T(without VS),
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*> 1/ulp otherwise
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*> If workspace sufficient, also compare T with and without
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*> reciprocal condition numbers
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*> (with sorting of eigenvalues)
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*>
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*> (12) 0 if eigenvalues(with VS) = eigenvalues(without VS),
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*> 1/ulp otherwise
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*> If workspace sufficient, also compare VS with and without
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*> reciprocal condition numbers
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*> (with sorting of eigenvalues)
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*>
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*> (13) if sorting worked and SDIM is the number of
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*> eigenvalues which were SELECTed
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*> If workspace sufficient, also compare SDIM with and
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*> without reciprocal condition numbers
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*>
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*> (14) if RCONDE the same no matter if VS and/or RCONDV computed
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*>
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*> (15) if RCONDV the same no matter if VS and/or RCONDE 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 complex angles.
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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 complex angles.
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*> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
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*> and random complex angles.
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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 unitary and
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*> T has evenly spaced entries 1, ..., ULP with random
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*> complex angles on the diagonal and random O(1) entries in
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*> the upper triangle.
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*>
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*> (10) A matrix of the form U' T U, where U is unitary and
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*> T has geometrically spaced entries 1, ..., ULP with random
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*> complex angles on the diagonal and random O(1) entries in
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*> the upper 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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*> complex angles on the diagonal and random O(1) entries in
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*> the upper triangle.
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*>
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*> (12) A matrix of the form U' T U, where U is unitary and
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*> T has complex eigenvalues randomly chosen from
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*> ULP < |z| < 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 complex angles on the diagonal and random O(1)
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*> entries 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 complex angles on the diagonal
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*> and random 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 complex angles on the diagonal and random O(1)
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*> entries 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 complex eigenvalues randomly chosen
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*> from ULP < |z| < 1 and random O(1) entries in the upper
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*> 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 eigenvalue
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*> average and right invariant subspace. For these matrices, in
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*> addition to tests (1) to (15) we will compute the following two
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*> tests:
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*>
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*> (16) |RCONDE - RCDEIN| / cond(RCONDE)
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*>
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*> RCONDE is the reciprocal average eigenvalue condition number
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*> computed by CGEESX 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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*>
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*> (17) |RCONDV - RCDVIN| / cond(RCONDV)
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*>
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*> RCONDV is the reciprocal right invariant subspace condition
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*> number computed by CGEESX and RCDVIN (the precomputed true
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*> value) is supplied as input. cond(RCONDV) is the condition
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*> number of RCONDV, and takes errors in computing RCONDV into
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*> account, so that the resulting quantity should be O(ULP).
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*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
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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 CDRVSX 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 REAL
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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 COMPLEX 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 COMPLEX array, dimension (LDA, max(NN))
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*> Another copy of the test matrix A, modified by CGEESX.
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*> \endverbatim
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*>
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*> \param[out] HT
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*> \verbatim
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*> HT is COMPLEX array, dimension (LDA, max(NN))
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*> Yet another copy of the test matrix A, modified by CGEESX.
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*> \endverbatim
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*>
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*> \param[out] W
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*> \verbatim
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*> W is COMPLEX array, dimension (max(NN))
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*> The computed eigenvalues of A.
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*> \endverbatim
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*>
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*> \param[out] WT
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*> \verbatim
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*> WT is COMPLEX array, dimension (max(NN))
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*> Like W, this array contains the eigenvalues of A,
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*> but those computed when CGEESX only computes a partial
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*> eigendecomposition, i.e. not Schur vectors
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*> \endverbatim
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*>
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*> \param[out] WTMP
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*> \verbatim
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*> WTMP is COMPLEX array, dimension (max(NN))
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*> More temporary storage for eigenvalues.
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*> \endverbatim
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*>
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*> \param[out] VS
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*> \verbatim
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*> VS is COMPLEX array, dimension (LDVS, max(NN))
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*> VS holds the computed Schur vectors.
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*> \endverbatim
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*>
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*> \param[in] LDVS
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*> \verbatim
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*> LDVS is INTEGER
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*> Leading dimension of VS. Must be at least max(1,max(NN)).
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*> \endverbatim
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*>
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*> \param[out] VS1
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*> \verbatim
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*> VS1 is COMPLEX array, dimension (LDVS, max(NN))
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*> VS1 holds another copy of the computed Schur vectors.
