998 lines
33 KiB
Fortran
998 lines
33 KiB
Fortran
*> \brief \b CCHKBD
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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 CCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
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* ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
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* Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
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* RWORK, NOUT, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
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* $ NSIZES, NTYPES
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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER ISEED( 4 ), MVAL( * ), NVAL( * )
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* REAL BD( * ), BE( * ), RWORK( * ), S1( * ), S2( * )
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* COMPLEX A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
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* $ U( LDPT, * ), VT( LDPT, * ), WORK( * ),
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* $ X( LDX, * ), Y( LDX, * ), Z( LDX, * )
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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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*> CCHKBD checks the singular value decomposition (SVD) routines.
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*>
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*> CGEBRD reduces a complex general m by n matrix A to real upper or
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*> lower bidiagonal form by an orthogonal transformation: Q' * A * P = B
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*> (or A = Q * B * P'). The matrix B is upper bidiagonal if m >= n
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*> and lower bidiagonal if m < n.
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*>
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*> CUNGBR generates the orthogonal matrices Q and P' from CGEBRD.
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*> Note that Q and P are not necessarily square.
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*>
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*> CBDSQR computes the singular value decomposition of the bidiagonal
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*> matrix B as B = U S V'. It is called three times to compute
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*> 1) B = U S1 V', where S1 is the diagonal matrix of singular
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*> values and the columns of the matrices U and V are the left
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*> and right singular vectors, respectively, of B.
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*> 2) Same as 1), but the singular values are stored in S2 and the
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*> singular vectors are not computed.
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*> 3) A = (UQ) S (P'V'), the SVD of the original matrix A.
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*> In addition, CBDSQR has an option to apply the left orthogonal matrix
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*> U to a matrix X, useful in least squares applications.
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*>
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*> For each pair of matrix dimensions (M,N) and each selected matrix
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*> type, an M by N matrix A and an M by NRHS matrix X are generated.
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*> The problem dimensions are as follows
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*> A: M x N
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*> Q: M x min(M,N) (but M x M if NRHS > 0)
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*> P: min(M,N) x N
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*> B: min(M,N) x min(M,N)
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*> U, V: min(M,N) x min(M,N)
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*> S1, S2 diagonal, order min(M,N)
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*> X: M x NRHS
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*>
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*> For each generated matrix, 14 tests are performed:
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*>
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*> Test CGEBRD and CUNGBR
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*>
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*> (1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'
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*>
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*> (2) | I - Q' Q | / ( M ulp )
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*>
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*> (3) | I - PT PT' | / ( N ulp )
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*>
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*> Test CBDSQR on bidiagonal matrix B
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*>
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*> (4) | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'
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*>
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*> (5) | Y - U Z | / ( |Y| max(min(M,N),k) ulp ), where Y = Q' X
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*> and Z = U' Y.
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*> (6) | I - U' U | / ( min(M,N) ulp )
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*>
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*> (7) | I - VT VT' | / ( min(M,N) ulp )
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*>
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*> (8) S1 contains min(M,N) nonnegative values in decreasing order.
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*> (Return 0 if true, 1/ULP if false.)
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*>
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*> (9) 0 if the true singular values of B are within THRESH of
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*> those in S1. 2*THRESH if they are not. (Tested using
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*> SSVDCH)
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*>
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*> (10) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
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*> computing U and V.
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*>
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*> Test CBDSQR on matrix A
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*>
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*> (11) | A - (QU) S (VT PT) | / ( |A| max(M,N) ulp )
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*>
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*> (12) | X - (QU) Z | / ( |X| max(M,k) ulp )
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*>
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*> (13) | I - (QU)'(QU) | / ( M ulp )
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*>
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*> (14) | I - (VT PT) (PT'VT') | / ( N ulp )
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*>
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*> The possible matrix types are
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*>
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*> (1) The zero matrix.
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*> (2) The identity matrix.
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*>
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*> (3) 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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*> (4) A diagonal matrix with geometrically spaced entries
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*> 1, ..., ULP and random signs.
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*> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
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*> and random signs.
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*>
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*> (6) Same as (3), but multiplied by SQRT( overflow threshold )
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*> (7) Same as (3), but multiplied by SQRT( underflow threshold )
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*>
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*> (8) A matrix of the form U D V, where U and V are orthogonal and
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*> D has evenly spaced entries 1, ..., ULP with random signs
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*> on the diagonal.
