1103 lines
38 KiB
Fortran
1103 lines
38 KiB
Fortran
*> \brief \b CCHKHS
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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 CCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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* NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, W1,
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* W3, EVECTL, EVECTR, EVECTY, EVECTX, UU, TAU,
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* WORK, NWORK, RWORK, IWORK, SELECT, RESULT,
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* INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK
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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * ), SELECT( * )
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* INTEGER ISEED( 4 ), IWORK( * ), NN( * )
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* REAL RESULT( 14 ), RWORK( * )
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* COMPLEX A( LDA, * ), EVECTL( LDU, * ),
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* $ EVECTR( LDU, * ), EVECTX( LDU, * ),
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* $ EVECTY( LDU, * ), H( LDA, * ), T1( LDA, * ),
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* $ T2( LDA, * ), TAU( * ), U( LDU, * ),
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* $ UU( LDU, * ), UZ( LDU, * ), W1( * ), W3( * ),
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* $ WORK( * ), Z( LDU, * )
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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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*> CCHKHS checks the nonsymmetric eigenvalue problem routines.
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*>
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*> CGEHRD factors A as U H U' , where ' means conjugate
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*> transpose, H is hessenberg, and U is unitary.
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*>
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*> CUNGHR generates the unitary matrix U.
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*>
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*> CUNMHR multiplies a matrix by the unitary matrix U.
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*>
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*> CHSEQR factors H as Z T Z' , where Z is unitary and T
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*> is upper triangular. It also computes the eigenvalues,
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*> w(1), ..., w(n); we define a diagonal matrix W whose
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*> (diagonal) entries are the eigenvalues.
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*>
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*> CTREVC computes the left eigenvector matrix L and the
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*> right eigenvector matrix R for the matrix T. The
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*> columns of L are the complex conjugates of the left
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*> eigenvectors of T. The columns of R are the right
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*> eigenvectors of T. L is lower triangular, and R is
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*> upper triangular.
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*>
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*> CHSEIN computes the left eigenvector matrix Y and the
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*> right eigenvector matrix X for the matrix H. The
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*> columns of Y are the complex conjugates of the left
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*> eigenvectors of H. The columns of X are the right
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*> eigenvectors of H. Y is lower triangular, and X is
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*> upper triangular.
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*>
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*> When CCHKHS 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, 14
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*> tests will be performed:
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*>
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*> (1) | A - U H U**H | / ( |A| n ulp )
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*>
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*> (2) | I - UU**H | / ( n ulp )
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*>
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*> (3) | H - Z T Z**H | / ( |H| n ulp )
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*>
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*> (4) | I - ZZ**H | / ( n ulp )
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*>
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*> (5) | A - UZ H (UZ)**H | / ( |A| n ulp )
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*>
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*> (6) | I - UZ (UZ)**H | / ( n ulp )
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*>
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*> (7) | T(Z computed) - T(Z not computed) | / ( |T| ulp )
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*>
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*> (8) | W(Z computed) - W(Z not computed) | / ( |W| ulp )
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*>
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*> (9) | TR - RW | / ( |T| |R| ulp )
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*>
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*> (10) | L**H T - W**H L | / ( |T| |L| ulp )
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*>
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*> (11) | HX - XW | / ( |H| |X| ulp )
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*>
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*> (12) | Y**H H - W**H Y | / ( |H| |Y| ulp )
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*>
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*> (13) | AX - XW | / ( |A| |X| ulp )
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*>
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*> (14) | Y**H A - W**H Y | / ( |A| |Y| ulp )
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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 SQRT( overflow threshold )
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*> (8) Same as (4), but multiplied by SQRT( 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 complex
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*> angles 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 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 unitary 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 SQRT( overflow threshold )
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*> (18) Same as (16), but multiplied by SQRT( underflow threshold )
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*>
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*> (19) Nonsymmetric matrix with random entries chosen from |z| < 1
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*> (20) Same as (19), but multiplied by SQRT( overflow threshold )
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*> (21) Same as (19), but multiplied by SQRT( 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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*> \verbatim
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*> NSIZES - INTEGER
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*> The number of sizes of matrices to use. If it is zero,
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*> CCHKHS does nothing. It must be at least zero.
