1103 lines
36 KiB
Fortran
1103 lines
36 KiB
Fortran
*> \brief \b SCHKBD
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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 SCHKBD( 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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* IWORK, 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 ), IWORK( * ), MVAL( * ), NVAL( * )
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* REAL A( LDA, * ), BD( * ), BE( * ), PT( LDPT, * ),
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* $ Q( LDQ, * ), S1( * ), S2( * ), U( LDPT, * ),
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* $ VT( LDPT, * ), WORK( * ), X( LDX, * ),
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* $ 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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*> SCHKBD checks the singular value decomposition (SVD) routines.
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*>
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*> SGEBRD reduces a real general m by n matrix A to upper or lower
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*> bidiagonal form B 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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*> SORGBR generates the orthogonal matrices Q and P' from SGEBRD.
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*> Note that Q and P are not necessarily square.
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*>
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*> SBDSQR 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, SBDSQR 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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*> SBDSDC computes the singular value decomposition of the bidiagonal
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*> matrix B as B = U S V' using divide-and-conquer. It is called twice
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*> 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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*>
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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 SGEBRD and SORGBR
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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 SBDSQR 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) | 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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*> (10) 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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*> Test SBDSQR 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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*> Test SBDSDC on bidiagonal matrix B
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*>
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*> (15) | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'
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*>
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*> (16) | I - U' U | / ( min(M,N) ulp )
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*>
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*> (17) | I - VT VT' | / ( min(M,N) ulp )
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*>
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*> (18) 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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*> (19) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
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*> computing U and V.
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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) SGEBRD 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, SCHKBD
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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 SBDSQR. 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 SCHKBD 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension at least 8*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: LDPT< 1 or LDPT< MNMAX.
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*> -27: LWORK too small.
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*> If SLATMR, SLATMS, SGEBRD, SORGBR, or SBDSQR,
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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 single_eig
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*
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* =====================================================================
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SUBROUTINE SCHKBD( 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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$ IWORK, 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 ), IWORK( * ), MVAL( * ), NVAL( * )
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REAL A( LDA, * ), BD( * ), BE( * ), PT( LDPT, * ),
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$ Q( LDQ, * ), S1( * ), S2( * ), U( LDPT, * ),
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$ VT( LDPT, * ), WORK( * ), X( LDX, * ),
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$ 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,
|
|
$ HALF = 0.5E0 )
|
|
INTEGER MAXTYP
|
|
PARAMETER ( MAXTYP = 16 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL BADMM, BADNN, BIDIAG
|
|
CHARACTER UPLO
|
|
CHARACTER*3 PATH
|
|
INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JSIZE, JTYPE,
|
|
$ LOG2UI, M, MINWRK, MMAX, MNMAX, MNMIN, MQ,
|
|
$ MTYPES, N, NFAIL, NMAX, NTEST
|
|
REAL AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
|
|
$ TEMP1, TEMP2, ULP, ULPINV, UNFL
|
|
* ..
|
|
* .. Local Arrays ..
|
|
INTEGER IDUM( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
|
|
$ KMODE( MAXTYP ), KTYPE( MAXTYP )
|
|
REAL DUM( 1 ), DUMMA( 1 ), RESULT( 19 )
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH, SLARND
|
|
EXTERNAL SLAMCH, SLARND
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL ALASUM, SBDSDC, SBDSQR, SBDT01, SBDT02, SBDT03,
|
|
$ SCOPY, SGEBRD, SGEMM, SLABAD, SLACPY, SLAHD2,
|
|
$ SLASET, SLATMR, SLATMS, SORGBR, SORT01, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, EXP, INT, LOG, MAX, MIN, SQRT
|
|
* ..
|
|
* .. Scalars in Common ..
|
|
LOGICAL LERR, OK
|
|
CHARACTER*32 SRNAMT
|
|
INTEGER INFOT, NUNIT
|
|
* ..
|
|
* .. Common blocks ..
|
|
COMMON / INFOC / INFOT, NUNIT, OK, LERR
|
|
COMMON / SRNAMC / SRNAMT
|
|
* ..
