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1207 lines
42 KiB
1207 lines
42 KiB
2 years ago
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*> \brief \b SCHKHS
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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 SCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
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* NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, WR1,
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* WI1, WR2, WI2, WR3, WI3, EVECTL, EVECTR, EVECTY,
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* EVECTX, UU, TAU, WORK, NWORK, IWORK, SELECT,
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* RESULT, 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 A( LDA, * ), EVECTL( LDU, * ),
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* $ EVECTR( LDU, * ), EVECTX( LDU, * ),
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* $ EVECTY( LDU, * ), H( LDA, * ), RESULT( 16 ),
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* $ T1( LDA, * ), T2( LDA, * ), TAU( * ),
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* $ U( LDU, * ), UU( LDU, * ), UZ( LDU, * ),
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* $ WI1( * ), WI2( * ), WI3( * ), WORK( * ),
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* $ WR1( * ), WR2( * ), WR3( * ), 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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*> SCHKHS checks the nonsymmetric eigenvalue problem routines.
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*>
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*> SGEHRD factors A as U H U' , where ' means transpose,
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*> H is hessenberg, and U is an orthogonal matrix.
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*>
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*> SORGHR generates the orthogonal matrix U.
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*>
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*> SORMHR multiplies a matrix by the orthogonal matrix U.
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*>
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*> SHSEQR factors H as Z T Z' , where Z is orthogonal and
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*> T is "quasi-triangular", and the eigenvalue vector W.
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*>
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*> STREVC computes the left and right eigenvector matrices
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*> L and R for T.
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*>
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*> SHSEIN computes the left and right eigenvector matrices
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*> Y and X for H, using inverse iteration.
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*>
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*> STREVC3 computes left and right eigenvector matrices
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*> from a Schur matrix T and backtransforms them with Z
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*> to eigenvector matrices L and R for A. L and R are
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*> GE matrices.
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*>
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*> When SCHKHS 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, 16
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*> tests will be performed:
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*>
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*> (1) | A - U H U**T | / ( |A| n ulp )
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*>
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*> (2) | I - UU**T | / ( n ulp )
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*>
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*> (3) | H - Z T Z**T | / ( |H| n ulp )
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*>
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*> (4) | I - ZZ**T | / ( n ulp )
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*>
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*> (5) | A - UZ H (UZ)**T | / ( |A| n ulp )
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*>
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*> (6) | I - UZ (UZ)**T | / ( 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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*> (15) | AR - RW | / ( |A| |R| ulp )
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*>
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*> (16) | LA - WL | / ( |A| |L| 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 signs.
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*> (ULP = (first number larger than 1) - 1 )
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*> (5) A diagonal matrix with geometrically spaced entries
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*> 1, ..., ULP and random signs.
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*> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
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*> and random signs.
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*>
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*> (7) Same as (4), but multiplied by 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 orthogonal and
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*> T has evenly spaced entries 1, ..., ULP with random signs
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*> on the diagonal and random O(1) entries in the upper
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*> triangle.
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*>
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*> (10) A matrix of the form U' T U, where U is orthogonal and
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*> T has geometrically spaced entries 1, ..., ULP with random
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*> signs on the diagonal and random O(1) entries in the upper
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*> triangle.
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*>
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*> (11) A matrix of the form U' T U, where U is orthogonal and
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*> T has "clustered" entries 1, ULP,..., ULP with random
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*> signs on the diagonal and random O(1) entries in the upper
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*> triangle.
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*>
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*> (12) A matrix of the form U' T U, where U is orthogonal and
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*> T has real or complex conjugate paired eigenvalues randomly
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*> chosen from ( ULP, 1 ) and random O(1) entries in the upper
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*> triangle.
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*>
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*> (13) A matrix of the form X' T X, where X has condition
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*> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
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*> with random signs on the diagonal and random O(1) entries
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*> in the upper triangle.
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*>
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*> (14) A matrix of the form X' T X, where X has condition
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*> SQRT( ULP ) and T has geometrically spaced entries
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*> 1, ..., ULP with random signs on the diagonal and random
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*> O(1) entries in the upper triangle.
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*>
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*> (15) A matrix of the form X' T X, where X has condition
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*> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
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*> with random signs on the diagonal and random O(1) entries
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*> in the upper triangle.
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*>
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*> (16) A matrix of the form X' T X, where X has condition
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*> SQRT( ULP ) and T has real or complex conjugate paired
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*> eigenvalues randomly chosen from ( ULP, 1 ) and random
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*> O(1) entries in the upper triangle.
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*>
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*> (17) Same as (16), but multiplied by 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 (-1,1).