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*> Not modified.
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*>
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*> NN - 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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*> Not modified.
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*>
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*> NTYPES - INTEGER
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*> The number of elements in DOTYPE. If it is zero, CCHKHS
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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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*> Not modified.
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*>
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*> DOTYPE - 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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*> Not modified.
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*>
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*> ISEED - INTEGER array, dimension (4)
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*> On entry ISEED specifies the seed of the random number
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*> generator. 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 CCHKHS to continue the same random number
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*> sequence.
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*> Modified.
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*>
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*> THRESH - 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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*> Not modified.
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*>
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*> NOUNIT - INTEGER
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*> The FORTRAN unit number for printing out error messages
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*> (e.g., if a routine returns IINFO not equal to 0.)
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*> Not modified.
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*>
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*> A - 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
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*> used.
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*> Modified.
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*>
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*> LDA - INTEGER
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*> The leading dimension of A, H, T1 and T2. It must be at
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*> least 1 and at least max( NN ).
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*> Not modified.
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*>
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*> H - COMPLEX array, dimension (LDA,max(NN))
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*> The upper hessenberg matrix computed by CGEHRD. On exit,
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*> H contains the Hessenberg form of the matrix in A.
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*> Modified.
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*>
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*> T1 - COMPLEX array, dimension (LDA,max(NN))
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*> The Schur (="quasi-triangular") matrix computed by CHSEQR
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*> if Z is computed. On exit, T1 contains the Schur form of
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*> the matrix in A.
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*> Modified.
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*>
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*> T2 - COMPLEX array, dimension (LDA,max(NN))
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*> The Schur matrix computed by CHSEQR when Z is not computed.
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*> This should be identical to T1.
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*> Modified.
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*>
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*> LDU - INTEGER
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*> The leading dimension of U, Z, UZ and UU. It must be at
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*> least 1 and at least max( NN ).
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*> Not modified.
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*>
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*> U - COMPLEX array, dimension (LDU,max(NN))
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*> The unitary matrix computed by CGEHRD.
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*> Modified.
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*>
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*> Z - COMPLEX array, dimension (LDU,max(NN))
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*> The unitary matrix computed by CHSEQR.
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*> Modified.
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*>
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*> UZ - COMPLEX array, dimension (LDU,max(NN))
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*> The product of U times Z.
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*> Modified.
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*>
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*> W1 - COMPLEX array, dimension (max(NN))
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*> The eigenvalues of A, as computed by a full Schur
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*> decomposition H = Z T Z'. On exit, W1 contains the
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*> eigenvalues of the matrix in A.
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*> Modified.
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*>
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*> W3 - COMPLEX array, dimension (max(NN))
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*> The eigenvalues of A, as computed by a partial Schur
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*> decomposition (Z not computed, T only computed as much
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*> as is necessary for determining eigenvalues). On exit,
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*> W3 contains the eigenvalues of the matrix in A, possibly
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*> perturbed by CHSEIN.
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*> Modified.
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*>
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*> EVECTL - COMPLEX array, dimension (LDU,max(NN))
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*> The conjugate transpose of the (upper triangular) left
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*> eigenvector matrix for the matrix in T1.
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*> Modified.
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*>
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*> EVECTR - COMPLEX array, dimension (LDU,max(NN))
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*> The (upper triangular) right eigenvector matrix for the
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*> matrix in T1.
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*> Modified.
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*>
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*> EVECTY - COMPLEX array, dimension (LDU,max(NN))
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*> The conjugate transpose of the left eigenvector matrix
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*> for the matrix in H.
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*> Modified.
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*>
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*> EVECTX - COMPLEX array, dimension (LDU,max(NN))
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*> The right eigenvector matrix for the matrix in H.
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*> Modified.
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*>
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*> UU - COMPLEX array, dimension (LDU,max(NN))
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*> Details of the unitary matrix computed by CGEHRD.
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*> Modified.
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*>
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*> TAU - COMPLEX array, dimension (max(NN))
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*> Further details of the unitary matrix computed by CGEHRD.