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*>
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*> (9) A matrix of the form U D V, where U and V are orthogonal and
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*> D has geometrically spaced entries 1, ..., ULP with random
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*> signs on the diagonal.
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*>
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*> (10) A matrix of the form U D V, where U and V are orthogonal and
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*> D has "clustered" entries 1, ULP,..., ULP with random
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*> signs on the diagonal.
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*>
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*> (11) Same as (8), but multiplied by SQRT( overflow threshold )
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*> (12) Same as (8), but multiplied by SQRT( underflow threshold )
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*>
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*> (13) Rectangular matrix with random entries chosen from (-1,1).
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*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
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*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
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*>
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*> Special case:
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*> (16) A bidiagonal matrix with random entries chosen from a
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*> logarithmic distribution on [ulp^2,ulp^(-2)] (I.e., each
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*> entry is e^x, where x is chosen uniformly on
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*> [ 2 log(ulp), -2 log(ulp) ] .) For *this* type:
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*> (a) CGEBRD is not called to reduce it to bidiagonal form.
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*> (b) the bidiagonal is min(M,N) x min(M,N); if M<N, the
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*> matrix will be lower bidiagonal, otherwise upper.
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*> (c) only tests 5--8 and 14 are performed.
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*>
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*> A subset of the full set of matrix types may be selected through
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*> the logical array DOTYPE.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NSIZES
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*> \verbatim
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*> NSIZES is INTEGER
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*> The number of values of M and N contained in the vectors
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*> MVAL and NVAL. The matrix sizes are used in pairs (M,N).
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*> \endverbatim
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*>
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*> \param[in] MVAL
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*> \verbatim
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*> MVAL is INTEGER array, dimension (NM)
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*> The values of the matrix row dimension M.
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*> \endverbatim
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*>
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*> \param[in] NVAL
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*> \verbatim
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*> NVAL is INTEGER array, dimension (NM)
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*> The values of the matrix column dimension N.
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*> \endverbatim
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*>
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*> \param[in] NTYPES
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*> \verbatim
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*> NTYPES is INTEGER
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*> The number of elements in DOTYPE. If it is zero, CCHKBD
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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 matrices are in A and B.
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*> This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
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*> DOTYPE(MAXTYP+1) is .TRUE. .
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*> \endverbatim
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*>
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*> \param[in] DOTYPE
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*> \verbatim
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*> DOTYPE is LOGICAL array, dimension (NTYPES)
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*> If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix
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*> of type j will be generated. If NTYPES is smaller than the
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*> maximum number of types defined (PARAMETER MAXTYP), then
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*> types NTYPES+1 through MAXTYP will not be generated. If
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*> NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through
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*> DOTYPE(NTYPES) will be ignored.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of columns in the "right-hand side" matrices X, Y,
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*> and Z, used in testing CBDSQR. If NRHS = 0, then the
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*> operations on the right-hand side will not be tested.
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*> NRHS must be at least 0.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry ISEED specifies the seed of the random number
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*> generator. The array elements should be between 0 and 4095;
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*> if not they will be reduced mod 4096. Also, ISEED(4) must
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*> be odd. The values of ISEED are changed on exit, and can be
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*> used in the next call to CCHKBD to continue the same random
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*> number sequence.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is REAL
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*> The threshold value for the test ratios. A result is
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*> included in the output file if RESULT >= THRESH. To have
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*> every test ratio printed, use THRESH = 0. Note that the
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*> expected value of the test ratios is O(1), so THRESH should
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*> be a reasonably small multiple of 1, e.g., 10 or 100.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA,NMAX)
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*> where NMAX is the maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,MMAX),
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*> where MMAX is the maximum value of M in MVAL.
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*> \endverbatim
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*>
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*> \param[out] BD
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*> \verbatim
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*> BD is REAL array, dimension
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*> (max(min(MVAL(j),NVAL(j))))
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*> \endverbatim
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*>
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*> \param[out] BE
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*> \verbatim
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*> BE is REAL array, dimension
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*> (max(min(MVAL(j),NVAL(j))))
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*> \endverbatim
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*>
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*> \param[out] S1
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*> \verbatim
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*> S1 is REAL array, dimension
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*> (max(min(MVAL(j),NVAL(j))))
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*> \endverbatim
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*>
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*> \param[out] S2
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*> \verbatim
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*> S2 is REAL array, dimension
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*> (max(min(MVAL(j),NVAL(j))))
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is COMPLEX array, dimension (LDX,NRHS)
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of the arrays X, Y, and Z.