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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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*> SCHKHS 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, SCHKHS
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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 SCHKHS 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 - REAL 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 - REAL array, dimension (LDA,max(NN))
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*> The upper hessenberg matrix computed by SGEHRD. 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 - REAL array, dimension (LDA,max(NN))
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*> The Schur (="quasi-triangular") matrix computed by SHSEQR
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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 - REAL array, dimension (LDA,max(NN))
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*> The Schur matrix computed by SHSEQR 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 - REAL array, dimension (LDU,max(NN))
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*> The orthogonal matrix computed by SGEHRD.
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*> Modified.
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*>
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*> Z - REAL array, dimension (LDU,max(NN))
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*> The orthogonal matrix computed by SHSEQR.
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*> Modified.
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*>
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*> UZ - REAL 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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*> WR1 - REAL array, dimension (max(NN))
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*> WI1 - REAL array, dimension (max(NN))
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*> The real and imaginary parts of the eigenvalues of A,
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*> as computed when Z is computed.
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*> On exit, WR1 + WI1*i are the eigenvalues of the matrix in A.
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*> Modified.
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*>
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*> WR2 - REAL array, dimension (max(NN))
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*> WI2 - REAL array, dimension (max(NN))
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*> The real and imaginary parts of the eigenvalues of A,
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*> as computed when T is computed but not Z.
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*> On exit, WR2 + WI2*i are the eigenvalues of the matrix in A.
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*> Modified.
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*>
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*> WR3 - REAL array, dimension (max(NN))
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*> WI3 - REAL array, dimension (max(NN))
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*> Like WR1, WI1, these arrays contain the eigenvalues of A,
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*> but those computed when SHSEQR only computes the
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*> eigenvalues, i.e., not the Schur vectors and no more of the
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*> Schur form than is necessary for computing the
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*> eigenvalues.
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*> Modified.
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*>
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*> EVECTL - REAL array, dimension (LDU,max(NN))
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*> The (upper triangular) left eigenvector matrix for the
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*> matrix in T1. For complex conjugate pairs, the real part
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*> is stored in one row and the imaginary part in the next.
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*> Modified.
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*>
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*> EVECTR - REAL array, dimension (LDU,max(NN))
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*> The (upper triangular) right eigenvector matrix for the
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*> matrix in T1. For complex conjugate pairs, the real part
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*> is stored in one column and the imaginary part in the next.
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*> Modified.
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*>
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*> EVECTY - REAL array, dimension (LDU,max(NN))
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*> The left eigenvector matrix for the
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*> matrix in H. For complex conjugate pairs, the real part
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*> is stored in one row and the imaginary part in the next.
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*> Modified.
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*>
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*> EVECTX - REAL array, dimension (LDU,max(NN))
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*> The right eigenvector matrix for the
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*> matrix in H. For complex conjugate pairs, the real part
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*> is stored in one column and the imaginary part in the next.
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*> Modified.
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*>
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*> UU - REAL array, dimension (LDU,max(NN))
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*> Details of the orthogonal matrix computed by SGEHRD.
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*> Modified.
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*>
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*> TAU - REAL array, dimension(max(NN))
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*> Further details of the orthogonal matrix computed by SGEHRD.
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*> Modified.
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*>
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*> WORK - REAL 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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*> IWORK - INTEGER array, dimension (max(NN))
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*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> SELECT - LOGICAL array, dimension (max(NN))
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> RESULT - REAL array, dimension (16)
|
||
|
|
*> The values computed by the fourteen tests described above.
|
||
|
|
*> The values are currently limited to 1/ulp, to avoid
|
||
|
|
*> overflow.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> INFO - INTEGER
|
||
|
|
*> If 0, then everything ran OK.
|
||
|
|
*> -1: NSIZES < 0
|
||
|
|
*> -2: Some NN(j) < 0
|
||
|
|
*> -3: NTYPES < 0
|
||
|
|
*> -6: THRESH < 0
|
||
|
|
*> -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
|
||
|
|
*> -14: LDU < 1 or LDU < NMAX.
|
||
|
|
*> -28: NWORK too small.
|
||
|
|
*> If SLATMR, SLATMS, or SLATME returns an error code, the
|
||
|
|
*> absolute value of it is returned.
|
||
|
|
*> If 1, then SHSEQR could not find all the shifts.
|
||
|
|
*> If 2, then the EISPACK code (for small blocks) failed.
|
||
|
|
*> If >2, then 30*N iterations were not enough to find an
|
||
|
|
*> eigenvalue or to decompose the problem.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*>-----------------------------------------------------------------------
|
||
|
|
*>
|
||
|
|
*> Some Local Variables and Parameters:
|
||
|
|
*> ---- ----- --------- --- ----------
|
||
|
|
*>
|
||
|
|
*> ZERO, ONE Real 0 and 1.
|
||
|
|
*> MAXTYP The number of types defined.
|
||
|
|
*> MTEST The number of tests defined: care must be taken
|
||
|
|
*> that (1) the size of RESULT, (2) the number of
|
||
|
|
*> tests actually performed, and (3) MTEST agree.