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*> Modified.
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*>
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*> WORK - COMPLEX array, dimension (NWORK)
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*> Workspace.
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*> Modified.
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*>
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*> NWORK - INTEGER
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*> The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2.
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*>
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*> RWORK - REAL array, dimension (max(NN))
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*> Workspace. Could be equivalenced to IWORK, but not SELECT.
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*> Modified.
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*>
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*> IWORK - INTEGER array, dimension (max(NN))
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*> Workspace.
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*> Modified.
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*>
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*> SELECT - LOGICAL array, dimension (max(NN))
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*> Workspace. Could be equivalenced to IWORK, but not RWORK.
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*> Modified.
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*>
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*> RESULT - REAL array, dimension (14)
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*> The values computed by the fourteen tests described above.
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*> The values are currently limited to 1/ulp, to avoid
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*> overflow.
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*> Modified.
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*>
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*> INFO - 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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*> -14: LDU < 1 or LDU < NMAX.
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*> -26: NWORK too small.
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*> If CLATMR, CLATMS, or CLATME returns an error code, the
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*> absolute value of it is returned.
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*> If 1, then CHSEQR could not find all the shifts.
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*> If 2, then the EISPACK code (for small blocks) failed.
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*> If >2, then 30*N iterations were not enough to find an
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*> eigenvalue or to decompose the problem.
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*> Modified.
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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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*> MTEST The number of tests defined: care must be taken
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*> that (1) the size of RESULT, (2) the number of
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*> tests actually performed, and (3) MTEST agree.
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*> NTEST The number of tests performed on this matrix
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*> so far. This should be less than MTEST, and
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*> equal to it by the last test. It will be less
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*> if any of the routines being tested indicates
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*> that it could not compute the matrices that
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*> would be tested.
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*> NMAX Largest value in NN.
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*> NMATS The number of matrices generated so far.
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*> NERRS The number of tests which have exceeded THRESH
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*> so far (computed by SLAFTS).
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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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*> RTOVFL, RTUNFL,
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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) Selects 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 November 2011
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*
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*> \ingroup complex_eig
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*
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* =====================================================================
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SUBROUTINE CCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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$ NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, W1,
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$ W3, EVECTL, EVECTR, EVECTY, EVECTX, UU, TAU,
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$ WORK, NWORK, RWORK, IWORK, SELECT, RESULT,
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$ INFO )
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*
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* -- LAPACK test routine (version 3.4.0) --
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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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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK
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REAL THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * ), SELECT( * )
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INTEGER ISEED( 4 ), IWORK( * ), NN( * )
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REAL RESULT( 14 ), RWORK( * )
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COMPLEX A( LDA, * ), EVECTL( LDU, * ),
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$ EVECTR( LDU, * ), EVECTX( LDU, * ),
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$ EVECTY( LDU, * ), H( LDA, * ), T1( LDA, * ),
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$ T2( LDA, * ), TAU( * ), U( LDU, * ),
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$ UU( LDU, * ), UZ( LDU, * ), W1( * ), W3( * ),
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$ WORK( * ), Z( LDU, * )
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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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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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COMPLEX CZERO, CONE
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PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
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$ CONE = ( 1.0E+0, 0.0E+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, MATCH
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INTEGER I, IHI, IINFO, ILO, IMODE, IN, ITYPE, J, JCOL,
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$ JJ, JSIZE, JTYPE, K, MTYPES, N, N1, NERRS,
|
|
$ NMATS, NMAX, NTEST, NTESTT
|
|
REAL ANINV, ANORM, COND, CONDS, OVFL, RTOVFL, RTULP,
|
|
$ RTULPI, RTUNFL, TEMP1, TEMP2, ULP, ULPINV, UNFL
|
|
* ..
|
|
* .. Local Arrays ..