|
|
* .. Data statements ..
|
|
DATA KTYPE / 1, 2, 5*4, 5*6, 3*9, 10 /
|
|
DATA KMAGN / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
|
|
DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
|
|
$ 0, 0, 0 /
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Check for errors
|
|
*
|
|
INFO = 0
|
|
*
|
|
BADMM = .FALSE.
|
|
BADNN = .FALSE.
|
|
MMAX = 1
|
|
NMAX = 1
|
|
MNMAX = 1
|
|
MINWRK = 1
|
|
DO 10 J = 1, NSIZES
|
|
MMAX = MAX( MMAX, MVAL( J ) )
|
|
IF( MVAL( J ).LT.0 )
|
|
$ BADMM = .TRUE.
|
|
NMAX = MAX( NMAX, NVAL( J ) )
|
|
IF( NVAL( J ).LT.0 )
|
|
$ BADNN = .TRUE.
|
|
MNMAX = MAX( MNMAX, MIN( MVAL( J ), NVAL( J ) ) )
|
|
MINWRK = MAX( MINWRK, 3*( MVAL( J )+NVAL( J ) ),
|
|
$ MVAL( J )*( MVAL( J )+MAX( MVAL( J ), NVAL( J ),
|
|
$ NRHS )+1 )+NVAL( J )*MIN( NVAL( J ), MVAL( J ) ) )
|
|
10 CONTINUE
|
|
*
|
|
* Check for errors
|
|
*
|
|
IF( NSIZES.LT.0 ) THEN
|
|
INFO = -1
|
|
ELSE IF( BADMM ) THEN
|
|
INFO = -2
|
|
ELSE IF( BADNN ) THEN
|
|
INFO = -3
|
|
ELSE IF( NTYPES.LT.0 ) THEN
|
|
INFO = -4
|
|
ELSE IF( NRHS.LT.0 ) THEN
|
|
INFO = -6
|
|
ELSE IF( LDA.LT.MMAX ) THEN
|
|
INFO = -11
|
|
ELSE IF( LDX.LT.MMAX ) THEN
|
|
INFO = -17
|
|
ELSE IF( LDQ.LT.MMAX ) THEN
|
|
INFO = -21
|
|
ELSE IF( LDPT.LT.MNMAX ) THEN
|
|
INFO = -23
|
|
ELSE IF( MINWRK.GT.LWORK ) THEN
|
|
INFO = -27
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'SCHKBD', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Initialize constants
|
|
*
|
|
PATH( 1: 1 ) = 'Single precision'
|
|
PATH( 2: 3 ) = 'BD'
|
|
NFAIL = 0
|
|
NTEST = 0
|
|
UNFL = SLAMCH( 'Safe minimum' )
|
|
OVFL = SLAMCH( 'Overflow' )
|
|
CALL SLABAD( UNFL, OVFL )
|
|
ULP = SLAMCH( 'Precision' )
|
|
ULPINV = ONE / ULP
|
|
LOG2UI = INT( LOG( ULPINV ) / LOG( TWO ) )
|
|
RTUNFL = SQRT( UNFL )
|
|
RTOVFL = SQRT( OVFL )
|
|
INFOT = 0
|
|
*
|
|
* Loop over sizes, types
|
|
*
|
|
DO 200 JSIZE = 1, NSIZES
|
|
M = MVAL( JSIZE )
|
|
N = NVAL( JSIZE )
|
|
MNMIN = MIN( M, N )
|
|
AMNINV = ONE / MAX( M, N, 1 )
|
|
*
|
|
IF( NSIZES.NE.1 ) THEN
|
|
MTYPES = MIN( MAXTYP, NTYPES )
|
|
ELSE
|
|
MTYPES = MIN( MAXTYP+1, NTYPES )
|
|
END IF
|
|
*
|
|
DO 190 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 190
|
|
*
|
|
DO 20 J = 1, 4
|
|
IOLDSD( J ) = ISEED( J )
|
|
20 CONTINUE
|
|
*
|
|
DO 30 J = 1, 14
|
|
RESULT( J ) = -ONE
|
|
30 CONTINUE
|
|
*
|
|
UPLO = ' '
|
|
*
|
|
* Compute "A"
|
|
*
|
|
* Control parameters:
|
|
*
|
|
* KMAGN KMODE KTYPE
|
|
* =1 O(1) clustered 1 zero
|
|
* =2 large clustered 2 identity
|
|
* =3 small exponential (none)
|
|
* =4 arithmetic diagonal, (w/ eigenvalues)
|
|
* =5 random symmetric, w/ eigenvalues
|
|
* =6 nonsymmetric, w/ singular values
|
|
* =7 random diagonal
|
|
* =8 random symmetric
|
|
* =9 random nonsymmetric
|
|
* =10 random bidiagonal (log. distrib.)