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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 REAL array, dimension (17)
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*> The values computed by the 17 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 COMPLEX array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The number of entries in WORK. This must be at least
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*> max(1,2*NN(j)**2) for all j.
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (max(NN))
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*> \endverbatim
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*>
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*> \param[out] BWORK
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*> \verbatim
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*> BWORK is LOGICAL 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, successful exit.
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*> <0, input parameter -INFO is incorrect
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*> >0, CLATMR, CLATMS, CLATME or CGET24 returned an error
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*> code and INFO is its absolute value
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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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*> 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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*> 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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*> \ingroup complex_eig
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*
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* =====================================================================
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SUBROUTINE CDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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$ NIUNIT, NOUNIT, A, LDA, H, HT, W, WT, WTMP, VS,
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$ LDVS, VS1, RESULT, WORK, LWORK, RWORK, BWORK,
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$ INFO )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
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$ NTYPES
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REAL THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL BWORK( * ), DOTYPE( * )
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INTEGER ISEED( 4 ), NN( * )
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REAL RESULT( 17 ), RWORK( * )
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COMPLEX A( LDA, * ), H( LDA, * ), HT( LDA, * ),
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$ VS( LDVS, * ), VS1( LDVS, * ), W( * ),
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$ WORK( * ), WT( * ), WTMP( * )
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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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COMPLEX CZERO
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PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) )
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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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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 I, IINFO, IMODE, ISRT, ITYPE, IWK, J, JCOL,
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$ JSIZE, JTYPE, MTYPES, N, NERRS, NFAIL,
|
|
$ NMAX, NNWORK, NSLCT, NTEST, NTESTF, NTESTT
|
|
REAL ANORM, COND, CONDS, OVFL, RCDEIN, RCDVIN,
|
|
$ RTULP, RTULPI, ULP, ULPINV, UNFL
|
|
* ..
|
|
* .. Local Arrays ..
|
|
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISLCT( 20 ),
|
|
$ KCONDS( MAXTYP ), KMAGN( MAXTYP ),
|
|
$ KMODE( MAXTYP ), KTYPE( MAXTYP )
|
|
* ..
|
|
* .. Arrays in Common ..
|
|
LOGICAL SELVAL( 20 )
|
|
REAL SELWI( 20 ), SELWR( 20 )
|
|
* ..
|
|
* .. Scalars in Common ..
|
|
INTEGER SELDIM, SELOPT
|
|
* ..
|
|
* .. Common blocks ..
|
|
COMMON / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH
|
|
EXTERNAL SLAMCH
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CGET24, CLATME, CLATMR, CLATMS, CLASET,
|
|
$ SLASUM, 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 /
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
PATH( 1: 1 ) = 'Complex precision'
|
|
PATH( 2: 3 ) = 'SX'
|
|
*
|
|
* Check for errors
|
|
*
|
|
NTESTT = 0
|
|
NTESTF = 0
|
|
INFO = 0
|
|
*
|
|
* Important constants
|
|
*
|
|
BADNN = .FALSE.