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*> LDX >= max(1,MMAX).
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*> \endverbatim
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*>
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*> \param[out] Y
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*> \verbatim
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*> Y is COMPLEX array, dimension (LDX,NRHS)
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*> \endverbatim
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*>
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*> \param[out] Z
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*> \verbatim
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*> Z is COMPLEX array, dimension (LDX,NRHS)
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*> \endverbatim
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*>
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*> \param[out] Q
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*> \verbatim
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*> Q is COMPLEX array, dimension (LDQ,MMAX)
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*> \endverbatim
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*>
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*> \param[in] LDQ
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*> \verbatim
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*> LDQ is INTEGER
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*> The leading dimension of the array Q. LDQ >= max(1,MMAX).
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*> \endverbatim
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*>
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*> \param[out] PT
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*> \verbatim
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*> PT is COMPLEX array, dimension (LDPT,NMAX)
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*> \endverbatim
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*>
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*> \param[in] LDPT
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*> \verbatim
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*> LDPT is INTEGER
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*> The leading dimension of the arrays PT, U, and V.
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*> LDPT >= max(1, max(min(MVAL(j),NVAL(j)))).
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*> \endverbatim
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*>
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*> \param[out] U
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*> \verbatim
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*> U is COMPLEX array, dimension
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*> (LDPT,max(min(MVAL(j),NVAL(j))))
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*> \endverbatim
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*>
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*> \param[out] VT
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*> \verbatim
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*> VT is COMPLEX array, dimension
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*> (LDPT,max(min(MVAL(j),NVAL(j))))
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The number of entries in WORK. This must be at least
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*> 3(M+N) and M(M + max(M,N,k) + 1) + N*min(M,N) for all
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*> pairs (M,N)=(MM(j),NN(j))
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension
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*> (5*max(min(M,N)))
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*> \endverbatim
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*>
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*> \param[in] NOUT
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*> \verbatim
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*> NOUT is INTEGER
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*> The FORTRAN unit number for printing out error messages
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*> (e.g., if a routine returns IINFO not equal to 0.)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> If 0, then everything ran OK.
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*> -1: NSIZES < 0
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*> -2: Some MM(j) < 0
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*> -3: Some NN(j) < 0
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*> -4: NTYPES < 0
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*> -6: NRHS < 0
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*> -8: THRESH < 0
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*> -11: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
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*> -17: LDB < 1 or LDB < MMAX.
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*> -21: LDQ < 1 or LDQ < MMAX.
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*> -23: LDP < 1 or LDP < MNMAX.
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*> -27: LWORK too small.
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*> If CLATMR, CLATMS, CGEBRD, CUNGBR, or CBDSQR,
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*> returns an error code, the
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*> absolute value of it is returned.
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*>
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*>-----------------------------------------------------------------------
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*>
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*> Some Local Variables and Parameters:
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*> ---- ----- --------- --- ----------
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*>
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*> ZERO, ONE Real 0 and 1.
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*> MAXTYP The number of types defined.
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*> NTEST The number of tests performed, or which can
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*> be performed so far, for the current matrix.
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*> MMAX Largest value in NN.
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*> NMAX Largest value in NN.
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*> MNMIN min(MM(j), NN(j)) (the dimension of the bidiagonal
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*> matrix.)
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*> MNMAX The maximum value of MNMIN for j=1,...,NSIZES.
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*> NFAIL The number of tests which have exceeded THRESH
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*> COND, 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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*> RTOVFL, RTUNFL Square roots of the previous 2 values.
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*> ULP, ULPINV Finest relative precision and its inverse.