|
||
|
|
*> NTEST The number of tests performed on this matrix
|
||
|
|
*> so far. This should be less than MTEST, and
|
||
|
|
*> equal to it by the last test. It will be less
|
||
|
|
*> if any of the routines being tested indicates
|
||
|
|
*> that it could not compute the matrices that
|
||
|
|
*> would be tested.
|
||
|
|
*> NMAX Largest value in NN.
|
||
|
|
*> NMATS The number of matrices generated so far.
|
||
|
|
*> NERRS The number of tests which have exceeded THRESH
|
||
|
|
*> so far (computed by SLAFTS).
|
||
|
|
*> COND, CONDS,
|
||
|
|
*> IMODE Values to be passed to the matrix generators.
|
||
|
|
*> ANORM Norm of A; passed to matrix generators.
|
||
|
|
*>
|
||
|
|
*> OVFL, UNFL Overflow and underflow thresholds.
|
||
|
|
*> ULP, ULPINV Finest relative precision and its inverse.
|
||
|
|
*> RTOVFL, RTUNFL,
|
||
|
|
*> RTULP, RTULPI Square roots of the previous 4 values.
|
||
|
|
*>
|
||
|
|
*> The following four arrays decode JTYPE:
|
||
|
|
*> KTYPE(j) The general type (1-10) for type "j".
|
||
|
|
*> KMODE(j) The MODE value to be passed to the matrix
|
||
|
|
*> generator for type "j".
|
||
|
|
*> KMAGN(j) The order of magnitude ( O(1),
|
||
|
|
*> O(overflow^(1/2) ), O(underflow^(1/2) )
|
||
|
|
*> KCONDS(j) Selects whether CONDS is to be 1 or
|
||
|
|
*> 1/sqrt(ulp). (0 means irrelevant.)
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup single_eig
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE SCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
|
||
|
|
$ NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, WR1,
|
||
|
|
$ WI1, WR2, WI2, WR3, WI3, EVECTL, EVECTR,
|
||
|
|
$ EVECTY, EVECTX, UU, TAU, WORK, NWORK, IWORK,
|
||
|
|
$ SELECT, RESULT, INFO )
|
||
|
|
*
|
||
|
|
* -- LAPACK test routine --
|
||
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK
|
||
|
|
REAL THRESH
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
LOGICAL DOTYPE( * ), SELECT( * )
|
||
|
|
INTEGER ISEED( 4 ), IWORK( * ), NN( * )
|
||
|
|
REAL A( LDA, * ), EVECTL( LDU, * ),
|
||
|
|
$ EVECTR( LDU, * ), EVECTX( LDU, * ),
|
||
|
|
$ EVECTY( LDU, * ), H( LDA, * ), RESULT( 16 ),
|
||
|
|
$ T1( LDA, * ), T2( LDA, * ), TAU( * ),
|
||
|
|
$ U( LDU, * ), UU( LDU, * ), UZ( LDU, * ),
|
||
|
|
$ WI1( * ), WI2( * ), WI3( * ), WORK( * ),
|
||
|
|
$ WR1( * ), WR2( * ), WR3( * ), Z( LDU, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
REAL ZERO, ONE
|
||
|
|
PARAMETER ( ZERO = 0.0, ONE = 1.0 )
|
||
|
|
INTEGER MAXTYP
|
||
|
|
PARAMETER ( MAXTYP = 21 )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
LOGICAL BADNN, MATCH
|
||
|
|
INTEGER I, IHI, IINFO, ILO, IMODE, IN, ITYPE, J, JCOL,
|
||
|
|
$ JJ, JSIZE, JTYPE, K, MTYPES, N, N1, NERRS,
|
||
|
|
$ NMATS, NMAX, NSELC, NSELR, NTEST, NTESTT
|
||
|
|
REAL ANINV, ANORM, COND, CONDS, OVFL, RTOVFL, RTULP,
|
||
|
|
$ RTULPI, RTUNFL, TEMP1, TEMP2, ULP, ULPINV, UNFL
|
||
|
|
* ..
|
||
|
|
* .. Local Arrays ..