|
|
*
|
|
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 )*AMNINV
|
|
GO TO 70
|
|
*
|
|
60 CONTINUE
|
|
ANORM = RTUNFL*MAX( M, N )*ULPINV
|
|
GO TO 70
|
|
*
|
|
70 CONTINUE
|
|
*
|
|
CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
|
|
IINFO = 0
|
|
COND = ULPINV
|
|
*
|
|
BIDIAG = .FALSE.
|
|
IF( ITYPE.EQ.1 ) THEN
|
|
*
|
|
* Zero matrix
|
|
*
|
|
IINFO = 0
|
|
*
|
|
ELSE IF( ITYPE.EQ.2 ) THEN
|
|
*
|
|
* Identity
|
|
*
|
|
DO 80 JCOL = 1, MNMIN
|
|
A( JCOL, JCOL ) = ANORM
|
|
80 CONTINUE
|
|
*
|
|
ELSE IF( ITYPE.EQ.4 ) THEN
|
|
*
|
|
* Diagonal Matrix, [Eigen]values Specified
|
|
*
|
|
CALL SLATMS( MNMIN, MNMIN, 'S', ISEED, 'N', WORK, IMODE,
|
|
$ COND, ANORM, 0, 0, 'N', A, LDA,
|
|
$ WORK( MNMIN+1 ), IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.5 ) THEN
|
|
*
|
|
* Symmetric, eigenvalues specified
|
|
*
|
|
CALL SLATMS( MNMIN, MNMIN, 'S', ISEED, 'S', WORK, IMODE,
|
|
$ COND, ANORM, M, N, 'N', A, LDA,
|
|
$ WORK( MNMIN+1 ), IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.6 ) THEN
|
|
*
|
|
* Nonsymmetric, singular values specified
|
|
*
|
|
CALL SLATMS( M, N, 'S', ISEED, 'N', WORK, IMODE, COND,
|
|
$ ANORM, M, N, 'N', A, LDA, WORK( MNMIN+1 ),
|
|
$ IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.7 ) THEN
|
|
*
|
|
* Diagonal, random entries
|
|
*
|
|
CALL SLATMR( MNMIN, MNMIN, 'S', ISEED, 'N', WORK, 6, ONE,
|
|
$ ONE, 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
|
|
$ WORK( 2*MNMIN+1 ), 1, ONE, 'N', IWORK, 0, 0,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.8 ) THEN
|
|
*
|
|
* Symmetric, random entries
|
|
*
|
|
CALL SLATMR( MNMIN, MNMIN, 'S', ISEED, 'S', WORK, 6, ONE,
|
|
$ ONE, 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
|
|
$ WORK( M+MNMIN+1 ), 1, ONE, 'N', IWORK, M, N,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.9 ) THEN
|
|
*
|
|
* Nonsymmetric, random entries
|
|
*
|
|
CALL SLATMR( M, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
|
|
$ 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
|
|
$ WORK( M+MNMIN+1 ), 1, ONE, 'N', IWORK, M, N,
|
|
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
|
|
*
|
|
ELSE IF( ITYPE.EQ.10 ) THEN
|
|
*
|
|
* Bidiagonal, random entries
|
|
*
|
|
TEMP1 = -TWO*LOG( ULP )
|
|
DO 90 J = 1, MNMIN
|
|
BD( J ) = EXP( TEMP1*SLARND( 2, ISEED ) )
|
|
IF( J.LT.MNMIN )
|
|
$ BE( J ) = EXP( TEMP1*SLARND( 2, ISEED ) )
|
|
90 CONTINUE
|
|
*
|
|
IINFO = 0
|
|
BIDIAG = .TRUE.