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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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*> \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 CCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
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$ ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
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$ Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
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$ RWORK, NOUT, 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, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
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$ NSIZES, NTYPES
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REAL THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER ISEED( 4 ), MVAL( * ), NVAL( * )
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REAL BD( * ), BE( * ), RWORK( * ), S1( * ), S2( * )
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COMPLEX A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
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$ U( LDPT, * ), VT( LDPT, * ), WORK( * ),
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$ X( LDX, * ), Y( LDX, * ), Z( LDX, * )
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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, TWO, HALF
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
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$ HALF = 0.5E0 )
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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 = 16 )
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* ..
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* .. Local Scalars ..
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LOGICAL BADMM, BADNN, BIDIAG
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CHARACTER UPLO
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CHARACTER*3 PATH
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INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JSIZE, JTYPE,
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$ LOG2UI, M, MINWRK, MMAX, MNMAX, MNMIN, MQ,
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$ MTYPES, N, NFAIL, NMAX, NTEST
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REAL AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
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$ TEMP1, TEMP2, ULP, ULPINV, UNFL
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* ..
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* .. Local Arrays ..
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INTEGER IOLDSD( 4 ), IWORK( 1 ), KMAGN( MAXTYP ),
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$ KMODE( MAXTYP ), KTYPE( MAXTYP )
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REAL DUMMA( 1 ), RESULT( 14 )
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLARND
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EXTERNAL SLAMCH, SLARND
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* ..
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* .. External Subroutines ..
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EXTERNAL ALASUM, CBDSQR, CBDT01, CBDT02, CBDT03, CGEBRD,
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$ CGEMM, CLACPY, CLASET, CLATMR, CLATMS, CUNGBR,
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$ CUNT01, SCOPY, SLABAD, SLAHD2, SSVDCH, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, EXP, INT, LOG, MAX, MIN, SQRT
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* ..
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* .. Scalars in Common ..
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LOGICAL LERR, OK
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CHARACTER*32 SRNAMT
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INTEGER INFOT, NUNIT
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* ..
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* .. Common blocks ..
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COMMON / INFOC / INFOT, NUNIT, OK, LERR
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Data statements ..
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DATA KTYPE / 1, 2, 5*4, 5*6, 3*9, 10 /
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DATA KMAGN / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
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DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
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$ 0, 0, 0 /
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* ..
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* .. Executable Statements ..
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*
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* Check for errors
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*
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INFO = 0
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*
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BADMM = .FALSE.
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BADNN = .FALSE.
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MMAX = 1
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NMAX = 1
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MNMAX = 1
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MINWRK = 1
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DO 10 J = 1, NSIZES
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MMAX = MAX( MMAX, MVAL( J ) )
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IF( MVAL( J ).LT.0 )
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$ BADMM = .TRUE.
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NMAX = MAX( NMAX, NVAL( J ) )
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IF( NVAL( J ).LT.0 )
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$ BADNN = .TRUE.
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MNMAX = MAX( MNMAX, MIN( MVAL( J ), NVAL( J ) ) )
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MINWRK = MAX( MINWRK, 3*( MVAL( J )+NVAL( J ) ),
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$ MVAL( J )*( MVAL( J )+MAX( MVAL( J ), NVAL( J ),
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$ NRHS )+1 )+NVAL( J )*MIN( NVAL( J ), MVAL( J ) ) )
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10 CONTINUE
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*
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* Check for errors
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*
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IF( NSIZES.LT.0 ) THEN
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INFO = -1
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ELSE IF( BADMM ) THEN
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INFO = -2
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ELSE IF( BADNN ) THEN
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INFO = -3
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ELSE IF( NTYPES.LT.0 ) THEN
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INFO = -4
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -6
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ELSE IF( LDA.LT.MMAX ) THEN
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INFO = -11
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ELSE IF( LDX.LT.MMAX ) THEN
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INFO = -17
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ELSE IF( LDQ.LT.MMAX ) THEN
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INFO = -21
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ELSE IF( LDPT.LT.MNMAX ) THEN
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INFO = -23
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ELSE IF( MINWRK.GT.LWORK ) THEN
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INFO = -27
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CCHKBD', -INFO )
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RETURN