|
||
|
|
CHARACTER ADUMMA( 1 )
|
||
|
|
INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
|
||
|
|
$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
|
||
|
|
$ KTYPE( MAXTYP )
|
||
|
|
REAL DUMMA( 6 )
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
REAL SLAMCH
|
||
|
|
EXTERNAL SLAMCH
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL SCOPY, SGEHRD, SGEMM, SGET10, SGET22, SHSEIN,
|
||
|
|
$ SHSEQR, SHST01, SLACPY, SLAFTS, SLASET, SLASUM,
|
||
|
|
$ SLATME, SLATMR, SLATMS, SORGHR, SORMHR, STREVC,
|
||
|
|
$ STREVC3, 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 = -28
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
CALL XERBLA( 'SCHKHS', -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' )
|
||
|
|
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 270 JSIZE = 1, NSIZES
|
||
|
|
N = NN( JSIZE )
|
||
|
|
IF( N.EQ.0 )
|
||
|
|
$ GO TO 270
|
||
|
|
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 260 JTYPE = 1, MTYPES
|
||
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
||
|
|
$ GO TO 260
|
||
|
|
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, 16
|
||
|
|
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 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 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 SLASET( 'Full', LDA, N, ZERO, ZERO, 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 SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
|
||
|
|
$ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
|
||
|
|
$ IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.5 ) THEN
|
||
|
|
*
|
||
|
|
* Symmetric, eigenvalues specified
|
||
|
|
*
|
||
|
|
CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
|
||
|
|
$ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
|
||
|
|
$ IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.6 ) THEN
|
||
|
|
*
|
||
|
|
* General, eigenvalues specified
|
||
|
|
*
|
||
|
|
IF( KCONDS( JTYPE ).EQ.1 ) THEN
|
||
|
|
CONDS = ONE
|
||
|
|
ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN
|
||
|
|
CONDS = RTULPI
|
||
|
|
ELSE
|
||
|
|
CONDS = ZERO
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ADUMMA( 1 ) = ' '
|
||
|
|
CALL SLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE,
|
||
|
|
$ ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4,
|
||
|
|
$ CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ),
|
||
|
|
$ IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.7 ) THEN
|
||
|
|
*
|
||
|
|
* Diagonal, random eigenvalues
|
||
|
|
*
|
||
|
|
CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
|
||
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
||
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
|
||
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.8 ) THEN
|
||
|
|
*
|
||
|
|
* Symmetric, random eigenvalues
|
||
|
|
*
|
||
|
|
CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
|
||
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
||
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
|
||
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.9 ) THEN
|
||
|
|
*
|
||
|
|
* General, random eigenvalues
|
||
|
|
*
|
||
|
|
CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
|
||
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
||
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
|
||
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.10 ) THEN
|
||
|
|
*
|
||
|
|
* Triangular, random eigenvalues
|
||
|
|
*
|
||
|
|
CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
|
||
|
|
$ 'T', 'N', WORK( N+1 ), 1, ONE,
|
||
|
|
$ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
|
||
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
IINFO = 1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
100 CONTINUE
|
||
|
|
*
|
||
|
|
* Call SGEHRD to compute H and U, do tests.
|
||
|
|
*
|
||
|
|
CALL SLACPY( ' ', N, N, A, LDA, H, LDA )
|
||
|
|
*
|
||
|
|
NTEST = 1
|
||
|
|
*
|
||
|
|
ILO = 1
|
||
|
|
IHI = N
|
||
|
|
*
|
||
|
|
CALL SGEHRD( N, ILO, IHI, H, LDA, WORK, WORK( N+1 ),
|
||
|
|
$ NWORK-N, IINFO )
|
||
|
|
*
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
RESULT( 1 ) = ULPINV
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'SGEHRD', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
DO 120 J = 1, N - 1
|
||
|
|
UU( J+1, J ) = ZERO
|
||
|
|
DO 110 I = J + 2, N
|
||
|
|
U( I, J ) = H( I, J )
|
||
|
|
UU( I, J ) = H( I, J )
|
||
|
|
H( I, J ) = ZERO
|
||
|
|
110 CONTINUE
|
||
|
|
120 CONTINUE
|
||
|
|
CALL SCOPY( N-1, WORK, 1, TAU, 1 )
|
||
|
|
CALL SORGHR( N, ILO, IHI, U, LDU, WORK, WORK( N+1 ),
|
||
|
|
$ NWORK-N, IINFO )
|
||
|
|
NTEST = 2
|
||
|
|
*
|
||
|
|
CALL SHST01( N, ILO, IHI, A, LDA, H, LDA, U, LDU, WORK,
|
||
|
|
$ NWORK, RESULT( 1 ) )
|
||
|
|
*
|
||
|
|
* Call SHSEQR to compute T1, T2 and Z, do tests.