|
|
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
|
|
$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
|
|
$ KTYPE( MAXTYP )
|
|
REAL DUMMA( 4 )
|
|
COMPLEX CDUMMA( 4 )
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH
|
|
EXTERNAL SLAMCH
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CCOPY, CGEHRD, CGEMM, CGET10, CGET22, CHSEIN,
|
|
$ CHSEQR, CHST01, CLACPY, CLASET, CLATME, CLATMR,
|
|
$ CLATMS, CTREVC, CUNGHR, CUNMHR, SLABAD, SLAFTS,
|
|
$ SLASUM, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, MAX, MIN, REAL, 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 ..
|
|
*
|
|
* Check for errors
|
|
*
|
|
NTESTT = 0
|
|
INFO = 0
|
|
*
|
|
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( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
|
|
INFO = -9
|
|
ELSE IF( LDU.LE.1 .OR. LDU.LT.NMAX ) THEN
|
|
INFO = -14
|
|
ELSE IF( 4*NMAX*NMAX+2.GT.NWORK ) THEN
|
|
INFO = -26
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CCHKHS', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
* More important constants
|
|
*
|
|
UNFL = SLAMCH( 'Safe minimum' )
|
|
OVFL = SLAMCH( 'Overflow' )
|
|
CALL SLABAD( UNFL, OVFL )
|
|
ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
|
|
ULPINV = ONE / ULP
|
|
RTUNFL = SQRT( UNFL )
|
|
RTOVFL = SQRT( OVFL )
|
|
RTULP = SQRT( ULP )
|
|
RTULPI = ONE / RTULP
|
|
*
|
|
* Loop over sizes, types
|
|
*
|
|
NERRS = 0
|
|
NMATS = 0
|
|
*
|
|
DO 260 JSIZE = 1, NSIZES
|
|
N = NN( JSIZE )
|
|
IF( N.EQ.0 )
|
|
$ GO TO 260
|
|
N1 = MAX( 1, N )
|
|
ANINV = ONE / REAL( N1 )
|
|
*
|
|
IF( NSIZES.NE.1 ) THEN
|
|
MTYPES = MIN( MAXTYP, NTYPES )
|
|
ELSE
|
|
MTYPES = MIN( MAXTYP+1, NTYPES )
|
|
END IF
|
|
*
|
|
DO 250 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 250
|
|
NMATS = NMATS + 1
|
|
NTEST = 0
|
|
*
|
|
* Save ISEED in case of an error.
|
|
*
|
|
DO 20 J = 1, 4
|
|
IOLDSD( J ) = ISEED( J )
|
|
20 CONTINUE
|
|
*
|
|
* Initialize RESULT
|
|
*
|
|
DO 30 J = 1, 14
|
|
RESULT( J ) = ZERO
|
|
30 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 hermitian, w/ eigenvalues
|
|
* =6 random general, w/ eigenvalues
|
|
* =7 random diagonal
|
|
* =8 random hermitian
|
|
* =9 random general
|
|
* =10 random triangular
|
|
*
|
|
IF( MTYPES.GT.MAXTYP )
|
|
$ GO TO 100
|
|
*
|
|
ITYPE = KTYPE( JTYPE )
|
|
IMODE = KMODE( JTYPE )
|
|
*
|
|
* Compute norm
|
|
*
|
|
GO TO ( 40, 50, 60 )KMAGN( JTYPE )
|
|
*
|
|
40 CONTINUE
|
|
ANORM = ONE
|
|
GO TO 70
|
|
*
|
|
50 CONTINUE
|
|
ANORM = ( RTOVFL*ULP )*ANINV
|
|
GO TO 70
|
|
*
|
|
60 CONTINUE
|
|
ANORM = RTUNFL*N*ULPINV
|
|
GO TO 70
|
|
*
|
|
70 CONTINUE
|
|
*
|
|
CALL CLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
|
|
IINFO = 0
|
|
COND = ULPINV
|
|
*
|
|
* Special Matrices
|
|
*
|
|
IF( ITYPE.EQ.1 ) THEN
|