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END IF
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*
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* Initialize constants
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*
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PATH( 1: 1 ) = 'Complex precision'
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PATH( 2: 3 ) = 'BD'
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NFAIL = 0
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NTEST = 0
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UNFL = SLAMCH( 'Safe minimum' )
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OVFL = SLAMCH( 'Overflow' )
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CALL SLABAD( UNFL, OVFL )
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ULP = SLAMCH( 'Precision' )
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ULPINV = ONE / ULP
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LOG2UI = INT( LOG( ULPINV ) / LOG( TWO ) )
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RTUNFL = SQRT( UNFL )
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RTOVFL = SQRT( OVFL )
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INFOT = 0
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*
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* Loop over sizes, types
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*
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DO 180 JSIZE = 1, NSIZES
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M = MVAL( JSIZE )
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N = NVAL( JSIZE )
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MNMIN = MIN( M, N )
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AMNINV = ONE / MAX( M, N, 1 )
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*
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IF( NSIZES.NE.1 ) THEN
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MTYPES = MIN( MAXTYP, NTYPES )
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ELSE
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MTYPES = MIN( MAXTYP+1, NTYPES )
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END IF
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*
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DO 170 JTYPE = 1, MTYPES
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IF( .NOT.DOTYPE( JTYPE ) )
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$ GO TO 170
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*
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DO 20 J = 1, 4
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IOLDSD( J ) = ISEED( J )
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20 CONTINUE
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*
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DO 30 J = 1, 14
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RESULT( J ) = -ONE
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30 CONTINUE
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*
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UPLO = ' '
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*
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* Compute "A"
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*
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* Control parameters:
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*
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* KMAGN KMODE KTYPE
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* =1 O(1) clustered 1 zero
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* =2 large clustered 2 identity
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* =3 small exponential (none)
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* =4 arithmetic diagonal, (w/ eigenvalues)
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* =5 random symmetric, w/ eigenvalues
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* =6 nonsymmetric, w/ singular values
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* =7 random diagonal
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* =8 random symmetric
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* =9 random nonsymmetric
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* =10 random bidiagonal (log. distrib.)
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*
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IF( MTYPES.GT.MAXTYP )
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$ GO TO 100
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*
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ITYPE = KTYPE( JTYPE )
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IMODE = KMODE( JTYPE )
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*
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* Compute norm
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*
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GO TO ( 40, 50, 60 )KMAGN( JTYPE )
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*
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40 CONTINUE
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ANORM = ONE
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GO TO 70
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*
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50 CONTINUE
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ANORM = ( RTOVFL*ULP )*AMNINV
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GO TO 70
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*
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60 CONTINUE
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ANORM = RTUNFL*MAX( M, N )*ULPINV
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GO TO 70
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*
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70 CONTINUE
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*
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CALL CLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
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IINFO = 0
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COND = ULPINV
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*
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BIDIAG = .FALSE.
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IF( ITYPE.EQ.1 ) THEN
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*
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* Zero matrix
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*
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IINFO = 0
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*
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ELSE IF( ITYPE.EQ.2 ) THEN
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*
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* Identity
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*
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DO 80 JCOL = 1, MNMIN
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A( JCOL, JCOL ) = ANORM
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80 CONTINUE
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*
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ELSE IF( ITYPE.EQ.4 ) THEN
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*
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* Diagonal Matrix, [Eigen]values Specified
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*
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CALL CLATMS( MNMIN, MNMIN, 'S', ISEED, 'N', RWORK, IMODE,
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$ COND, ANORM, 0, 0, 'N', A, LDA, WORK,
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$ IINFO )
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*
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ELSE IF( ITYPE.EQ.5 ) THEN
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*
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* Symmetric, eigenvalues specified