|
||
|
|
*
|
||
|
|
* Eigenvalues only (WR3,WI3)
|
||
|
|
*
|
||
|
|
CALL SLACPY( ' ', N, N, H, LDA, T2, LDA )
|
||
|
|
NTEST = 3
|
||
|
|
RESULT( 3 ) = ULPINV
|
||
|
|
*
|
||
|
|
CALL SHSEQR( 'E', 'N', N, ILO, IHI, T2, LDA, WR3, WI3, UZ,
|
||
|
|
$ LDU, WORK, NWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'SHSEQR(E)', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
IF( IINFO.LE.N+2 ) THEN
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Eigenvalues (WR2,WI2) and Full Schur Form (T2)
|
||
|
|
*
|
||
|
|
CALL SLACPY( ' ', N, N, H, LDA, T2, LDA )
|
||
|
|
*
|
||
|
|
CALL SHSEQR( 'S', 'N', N, ILO, IHI, T2, LDA, WR2, WI2, UZ,
|
||
|
|
$ LDU, WORK, NWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'SHSEQR(S)', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Eigenvalues (WR1,WI1), Schur Form (T1), and Schur vectors
|
||
|
|
* (UZ)
|
||
|
|
*
|
||
|
|
CALL SLACPY( ' ', N, N, H, LDA, T1, LDA )
|
||
|
|
CALL SLACPY( ' ', N, N, U, LDU, UZ, LDU )
|
||
|
|
*
|
||
|
|
CALL SHSEQR( 'S', 'V', N, ILO, IHI, T1, LDA, WR1, WI1, UZ,
|
||
|
|
$ LDU, WORK, NWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'SHSEQR(V)', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compute Z = U' UZ
|
||
|
|
*
|
||
|
|
CALL SGEMM( 'T', 'N', N, N, N, ONE, U, LDU, UZ, LDU, ZERO,
|
||
|
|
$ Z, LDU )
|
||
|
|
NTEST = 8
|
||
|
|
*
|
||
|
|
* Do Tests 3: | H - Z T Z' | / ( |H| n ulp )
|
||
|
|
* and 4: | I - Z Z' | / ( n ulp )
|
||
|
|
*
|
||
|
|
CALL SHST01( N, ILO, IHI, H, LDA, T1, LDA, Z, LDU, WORK,
|
||
|
|
$ NWORK, RESULT( 3 ) )
|
||
|
|
*
|
||
|
|
* Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp )
|
||
|
|
* and 6: | I - UZ (UZ)' | / ( n ulp )
|
||
|
|
*
|
||
|
|
CALL SHST01( N, ILO, IHI, A, LDA, T1, LDA, UZ, LDU, WORK,
|
||
|
|
$ NWORK, RESULT( 5 ) )
|
||
|
|
*
|
||
|
|
* Do Test 7: | T2 - T1 | / ( |T| n ulp )
|
||
|
|
*
|
||
|
|
CALL SGET10( N, N, T2, LDA, T1, LDA, WORK, RESULT( 7 ) )
|
||
|
|
*
|
||
|
|
* Do Test 8: | W2 - W1 | / ( max(|W1|,|W2|) ulp )
|
||
|
|
*
|
||
|
|
TEMP1 = ZERO
|
||
|
|
TEMP2 = ZERO
|
||
|
|
DO 130 J = 1, N
|
||
|
|
TEMP1 = MAX( TEMP1, ABS( WR1( J ) )+ABS( WI1( J ) ),
|
||
|
|
$ ABS( WR2( J ) )+ABS( WI2( J ) ) )
|
||
|
|
TEMP2 = MAX( TEMP2, ABS( WR1( J )-WR2( J ) )+
|
||
|
|
$ ABS( WI1( J )-WI2( 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 last max(N/4,1) real, max(N/4,1) complex eigenvectors
|
||
|
|
*
|
||
|
|
NSELC = 0
|
||
|
|
NSELR = 0
|
||
|
|
J = N
|
||
|
|
140 CONTINUE
|
||
|
|
IF( WI1( J ).EQ.ZERO ) THEN
|
||
|
|
IF( NSELR.LT.MAX( N / 4, 1 ) ) THEN
|
||
|
|
NSELR = NSELR + 1
|
||
|
|
SELECT( J ) = .TRUE.
|
||
|
|
ELSE
|
||
|
|
SELECT( J ) = .FALSE.
|
||
|
|
END IF
|
||
|
|
J = J - 1
|
||
|
|
ELSE
|
||
|
|
IF( NSELC.LT.MAX( N / 4, 1 ) ) THEN
|
||
|
|
NSELC = NSELC + 1
|
||
|
|
SELECT( J ) = .TRUE.
|
||
|
|
SELECT( J-1 ) = .FALSE.
|
||
|
|
ELSE
|
||
|
|
SELECT( J ) = .FALSE.
|
||
|
|
SELECT( J-1 ) = .FALSE.