|
|
*
|
|
* 8 is the largest dimension in the input file of precomputed
|
|
* problems
|
|
*
|
|
NMAX = 8
|
|
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( NIUNIT.LE.0 ) THEN
|
|
INFO = -7
|
|
ELSE IF( NOUNIT.LE.0 ) THEN
|
|
INFO = -8
|
|
ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
|
|
INFO = -10
|
|
ELSE IF( LDVS.LT.1 .OR. LDVS.LT.NMAX ) THEN
|
|
INFO = -20
|
|
ELSE IF( MAX( 3*NMAX, 2*NMAX**2 ).GT.LWORK ) THEN
|
|
INFO = -24
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CDRVSX', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* If nothing to do check on NIUNIT
|
|
*
|
|
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
|
|
$ GO TO 150
|
|
*
|
|
* More Important constants
|
|
*
|
|
UNFL = SLAMCH( 'Safe minimum' )
|
|
OVFL = ONE / UNFL
|
|
ULP = SLAMCH( 'Precision' )
|
|
ULPINV = ONE / ULP
|
|
RTULP = SQRT( ULP )
|
|
RTULPI = ONE / RTULP
|
|
*
|
|
* Loop over sizes, types
|
|
*
|
|
NERRS = 0
|
|
*
|
|
DO 140 JSIZE = 1, NSIZES
|
|
N = NN( JSIZE )
|
|
IF( NSIZES.NE.1 ) THEN
|
|
MTYPES = MIN( MAXTYP, NTYPES )
|
|
ELSE
|
|
MTYPES = MIN( MAXTYP+1, NTYPES )
|
|
END IF
|
|
*
|
|
DO 130 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 130
|
|
*
|
|
* 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 CLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
|
|
IINFO = 0
|
|
COND = ULPINV
|
|
*
|
|
* Special Matrices -- Identity & Jordan block
|
|
*
|
|
IF( ITYPE.EQ.1 ) THEN
|
|
*
|
|
* Zero
|
|
*
|
|
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 ) = CONE
|
|
80 CONTINUE
|
|
*
|
|
ELSE IF( ITYPE.EQ.4 ) THEN
|
|
*
|
|
* Diagonal Matrix, [Eigen]values Specified
|
|
*
|
|
CALL CLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
|
|
$ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
|
|
$ IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.5 ) THEN
|
|
*
|
|
* Symmetric, eigenvalues specified
|
|
*
|
|
CALL CLATMS( N, N, 'S', ISEED, 'H', RWORK, 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
|
|
*
|
|
CALL CLATME( N, 'D', ISEED, WORK, IMODE, COND, CONE,
|
|
$ 'T', 'T', 'T', RWORK, 4, CONDS, N, N, ANORM,
|
|
$ A, LDA, WORK( 2*N+1 ), IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.7 ) THEN
|
|
*
|
|
* Diagonal, random eigenvalues
|
|
*
|
|
CALL CLATMR( N, N, 'D', ISEED, 'N', WORK, 6, ONE, CONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IDUMMA, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.8 ) THEN
|
|
*
|
|
* Symmetric, random eigenvalues
|
|
*
|
|
CALL CLATMR( N, N, 'D', ISEED, 'H', WORK, 6, ONE, CONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IDUMMA, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.9 ) THEN
|
|
*
|
|
* General, random eigenvalues
|
|
*
|
|
CALL CLATMR( N, N, 'D', ISEED, 'N', WORK, 6, ONE, CONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IDUMMA, IINFO )
|
|
IF( N.GE.4 ) THEN
|
|
CALL CLASET( 'Full', 2, N, CZERO, CZERO, A, LDA )
|
|
CALL CLASET( 'Full', N-3, 1, CZERO, CZERO, A( 3, 1 ),
|
|
$ LDA )
|
|
CALL CLASET( 'Full', N-3, 2, CZERO, CZERO,
|
|
$ A( 3, N-1 ), LDA )
|
|
CALL CLASET( 'Full', 1, N, CZERO, CZERO, A( N, 1 ),
|
|
$ LDA )
|
|
END IF
|
|
*
|
|
ELSE IF( ITYPE.EQ.10 ) THEN
|
|
*
|
|
* Triangular, random eigenvalues
|
|
*
|
|
CALL CLATMR( N, N, 'D', ISEED, 'N', WORK, 6, ONE, CONE,
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IDUMMA, IINFO )
|
|
*
|
|
ELSE
|
|
*
|
|
IINFO = 1
|
|
END IF
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9991 )'Generator', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
90 CONTINUE
|
|
*
|
|
* Test for minimal and generous workspace
|
|
*
|
|
DO 120 IWK = 1, 2
|
|
IF( IWK.EQ.1 ) THEN
|
|
NNWORK = 2*N
|
|
ELSE
|
|
NNWORK = MAX( 2*N, N*( N+1 ) / 2 )
|
|
END IF
|
|
NNWORK = MAX( NNWORK, 1 )
|
|
*
|
|
CALL CGET24( .FALSE., JTYPE, THRESH, IOLDSD, NOUNIT, N,
|
|