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*
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CALL CLATMS( MNMIN, MNMIN, 'S', ISEED, 'S', RWORK, IMODE,
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$ COND, ANORM, M, N, 'N', A, LDA, WORK,
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$ IINFO )
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*
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ELSE IF( ITYPE.EQ.6 ) THEN
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*
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* Nonsymmetric, singular values specified
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*
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CALL CLATMS( M, N, 'S', ISEED, 'N', RWORK, IMODE, COND,
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$ ANORM, M, N, 'N', A, LDA, WORK, IINFO )
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*
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ELSE IF( ITYPE.EQ.7 ) THEN
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*
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* Diagonal, random entries
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*
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CALL CLATMR( MNMIN, MNMIN, 'S', ISEED, 'N', WORK, 6, ONE,
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$ CONE, 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
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$ WORK( 2*MNMIN+1 ), 1, ONE, 'N', IWORK, 0, 0,
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$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
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*
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|
ELSE IF( ITYPE.EQ.8 ) THEN
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*
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* Symmetric, random entries
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*
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CALL CLATMR( MNMIN, MNMIN, 'S', ISEED, 'S', WORK, 6, ONE,
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$ CONE, 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
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$ WORK( M+MNMIN+1 ), 1, ONE, 'N', IWORK, M, N,
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$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
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*
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ELSE IF( ITYPE.EQ.9 ) THEN
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*
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* Nonsymmetric, random entries
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*
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CALL CLATMR( M, N, 'S', ISEED, 'N', WORK, 6, ONE, CONE,
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$ 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
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$ WORK( M+MNMIN+1 ), 1, ONE, 'N', IWORK, M, N,
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$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
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*
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|
ELSE IF( ITYPE.EQ.10 ) THEN
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*
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* Bidiagonal, random entries
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*
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|
TEMP1 = -TWO*LOG( ULP )
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DO 90 J = 1, MNMIN
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BD( J ) = EXP( TEMP1*SLARND( 2, ISEED ) )
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|
IF( J.LT.MNMIN )
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|
$ BE( J ) = EXP( TEMP1*SLARND( 2, ISEED ) )
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90 CONTINUE
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*
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|
IINFO = 0
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|
BIDIAG = .TRUE.
|
|
IF( M.GE.N ) THEN
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UPLO = 'U'
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ELSE
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UPLO = 'L'
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END IF
|
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ELSE
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|
IINFO = 1
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END IF
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*
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|
IF( IINFO.EQ.0 ) THEN
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*
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|
* Generate Right-Hand Side
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*
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|
IF( BIDIAG ) THEN
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|
CALL CLATMR( MNMIN, NRHS, 'S', ISEED, 'N', WORK, 6,
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$ ONE, CONE, 'T', 'N', WORK( MNMIN+1 ), 1,
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$ ONE, WORK( 2*MNMIN+1 ), 1, ONE, 'N',
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$ IWORK, MNMIN, NRHS, ZERO, ONE, 'NO', Y,
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$ LDX, IWORK, IINFO )
|
|
ELSE
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|
CALL CLATMR( M, NRHS, 'S', ISEED, 'N', WORK, 6, ONE,
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$ CONE, 'T', 'N', WORK( M+1 ), 1, ONE,
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$ WORK( 2*M+1 ), 1, ONE, 'N', IWORK, M,
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|
$ NRHS, ZERO, ONE, 'NO', X, LDX, IWORK,
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$ IINFO )
|
|
END IF
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END IF
|
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*
|
|
* Error Exit
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
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|
WRITE( NOUT, FMT = 9998 )'Generator', IINFO, M, N,
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$ JTYPE, IOLDSD
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|
INFO = ABS( IINFO )
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RETURN
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END IF
|
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*
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|
100 CONTINUE
|
|
*
|
|
* Call CGEBRD and CUNGBR to compute B, Q, and P, do tests.
|
|
*
|
|
IF( .NOT.BIDIAG ) THEN
|
|
*
|
|
* Compute transformations to reduce A to bidiagonal form:
|
|
* B := Q' * A * P.
|
|
*
|
|
CALL CLACPY( ' ', M, N, A, LDA, Q, LDQ )
|
|
CALL CGEBRD( M, N, Q, LDQ, BD, BE, WORK, WORK( MNMIN+1 ),
|
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$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
|
|
*
|
|
* Check error code from CGEBRD.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'CGEBRD', IINFO, M, N,
|
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$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
CALL CLACPY( ' ', M, N, Q, LDQ, PT, LDPT )
|
|
IF( M.GE.N ) THEN
|
|
UPLO = 'U'
|
|
ELSE
|
|
UPLO = 'L'
|
|
END IF
|
|
*
|
|
* Generate Q
|
|
*
|
|
MQ = M
|
|
IF( NRHS.LE.0 )
|
|
$ MQ = MNMIN
|
|
CALL CUNGBR( 'Q', M, MQ, N, Q, LDQ, WORK,
|
|
$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
|
|
*
|
|
* Check error code from CUNGBR.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'CUNGBR(Q)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Generate P'
|
|
*
|
|
CALL CUNGBR( 'P', MNMIN, N, M, PT, LDPT, WORK( MNMIN+1 ),
|
|
$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
|
|
*
|
|
* Check error code from CUNGBR.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'CUNGBR(P)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Apply Q' to an M by NRHS matrix X: Y := Q' * X.