|
*
|
|
* Zero
|
|
*
|
|
IINFO = 0
|
|
ELSE IF( ITYPE.EQ.2 ) THEN
|
|
*
|
|
* Identity
|
|
*
|
|
DO 80 JCOL = 1, N
|
|
A( JCOL, JCOL ) = ANORM
|
|
80 CONTINUE
|
|
*
|
|
ELSE IF( ITYPE.EQ.3 ) THEN
|
|
*
|
|
* Jordan Block
|
|
*
|
|
DO 90 JCOL = 1, N
|
|
A( JCOL, JCOL ) = ANORM
|
|
IF( JCOL.GT.1 )
|
|
$ A( JCOL, JCOL-1 ) = ONE
|
|
90 CONTINUE
|
|
*
|
|
ELSE IF( ITYPE.EQ.4 ) THEN
|
|
*
|
|
* Diagonal Matrix, [Eigen]values Specified
|
|
*
|
|
CALL CLATMR( N, N, 'D', ISEED, 'N', WORK, IMODE, COND,
|
|
$ CONE, '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.5 ) THEN
|
|
*
|
|
* Hermitian, eigenvalues specified
|
|
*
|
|
CALL CLATMS( N, N, 'D', ISEED, 'H', RWORK, IMODE, COND,
|
|
$ ANORM, N, N, 'N', A, LDA, WORK, 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( 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, IWORK, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.8 ) THEN
|
|
*
|
|
* Hermitian, 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, IWORK, 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, IWORK, IINFO )
|
|
*
|
|
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, IWORK, IINFO )
|
|
*
|
|
ELSE
|
|
*
|
|
IINFO = 1
|
|
END IF
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
100 CONTINUE
|
|
*
|
|
* Call CGEHRD to compute H and U, do tests.
|
|
*
|
|
CALL CLACPY( ' ', N, N, A, LDA, H, LDA )
|
|
NTEST = 1
|
|
*
|
|
ILO = 1
|
|
IHI = N
|
|
*
|
|
CALL CGEHRD( N, ILO, IHI, H, LDA, WORK, WORK( N+1 ),
|
|
$ NWORK-N, IINFO )
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
WRITE( NOUNIT, FMT = 9999 )'CGEHRD', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 240
|
|
END IF
|
|
*
|
|
DO 120 J = 1, N - 1
|
|
UU( J+1, J ) = CZERO
|
|
DO 110 I = J + 2, N
|
|
U( I, J ) = H( I, J )
|
|
UU( I, J ) = H( I, J )
|
|
H( I, J ) = CZERO
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
CALL CCOPY( N-1, WORK, 1, TAU, 1 )
|
|
CALL CUNGHR( N, ILO, IHI, U, LDU, WORK, WORK( N+1 ),
|
|
$ NWORK-N, IINFO )
|
|
NTEST = 2
|
|
*
|
|
CALL CHST01( N, ILO, IHI, A, LDA, H, LDA, U, LDU, WORK,
|
|
$ NWORK, RWORK, RESULT( 1 ) )
|
|
*
|
|
* Call CHSEQR to compute T1, T2 and Z, do tests.
|
|
*
|
|
* Eigenvalues only (W3)
|
|
*
|
|
CALL CLACPY( ' ', N, N, H, LDA, T2, LDA )
|
|
NTEST = 3
|
|
RESULT( 3 ) = ULPINV
|
|
*
|
|
CALL CHSEQR( 'E', 'N', N, ILO, IHI, T2, LDA, W3, UZ, LDU,
|
|
$ WORK, NWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CHSEQR(E)', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
IF( IINFO.LE.N+2 ) THEN
|
|
INFO = ABS( IINFO )
|
|
GO TO 240
|
|
END IF
|
|
END IF
|
|
*
|
|
* Eigenvalues (W1) and Full Schur Form (T2)
|
|
*
|
|
CALL CLACPY( ' ', N, N, H, LDA, T2, LDA )
|
|
*
|
|
CALL CHSEQR( 'S', 'N', N, ILO, IHI, T2, LDA, W1, UZ, LDU,
|
|
$ WORK, NWORK, IINFO )
|
|
IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CHSEQR(S)', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 240
|
|
END IF
|
|
*
|
|
* Eigenvalues (W1), Schur Form (T1), and Schur Vectors (UZ)
|
|
*
|
|
CALL CLACPY( ' ', N, N, H, LDA, T1, LDA )
|
|
CALL CLACPY( ' ', N, N, U, LDU, UZ, LDU )
|
|
*
|
|
CALL CHSEQR( 'S', 'V', N, ILO, IHI, T1, LDA, W1, UZ, LDU,
|
|
$ WORK, NWORK, IINFO )
|
|
IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CHSEQR(V)', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 240
|
|
END IF
|
|
*
|
|
* Compute Z = U' UZ
|
|
*
|
|
CALL CGEMM( 'C', 'N', N, N, N, CONE, U, LDU, UZ, LDU, CZERO,
|
|
$ Z, LDU )
|
|
NTEST = 8
|
|
*
|
|
* Do Tests 3: | H - Z T Z' | / ( |H| n ulp )
|
|
* and 4: | I - Z Z' | / ( n ulp )
|
|
*
|
|
CALL CHST01( N, ILO, IHI, H, LDA, T1, LDA, Z, LDU, WORK,
|
|
$ NWORK, RWORK, RESULT( 3 ) )
|
|
*
|
|
* Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp )
|
|
* and 6: | I - UZ (UZ)' | / ( n ulp )
|
|
*
|
|
CALL CHST01( N, ILO, IHI, A, LDA, T1, LDA, UZ, LDU, WORK,
|
|
$ NWORK, RWORK, RESULT( 5 ) )
|
|
*
|
|
* Do Test 7: | T2 - T1 | / ( |T| n ulp )
|
|
*
|
|
CALL CGET10( N, N, T2, LDA, T1, LDA, WORK, RWORK,
|
|
$ RESULT( 7 ) )
|
|
*
|
|
* Do Test 8: | W3 - W1 | / ( max(|W1|,|W3|) ulp )
|
|
*
|
|
TEMP1 = ZERO
|
|
TEMP2 = ZERO
|
|
DO 130 J = 1, N
|
|
TEMP1 = MAX( TEMP1, ABS( W1( J ) ), ABS( W3( J ) ) )
|
|
TEMP2 = MAX( TEMP2, ABS( W1( J )-W3( J ) ) )
|
|
130 CONTINUE
|
|
*
|
|
RESULT( 8 ) = TEMP2 / MAX( UNFL, ULP*MAX( TEMP1, TEMP2 ) )
|
|
*
|
|
* Compute the Left and Right Eigenvectors of T
|
|
*
|
|
* Compute the Right eigenvector Matrix:
|
|
*
|
|
NTEST = 9
|
|
RESULT( 9 ) = ULPINV
|
|
*
|
|
* Select every other eigenvector
|
|
*
|
|
DO 140 J = 1, N
|
|
SELECT( J ) = .FALSE.
|
|
140 CONTINUE
|
|
DO 150 J = 1, N, 2
|
|
SELECT( J ) = .TRUE.
|
|
150 CONTINUE
|
|
CALL CTREVC( 'Right', 'All', SELECT, N, T1, LDA, CDUMMA,
|
|
$ LDU, EVECTR, LDU, N, IN, WORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CTREVC(R,A)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 240
|
|
END IF
|
|
*
|
|
* Test 9: | TR - RW | / ( |T| |R| ulp )
|
|
*
|
|
CALL CGET22( 'N', 'N', 'N', N, T1, LDA, EVECTR, LDU, W1,
|
|
$ WORK, RWORK, DUMMA( 1 ) )
|
|
RESULT( 9 ) = DUMMA( 1 )
|
|
IF( DUMMA( 2 ).GT.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'Right', 'CTREVC',
|
|
$ DUMMA( 2 ), N, JTYPE, IOLDSD
|
|
END IF
|
|
*
|
|
* Compute selected right eigenvectors and confirm that
|
|
* they agree with previous right eigenvectors
|
|
*
|
|
CALL CTREVC( 'Right', 'Some', SELECT, N, T1, LDA, CDUMMA,
|
|
$ LDU, EVECTL, LDU, N, IN, WORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CTREVC(R,S)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 240
|
|
END IF
|
|
*
|
|
K = 1
|
|
MATCH = .TRUE.