|
||
|
|
END IF
|
||
|
|
J = J - 2
|
||
|
|
END IF
|
||
|
|
IF( J.GT.0 )
|
||
|
|
$ GO TO 140
|
||
|
|
*
|
||
|
|
CALL STREVC( 'Right', 'All', SELECT, N, T1, LDA, DUMMA, LDU,
|
||
|
|
$ EVECTR, LDU, N, IN, WORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'STREVC(R,A)', IINFO, N,
|
||
|
|
$ JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Test 9: | TR - RW | / ( |T| |R| ulp )
|
||
|
|
*
|
||
|
|
CALL SGET22( 'N', 'N', 'N', N, T1, LDA, EVECTR, LDU, WR1,
|
||
|
|
$ WI1, WORK, DUMMA( 1 ) )
|
||
|
|
RESULT( 9 ) = DUMMA( 1 )
|
||
|
|
IF( DUMMA( 2 ).GT.THRESH ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9998 )'Right', 'STREVC',
|
||
|
|
$ DUMMA( 2 ), N, JTYPE, IOLDSD
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compute selected right eigenvectors and confirm that
|
||
|
|
* they agree with previous right eigenvectors
|
||
|
|
*
|
||
|
|
CALL STREVC( 'Right', 'Some', SELECT, N, T1, LDA, DUMMA,
|
||
|
|
$ LDU, EVECTL, LDU, N, IN, WORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'STREVC(R,S)', IINFO, N,
|
||
|
|
$ JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
K = 1
|
||
|
|
MATCH = .TRUE.
|
||
|
|
DO 170 J = 1, N
|
||
|
|
IF( SELECT( J ) .AND. WI1( J ).EQ.ZERO ) THEN
|
||
|
|
DO 150 JJ = 1, N
|
||
|
|
IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) ) THEN
|
||
|
|
MATCH = .FALSE.
|
||
|
|
GO TO 180
|
||
|
|
END IF
|
||
|
|
150 CONTINUE
|
||
|
|
K = K + 1
|
||
|
|
ELSE IF( SELECT( J ) .AND. WI1( J ).NE.ZERO ) THEN
|
||
|
|
DO 160 JJ = 1, N
|
||
|
|
IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) .OR.
|
||
|
|
$ EVECTR( JJ, J+1 ).NE.EVECTL( JJ, K+1 ) ) THEN
|
||
|
|
MATCH = .FALSE.
|
||
|
|
GO TO 180
|
||
|
|
END IF
|
||
|
|
160 CONTINUE
|
||
|
|
K = K + 2
|
||
|
|
END IF
|
||
|
|
170 CONTINUE
|
||
|
|
180 CONTINUE
|
||
|
|
IF( .NOT.MATCH )
|
||
|
|
$ WRITE( NOUNIT, FMT = 9997 )'Right', 'STREVC', N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
*
|
||
|
|
* Compute the Left eigenvector Matrix:
|
||
|
|
*
|
||
|
|
NTEST = 10
|
||
|
|
RESULT( 10 ) = ULPINV
|
||
|
|
CALL STREVC( 'Left', 'All', SELECT, N, T1, LDA, EVECTL, LDU,
|
||
|
|
$ DUMMA, LDU, N, IN, WORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'STREVC(L,A)', IINFO, N,
|
||
|
|
$ JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Test 10: | LT - WL | / ( |T| |L| ulp )
|
||
|
|
*
|
||
|
|
CALL SGET22( 'Trans', 'N', 'Conj', N, T1, LDA, EVECTL, LDU,
|
||
|
|
$ WR1, WI1, WORK, DUMMA( 3 ) )
|
||
|
|
RESULT( 10 ) = DUMMA( 3 )
|
||
|
|
IF( DUMMA( 4 ).GT.THRESH ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9998 )'Left', 'STREVC', DUMMA( 4 ),
|
||
|
|
$ N, JTYPE, IOLDSD
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compute selected left eigenvectors and confirm that
|
||
|
|
* they agree with previous left eigenvectors
|
||
|
|
*
|
||
|
|
CALL STREVC( 'Left', 'Some', SELECT, N, T1, LDA, EVECTR,
|
||
|
|
$ LDU, DUMMA, LDU, N, IN, WORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'STREVC(L,S)', IINFO, N,
|
||
|
|
$ JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
K = 1
|
||
|
|
MATCH = .TRUE.
|
||
|
|
DO 210 J = 1, N
|
||
|
|
IF( SELECT( J ) .AND. WI1( J ).EQ.ZERO ) THEN
|
||
|
|
DO 190 JJ = 1, N
|
||
|
|
IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) ) THEN
|
||
|
|
MATCH = .FALSE.
|
||
|
|
GO TO 220
|
||
|
|
END IF
|
||
|
|
190 CONTINUE
|
||
|
|
K = K + 1
|
||
|
|
ELSE IF( SELECT( J ) .AND. WI1( J ).NE.ZERO ) THEN
|
||
|
|
DO 200 JJ = 1, N
|
||
|
|
IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) .OR.
|
||
|
|
$ EVECTL( JJ, J+1 ).NE.EVECTR( JJ, K+1 ) ) THEN
|
||
|
|
MATCH = .FALSE.