|
|
*
|
|
CALL CGEMM( 'Conjugate transpose', 'No transpose', M,
|
|
$ NRHS, M, CONE, Q, LDQ, X, LDX, CZERO, Y,
|
|
$ LDX )
|
|
*
|
|
* Test 1: Check the decomposition A := Q * B * PT
|
|
* 2: Check the orthogonality of Q
|
|
* 3: Check the orthogonality of PT
|
|
*
|
|
CALL CBDT01( M, N, 1, A, LDA, Q, LDQ, BD, BE, PT, LDPT,
|
|
$ WORK, RWORK, RESULT( 1 ) )
|
|
CALL CUNT01( 'Columns', M, MQ, Q, LDQ, WORK, LWORK,
|
|
$ RWORK, RESULT( 2 ) )
|
|
CALL CUNT01( 'Rows', MNMIN, N, PT, LDPT, WORK, LWORK,
|
|
$ RWORK, RESULT( 3 ) )
|
|
END IF
|
|
*
|
|
* Use CBDSQR to form the SVD of the bidiagonal matrix B:
|
|
* B := U * S1 * VT, and compute Z = U' * Y.
|
|
*
|
|
CALL SCOPY( MNMIN, BD, 1, S1, 1 )
|
|
IF( MNMIN.GT.0 )
|
|
$ CALL SCOPY( MNMIN-1, BE, 1, RWORK, 1 )
|
|
CALL CLACPY( ' ', M, NRHS, Y, LDX, Z, LDX )
|
|
CALL CLASET( 'Full', MNMIN, MNMIN, CZERO, CONE, U, LDPT )
|
|
CALL CLASET( 'Full', MNMIN, MNMIN, CZERO, CONE, VT, LDPT )
|
|
*
|
|
CALL CBDSQR( UPLO, MNMIN, MNMIN, MNMIN, NRHS, S1, RWORK, VT,
|
|
$ LDPT, U, LDPT, Z, LDX, RWORK( MNMIN+1 ),
|
|
$ IINFO )
|
|
*
|
|
* Check error code from CBDSQR.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'CBDSQR(vects)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 4 ) = ULPINV
|
|
GO TO 150
|
|
END IF
|
|
END IF
|
|
*
|
|
* Use CBDSQR to compute only the singular values of the
|
|
* bidiagonal matrix B; U, VT, and Z should not be modified.
|
|
*
|
|
CALL SCOPY( MNMIN, BD, 1, S2, 1 )
|
|
IF( MNMIN.GT.0 )
|
|
$ CALL SCOPY( MNMIN-1, BE, 1, RWORK, 1 )
|
|
*
|
|
CALL CBDSQR( UPLO, MNMIN, 0, 0, 0, S2, RWORK, VT, LDPT, U,
|
|
$ LDPT, Z, LDX, RWORK( MNMIN+1 ), IINFO )
|
|
*
|
|
* Check error code from CBDSQR.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'CBDSQR(values)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 9 ) = ULPINV
|
|
GO TO 150
|
|
END IF
|
|
END IF
|
|
*
|
|
* Test 4: Check the decomposition B := U * S1 * VT
|
|
* 5: Check the computation Z := U' * Y
|
|
* 6: Check the orthogonality of U
|
|
* 7: Check the orthogonality of VT
|
|
*
|
|
CALL CBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT,
|
|
$ WORK, RESULT( 4 ) )
|
|
CALL CBDT02( MNMIN, NRHS, Y, LDX, Z, LDX, U, LDPT, WORK,
|
|
$ RWORK, RESULT( 5 ) )
|
|
CALL CUNT01( 'Columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK,
|
|
$ RWORK, RESULT( 6 ) )
|
|
CALL CUNT01( 'Rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK,
|
|
$ RWORK, RESULT( 7 ) )
|
|
*
|
|
* Test 8: Check that the singular values are sorted in
|
|
* non-increasing order and are non-negative
|
|
*
|
|
RESULT( 8 ) = ZERO
|
|
DO 110 I = 1, MNMIN - 1
|
|
IF( S1( I ).LT.S1( I+1 ) )
|
|
$ RESULT( 8 ) = ULPINV
|
|