|
|
DO 170 J = 1, N
|
|
IF( SELECT( J ) ) THEN
|
|
DO 160 JJ = 1, N
|
|
IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) ) THEN
|
|
MATCH = .FALSE.
|
|
GO TO 180
|
|
END IF
|
|
160 CONTINUE
|
|
K = K + 1
|
|
END IF
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
IF( .NOT.MATCH )
|
|
$ WRITE( NOUNIT, FMT = 9997 )'Right', 'CTREVC', N, JTYPE,
|
|
$ IOLDSD
|
|
*
|
|
* Compute the Left eigenvector Matrix:
|
|
*
|
|
NTEST = 10
|
|
RESULT( 10 ) = ULPINV
|
|
CALL CTREVC( 'Left', 'All', SELECT, N, T1, LDA, EVECTL, LDU,
|
|
$ CDUMMA, LDU, N, IN, WORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CTREVC(L,A)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 240
|
|
END IF
|
|
*
|
|
* Test 10: | LT - WL | / ( |T| |L| ulp )
|
|
*
|
|
CALL CGET22( 'C', 'N', 'C', N, T1, LDA, EVECTL, LDU, W1,
|
|
$ WORK, RWORK, DUMMA( 3 ) )
|
|
RESULT( 10 ) = DUMMA( 3 )
|
|
IF( DUMMA( 4 ).GT.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'Left', 'CTREVC', DUMMA( 4 ),
|
|
$ N, JTYPE, IOLDSD
|
|
END IF
|
|
*
|
|
* Compute selected left eigenvectors and confirm that
|
|
* they agree with previous left eigenvectors
|
|
*
|
|
CALL CTREVC( 'Left', 'Some', SELECT, N, T1, LDA, EVECTR,
|
|
$ LDU, CDUMMA, LDU, N, IN, WORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CTREVC(L,S)', IINFO, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
GO TO 240
|
|
END IF
|
|
*
|
|
K = 1
|
|
MATCH = .TRUE.
|
|
DO 200 J = 1, N
|
|
IF( SELECT( J ) ) THEN
|
|
DO 190 JJ = 1, N
|
|
IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) ) THEN
|
|
MATCH = .FALSE.
|
|
GO TO 210
|
|
END IF
|
|
190 CONTINUE
|
|
K = K + 1
|
|
END IF
|
|
200 CONTINUE
|
|
210 CONTINUE
|
|
IF( .NOT.MATCH )
|
|
$ WRITE( NOUNIT, FMT = 9997 )'Left', 'CTREVC', N, JTYPE,
|
|
$ IOLDSD
|
|
*
|
|
* Call CHSEIN for Right eigenvectors of H, do test 11
|
|
*
|
|
NTEST = 11
|
|
RESULT( 11 ) = ULPINV
|
|
DO 220 J = 1, N
|
|
SELECT( J ) = .TRUE.
|
|
220 CONTINUE
|
|
*
|
|
CALL CHSEIN( 'Right', 'Qr', 'Ninitv', SELECT, N, H, LDA, W3,
|
|
$ CDUMMA, LDU, EVECTX, LDU, N1, IN, WORK, RWORK,
|
|
$ IWORK, IWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CHSEIN(R)', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 )
|
|
$ GO TO 240
|
|
ELSE
|
|
*
|
|
* Test 11: | HX - XW | / ( |H| |X| ulp )
|
|
*
|
|
* (from inverse iteration)
|
|
*
|
|
CALL CGET22( 'N', 'N', 'N', N, H, LDA, EVECTX, LDU, W3,
|
|
$ WORK, RWORK, DUMMA( 1 ) )
|
|
IF( DUMMA( 1 ).LT.ULPINV )
|
|
$ RESULT( 11 ) = DUMMA( 1 )*ANINV
|
|
IF( DUMMA( 2 ).GT.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'Right', 'CHSEIN',
|
|
$ DUMMA( 2 ), N, JTYPE, IOLDSD
|
|
END IF
|
|
END IF
|
|
*
|
|
* Call CHSEIN for Left eigenvectors of H, do test 12
|
|
*
|
|
NTEST = 12
|
|
RESULT( 12 ) = ULPINV
|
|
DO 230 J = 1, N
|
|
SELECT( J ) = .TRUE.