|
||
|
|
GO TO 220
|
||
|
|
END IF
|
||
|
|
200 CONTINUE
|
||
|
|
K = K + 2
|
||
|
|
END IF
|
||
|
|
210 CONTINUE
|
||
|
|
220 CONTINUE
|
||
|
|
IF( .NOT.MATCH )
|
||
|
|
$ WRITE( NOUNIT, FMT = 9997 )'Left', 'STREVC', N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
*
|
||
|
|
* Call SHSEIN for Right eigenvectors of H, do test 11
|
||
|
|
*
|
||
|
|
NTEST = 11
|
||
|
|
RESULT( 11 ) = ULPINV
|
||
|
|
DO 230 J = 1, N
|
||
|
|
SELECT( J ) = .TRUE.
|
||
|
|
230 CONTINUE
|
||
|
|
*
|
||
|
|
CALL SHSEIN( 'Right', 'Qr', 'Ninitv', SELECT, N, H, LDA,
|
||
|
|
$ WR3, WI3, DUMMA, LDU, EVECTX, LDU, N1, IN,
|
||
|
|
$ WORK, IWORK, IWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'SHSEIN(R)', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 )
|
||
|
|
$ GO TO 250
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Test 11: | HX - XW | / ( |H| |X| ulp )
|
||
|
|
*
|
||
|
|
* (from inverse iteration)
|
||
|
|
*
|
||
|
|
CALL SGET22( 'N', 'N', 'N', N, H, LDA, EVECTX, LDU, WR3,
|
||
|
|
$ WI3, WORK, DUMMA( 1 ) )
|
||
|
|
IF( DUMMA( 1 ).LT.ULPINV )
|
||
|
|
$ RESULT( 11 ) = DUMMA( 1 )*ANINV
|
||
|
|
IF( DUMMA( 2 ).GT.THRESH ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9998 )'Right', 'SHSEIN',
|
||
|
|
$ DUMMA( 2 ), N, JTYPE, IOLDSD
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Call SHSEIN for Left eigenvectors of H, do test 12
|
||
|
|
*
|
||
|
|
NTEST = 12
|
||
|
|
RESULT( 12 ) = ULPINV
|
||
|
|
DO 240 J = 1, N
|
||
|
|
SELECT( J ) = .TRUE.
|
||
|
|
240 CONTINUE
|
||
|
|
*
|
||
|
|
CALL SHSEIN( 'Left', 'Qr', 'Ninitv', SELECT, N, H, LDA, WR3,
|
||
|
|
$ WI3, EVECTY, LDU, DUMMA, LDU, N1, IN, WORK,
|
||
|
|
$ IWORK, IWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'SHSEIN(L)', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 )
|
||
|
|
$ GO TO 250
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Test 12: | YH - WY | / ( |H| |Y| ulp )
|
||
|
|
*
|
||
|
|
* (from inverse iteration)
|
||
|
|
*
|
||
|
|
CALL SGET22( 'C', 'N', 'C', N, H, LDA, EVECTY, LDU, WR3,
|
||
|
|
$ WI3, WORK, DUMMA( 3 ) )
|
||
|
|
IF( DUMMA( 3 ).LT.ULPINV )
|
||
|
|
$ RESULT( 12 ) = DUMMA( 3 )*ANINV
|
||
|
|
IF( DUMMA( 4 ).GT.THRESH ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9998 )'Left', 'SHSEIN',
|
||
|
|
$ DUMMA( 4 ), N, JTYPE, IOLDSD
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Call SORMHR for Right eigenvectors of A, do test 13
|
||
|
|
*
|
||
|
|
NTEST = 13
|
||
|
|
RESULT( 13 ) = ULPINV
|
||
|
|
*
|
||
|
|
CALL SORMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU,
|
||
|
|
$ LDU, TAU, EVECTX, LDU, WORK, NWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'SORMHR(R)', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 )
|
||
|
|
$ GO TO 250
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Test 13: | AX - XW | / ( |A| |X| ulp )
|
||
|
|
*
|
||
|
|
* (from inverse iteration)
|
||
|
|
*
|
||
|
|
CALL SGET22( 'N', 'N', 'N', N, A, LDA, EVECTX, LDU, WR3,
|
||
|
|
$ WI3, WORK, DUMMA( 1 ) )
|
||
|
|
IF( DUMMA( 1 ).LT.ULPINV )
|
||
|
|
$ RESULT( 13 ) = DUMMA( 1 )*ANINV
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Call SORMHR for Left eigenvectors of A, do test 14
|
||
|
|
*
|
||
|
|
NTEST = 14
|
||
|
|
RESULT( 14 ) = ULPINV
|
||
|
|
*
|
||
|
|
CALL SORMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU,
|
||
|
|
$ LDU, TAU, EVECTY, LDU, WORK, NWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'SORMHR(L)', IINFO, N, JTYPE,