IF( S1( I ).LT.ZERO )
|
|
$ RESULT( 8 ) = ULPINV
|
|
110 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( S1( MNMIN ).LT.ZERO )
|
|
$ RESULT( 8 ) = ULPINV
|
|
END IF
|
|
*
|
|
* Test 9: Compare CBDSQR with and without singular vectors
|
|
*
|
|
TEMP2 = ZERO
|
|
*
|
|
DO 120 J = 1, MNMIN
|
|
TEMP1 = ABS( S1( J )-S2( J ) ) /
|
|
$ MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
|
|
$ ULP*MAX( ABS( S1( J ) ), ABS( S2( J ) ) ) )
|
|
TEMP2 = MAX( TEMP1, TEMP2 )
|
|
120 CONTINUE
|
|
*
|
|
RESULT( 9 ) = TEMP2
|
|
*
|
|
* Test 10: Sturm sequence test of singular values
|
|
* Go up by factors of two until it succeeds
|
|
*
|
|
TEMP1 = THRESH*( HALF-ULP )
|
|
*
|
|
DO 130 J = 0, LOG2UI
|
|
CALL SSVDCH( MNMIN, BD, BE, S1, TEMP1, IINFO )
|
|
IF( IINFO.EQ.0 )
|
|
$ GO TO 140
|
|
TEMP1 = TEMP1*TWO
|
|
130 CONTINUE
|
|
*
|
|
140 CONTINUE
|
|
RESULT( 10 ) = TEMP1
|
|
*
|
|
* Use CBDSQR to form the decomposition A := (QU) S (VT PT)
|
|
* from the bidiagonal form A := Q B PT.
|
|
*
|
|
IF( .NOT.BIDIAG ) THEN
|
|
CALL SCOPY( MNMIN, BD, 1, S2, 1 )
|
|
IF( MNMIN.GT.0 )
|
|
$ CALL SCOPY( MNMIN-1, BE, 1, RWORK, 1 )
|
|
*
|
|
CALL CBDSQR( UPLO, MNMIN, N, M, NRHS, S2, RWORK, PT,
|
|
$ LDPT, Q, LDQ, Y, LDX, RWORK( MNMIN+1 ),
|
|
$ IINFO )
|
|
*
|
|
* Test 11: Check the decomposition A := Q*U * S2 * VT*PT
|
|
* 12: Check the computation Z := U' * Q' * X
|
|
* 13: Check the orthogonality of Q*U
|
|
* 14: Check the orthogonality of VT*PT
|
|
*
|
|
CALL CBDT01( M, N, 0, A, LDA, Q, LDQ, S2, DUMMA, PT,
|
|
$ LDPT, WORK, RWORK, RESULT( 11 ) )
|
|
CALL CBDT02( M, NRHS, X, LDX, Y, LDX, Q, LDQ, WORK,
|
|
$ RWORK, RESULT( 12 ) )
|
|
CALL CUNT01( 'Columns', M, MQ, Q, LDQ, WORK, LWORK,
|
|
$ RWORK, RESULT( 13 ) )
|
|
CALL CUNT01( 'Rows', MNMIN, N, PT, LDPT, WORK, LWORK,
|
|
$ RWORK, RESULT( 14 ) )
|
|
END IF
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
150 CONTINUE
|
|
DO 160 J = 1, 14
|
|
IF( RESULT( J ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 )
|
|
$ CALL SLAHD2( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9999 )M, N, JTYPE, IOLDSD, J,
|
|
$ RESULT( J )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
160 CONTINUE
|
|
IF( .NOT.BIDIAG ) THEN
|
|
NTEST = NTEST + 14
|
|
ELSE
|
|
NTEST = NTEST + 5
|
|
END IF
|
|
*
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NTEST, 0 )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CCHKBD
|
|
*
|
|
9999 FORMAT( ' M=', I5, ', N=', I5, ', type ', I2, ', seed=',
|
|
$ 4( I4, ',' ), ' test(', I2, ')=', G11.4 )
|
|
9998 FORMAT( ' CCHKBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
|
|
$ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
|
|
$ I5, ')' )
|
|
*
|
|
END
|