|
|
230 CONTINUE
|
|
*
|
|
CALL CHSEIN( 'Left', 'Qr', 'Ninitv', SELECT, N, H, LDA, W3,
|
|
$ EVECTY, LDU, CDUMMA, LDU, N1, IN, WORK, RWORK,
|
|
$ IWORK, IWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CHSEIN(L)', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 )
|
|
$ GO TO 240
|
|
ELSE
|
|
*
|
|
* Test 12: | YH - WY | / ( |H| |Y| ulp )
|
|
*
|
|
* (from inverse iteration)
|
|
*
|
|
CALL CGET22( 'C', 'N', 'C', N, H, LDA, EVECTY, LDU, W3,
|
|
$ WORK, RWORK, DUMMA( 3 ) )
|
|
IF( DUMMA( 3 ).LT.ULPINV )
|
|
$ RESULT( 12 ) = DUMMA( 3 )*ANINV
|
|
IF( DUMMA( 4 ).GT.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'Left', 'CHSEIN',
|
|
$ DUMMA( 4 ), N, JTYPE, IOLDSD
|
|
END IF
|
|
END IF
|
|
*
|
|
* Call CUNMHR for Right eigenvectors of A, do test 13
|
|
*
|
|
NTEST = 13
|
|
RESULT( 13 ) = ULPINV
|
|
*
|
|
CALL CUNMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU,
|
|
$ LDU, TAU, EVECTX, LDU, WORK, NWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CUNMHR(L)', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 )
|
|
$ GO TO 240
|
|
ELSE
|
|
*
|
|
* Test 13: | AX - XW | / ( |A| |X| ulp )
|
|
*
|
|
* (from inverse iteration)
|
|
*
|
|
CALL CGET22( 'N', 'N', 'N', N, A, LDA, EVECTX, LDU, W3,
|
|
$ WORK, RWORK, DUMMA( 1 ) )
|
|
IF( DUMMA( 1 ).LT.ULPINV )
|
|
$ RESULT( 13 ) = DUMMA( 1 )*ANINV
|
|
END IF
|
|
*
|
|
* Call CUNMHR for Left eigenvectors of A, do test 14
|
|
*
|
|
NTEST = 14
|
|
RESULT( 14 ) = ULPINV
|
|
*
|
|
CALL CUNMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU,
|
|
$ LDU, TAU, EVECTY, LDU, WORK, NWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )'CUNMHR(L)', IINFO, N, JTYPE,
|
|
$ IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 )
|
|
$ GO TO 240
|
|
ELSE
|
|
*
|
|
* Test 14: | YA - WY | / ( |A| |Y| ulp )
|
|
*
|
|
* (from inverse iteration)
|
|
*
|
|
CALL CGET22( 'C', 'N', 'C', N, A, LDA, EVECTY, LDU, W3,
|
|
$ WORK, RWORK, DUMMA( 3 ) )
|
|
IF( DUMMA( 3 ).LT.ULPINV )
|
|
$ RESULT( 14 ) = DUMMA( 3 )*ANINV
|
|
END IF
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
240 CONTINUE
|
|
*
|
|
NTESTT = NTESTT + NTEST
|
|
CALL SLAFTS( 'CHS', N, N, JTYPE, NTEST, RESULT, IOLDSD,
|
|
$ THRESH, NOUNIT, NERRS )
|
|
*
|
|
250 CONTINUE
|
|
260 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL SLASUM( 'CHS', NOUNIT, NERRS, NTESTT )
|
|
*
|
|
RETURN
|
|
*
|
|
9999 FORMAT( ' CCHKHS: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
9998 FORMAT( ' CCHKHS: ', A, ' Eigenvectors from ', A, ' incorrectly ',
|
|
$ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
|
|
$ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
|
|
$ ')' )
|
|
9997 FORMAT( ' CCHKHS: Selected ', A, ' Eigenvectors from ', A,
|
|
$ ' do not match other eigenvectors ', 9X, 'N=', I6,
|
|
$ ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
* End of CCHKHS
|
|
*
|
|
END
|