|
||
|
|
$ IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
IF( IINFO.LT.0 )
|
||
|
|
$ GO TO 250
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Test 14: | YA - WY | / ( |A| |Y| ulp )
|
||
|
|
*
|
||
|
|
* (from inverse iteration)
|
||
|
|
*
|
||
|
|
CALL SGET22( 'C', 'N', 'C', N, A, LDA, EVECTY, LDU, WR3,
|
||
|
|
$ WI3, WORK, DUMMA( 3 ) )
|
||
|
|
IF( DUMMA( 3 ).LT.ULPINV )
|
||
|
|
$ RESULT( 14 ) = DUMMA( 3 )*ANINV
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compute Left and Right Eigenvectors of A
|
||
|
|
*
|
||
|
|
* Compute a Right eigenvector matrix:
|
||
|
|
*
|
||
|
|
NTEST = 15
|
||
|
|
RESULT( 15 ) = ULPINV
|
||
|
|
*
|
||
|
|
CALL SLACPY( ' ', N, N, UZ, LDU, EVECTR, LDU )
|
||
|
|
*
|
||
|
|
CALL STREVC3( 'Right', 'Back', SELECT, N, T1, LDA, DUMMA,
|
||
|
|
$ LDU, EVECTR, LDU, N, IN, WORK, NWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'STREVC3(R,B)', IINFO, N,
|
||
|
|
$ JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Test 15: | AR - RW | / ( |A| |R| ulp )
|
||
|
|
*
|
||
|
|
* (from Schur decomposition)
|
||
|
|
*
|
||
|
|
CALL SGET22( 'N', 'N', 'N', N, A, LDA, EVECTR, LDU, WR1,
|
||
|
|
$ WI1, WORK, DUMMA( 1 ) )
|
||
|
|
RESULT( 15 ) = DUMMA( 1 )
|
||
|
|
IF( DUMMA( 2 ).GT.THRESH ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9998 )'Right', 'STREVC3',
|
||
|
|
$ DUMMA( 2 ), N, JTYPE, IOLDSD
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compute a Left eigenvector matrix:
|
||
|
|
*
|
||
|
|
NTEST = 16
|
||
|
|
RESULT( 16 ) = ULPINV
|
||
|
|
*
|
||
|
|
CALL SLACPY( ' ', N, N, UZ, LDU, EVECTL, LDU )
|
||
|
|
*
|
||
|
|
CALL STREVC3( 'Left', 'Back', SELECT, N, T1, LDA, EVECTL,
|
||
|
|
$ LDU, DUMMA, LDU, N, IN, WORK, NWORK, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9999 )'STREVC3(L,B)', IINFO, N,
|
||
|
|
$ JTYPE, IOLDSD
|
||
|
|
INFO = ABS( IINFO )
|
||
|
|
GO TO 250
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Test 16: | LA - WL | / ( |A| |L| ulp )
|
||
|
|
*
|
||
|
|
* (from Schur decomposition)
|
||
|
|
*
|
||
|
|
CALL SGET22( 'Trans', 'N', 'Conj', N, A, LDA, EVECTL, LDU,
|
||
|
|
$ WR1, WI1, WORK, DUMMA( 3 ) )
|
||
|
|
RESULT( 16 ) = DUMMA( 3 )
|
||
|
|
IF( DUMMA( 4 ).GT.THRESH ) THEN
|
||
|
|
WRITE( NOUNIT, FMT = 9998 )'Left', 'STREVC3', DUMMA( 4 ),
|
||
|
|
$ N, JTYPE, IOLDSD
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
||
|
|
*
|
||
|
|
250 CONTINUE
|
||
|
|
*
|
||
|
|
NTESTT = NTESTT + NTEST
|
||
|
|
CALL SLAFTS( 'SHS', N, N, JTYPE, NTEST, RESULT, IOLDSD,
|
||
|
|
$ THRESH, NOUNIT, NERRS )
|
||
|
|
*
|
||
|
|
260 CONTINUE
|
||
|
|
270 CONTINUE
|
||
|
|
*
|
||
|
|
* Summary
|
||
|
|
*
|
||
|
|
CALL SLASUM( 'SHS', NOUNIT, NERRS, NTESTT )
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
9999 FORMAT( ' SCHKHS: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
||
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
||
|
|
9998 FORMAT( ' SCHKHS: ', A, ' Eigenvectors from ', A, ' incorrectly ',
|
||
|
|
$ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
|
||
|
|
$ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
|
||
|
|
$ ')' )
|
||
|
|
9997 FORMAT( ' SCHKHS: Selected ', A, ' Eigenvectors from ', A,
|
||
|
|
$ ' do not match other eigenvectors ', 9X, 'N=', I6,
|
||
|
|
$ ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
||
|
|
*
|
||
|
|
* End of SCHKHS
|
||
|
|
*
|
||
|
|
END
|