$ A, LDA, H, HT, W, WT, WTMP, VS, LDVS, VS1,
|
|
$ RCDEIN, RCDVIN, NSLCT, ISLCT, 0, RESULT,
|
|
$ WORK, NNWORK, RWORK, BWORK, INFO )
|
|
*
|
|
* Check for RESULT(j) > THRESH
|
|
*
|
|
NTEST = 0
|
|
NFAIL = 0
|
|
DO 100 J = 1, 15
|
|
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
|
|
WRITE( NOUNIT, FMT = 9994 )
|
|
NTESTF = 2
|
|
END IF
|
|
*
|
|
DO 110 J = 1, 15
|
|
IF( RESULT( J ).GE.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9993 )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
|
|
*
|
|
* Read in data from file to check accuracy of condition estimation
|
|
* Read input data until N=0
|
|
*
|
|
JTYPE = 0
|
|
160 CONTINUE
|
|
READ( NIUNIT, FMT = *, END = 200 )N, NSLCT, ISRT
|
|
IF( N.EQ.0 )
|
|
$ GO TO 200
|
|
JTYPE = JTYPE + 1
|
|
ISEED( 1 ) = JTYPE
|
|
READ( NIUNIT, FMT = * )( ISLCT( I ), I = 1, NSLCT )
|
|
DO 170 I = 1, N
|
|
READ( NIUNIT, FMT = * )( A( I, J ), J = 1, N )
|
|
170 CONTINUE
|
|
READ( NIUNIT, FMT = * )RCDEIN, RCDVIN
|
|
*
|
|
CALL CGET24( .TRUE., 22, THRESH, ISEED, NOUNIT, N, A, LDA, H, HT,
|
|
$ W, WT, WTMP, VS, LDVS, VS1, RCDEIN, RCDVIN, NSLCT,
|
|
$ ISLCT, ISRT, RESULT, WORK, LWORK, RWORK, BWORK,
|
|
$ INFO )
|
|
*
|
|
* Check for RESULT(j) > THRESH
|
|
*
|
|
NTEST = 0
|
|
NFAIL = 0
|
|
DO 180 J = 1, 17
|
|
IF( RESULT( J ).GE.ZERO )
|
|
$ NTEST = NTEST + 1
|
|
IF( RESULT( J ).GE.THRESH )
|
|
$ NFAIL = NFAIL + 1
|
|
180 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
|
|
WRITE( NOUNIT, FMT = 9994 )
|
|
NTESTF = 2
|
|
END IF
|
|
DO 190 J = 1, 17
|
|
IF( RESULT( J ).GE.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9992 )N, JTYPE, J, RESULT( J )
|
|
END IF
|
|
190 CONTINUE
|
|
*
|
|
NERRS = NERRS + NFAIL
|
|
NTESTT = NTESTT + NTEST
|
|
GO TO 160
|
|
200 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL SLASUM( PATH, NOUNIT, NERRS, NTESTT )
|
|
*
|
|
9999 FORMAT( / 1X, A3, ' -- Complex Schur Form Decomposition Expert ',
|
|
$ 'Driver', / ' Matrix types (see CDRVSX 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. ', / )
|
|
9995 FORMAT( ' Tests performed with test threshold =', F8.2,
|
|
$ / ' ( A denotes A on input and T denotes A on output)',
|
|
$ / / ' 1 = 0 if T in Schur form (no sort), ',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
|
|
$ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ',
|
|
$ / ' 4 = 0 if W are eigenvalues of T (no sort),',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 5 = 0 if T same no matter if VS computed (no sort),',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 6 = 0 if W same no matter if VS computed (no sort)',
|
|
$ ', 1/ulp otherwise' )
|
|
9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise',
|
|
$ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
|
|
$ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
|
|
$ / ' 10 = 0 if W are eigenvalues of T (sort),',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 11 = 0 if T same no matter what else computed (sort),',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 12 = 0 if W same no matter what else computed ',
|
|
$ '(sort), 1/ulp otherwise', /
|
|
$ ' 13 = 0 if sorting successful, 1/ulp otherwise',
|
|
$ / ' 14 = 0 if RCONDE same no matter what else computed,',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 15 = 0 if RCONDv same no matter what else computed,',
|
|
$ ' 1/ulp otherwise', /
|
|
$ ' 16 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),',
|
|
$ / ' 17 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),' )
|
|
9993 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ),
|
|
$ ' type ', I2, ', test(', I2, ')=', G10.3 )
|
|
9992 FORMAT( ' N=', I5, ', input example =', I3, ', test(', I2, ')=',
|
|
$ G10.3 )
|
|
9991 FORMAT( ' CDRVSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CDRVSX
|
|
*
|
|
END
|
|
|