|
|
IF( M.GE.N ) THEN
|
|
UPLO = 'U'
|
|
ELSE
|
|
UPLO = 'L'
|
|
END IF
|
|
ELSE
|
|
IINFO = 1
|
|
END IF
|
|
*
|
|
IF( IINFO.EQ.0 ) THEN
|
|
*
|
|
* Generate Right-Hand Side
|
|
*
|
|
IF( BIDIAG ) THEN
|
|
CALL SLATMR( MNMIN, NRHS, 'S', ISEED, 'N', WORK, 6,
|
|
$ ONE, ONE, 'T', 'N', WORK( MNMIN+1 ), 1,
|
|
$ ONE, WORK( 2*MNMIN+1 ), 1, ONE, 'N',
|
|
$ IWORK, MNMIN, NRHS, ZERO, ONE, 'NO', Y,
|
|
$ LDX, IWORK, IINFO )
|
|
ELSE
|
|
CALL SLATMR( M, NRHS, 'S', ISEED, 'N', WORK, 6, ONE,
|
|
$ ONE, 'T', 'N', WORK( M+1 ), 1, ONE,
|
|
$ WORK( 2*M+1 ), 1, ONE, 'N', IWORK, M,
|
|
$ NRHS, ZERO, ONE, 'NO', X, LDX, IWORK,
|
|
$ IINFO )
|
|
END IF
|
|
END IF
|
|
*
|
|
* Error Exit
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'Generator', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
100 CONTINUE
|
|
*
|
|
* Call SGEBRD and SORGBR 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 SLACPY( ' ', M, N, A, LDA, Q, LDQ )
|
|
CALL SGEBRD( M, N, Q, LDQ, BD, BE, WORK, WORK( MNMIN+1 ),
|
|
$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
|
|
*
|
|
* Check error code from SGEBRD.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'SGEBRD', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
CALL SLACPY( ' ', 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 SORGBR( 'Q', M, MQ, N, Q, LDQ, WORK,
|
|
$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
|
|
*
|
|
* Check error code from SORGBR.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'SORGBR(Q)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Generate P'
|
|
*
|
|
CALL SORGBR( 'P', MNMIN, N, M, PT, LDPT, WORK( MNMIN+1 ),
|
|
$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
|
|
*
|
|
* Check error code from SORGBR.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'SORGBR(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 SGEMM( 'Transpose', 'No transpose', M, NRHS, M, ONE,
|
|
$ Q, LDQ, X, LDX, ZERO, Y, LDX )
|
|
*
|
|
* Test 1: Check the decomposition A := Q * B * PT
|
|
* 2: Check the orthogonality of Q
|
|
* 3: Check the orthogonality of PT
|
|
*
|
|
CALL SBDT01( M, N, 1, A, LDA, Q, LDQ, BD, BE, PT, LDPT,
|
|
$ WORK, RESULT( 1 ) )
|
|
CALL SORT01( 'Columns', M, MQ, Q, LDQ, WORK, LWORK,
|
|
$ RESULT( 2 ) )
|
|
CALL SORT01( 'Rows', MNMIN, N, PT, LDPT, WORK, LWORK,
|
|
$ RESULT( 3 ) )
|
|
END IF
|
|
*
|
|
* Use SBDSQR 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, WORK, 1 )
|
|
CALL SLACPY( ' ', M, NRHS, Y, LDX, Z, LDX )
|
|
CALL SLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, U, LDPT )
|
|
CALL SLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, VT, LDPT )
|
|
*
|
|
CALL SBDSQR( UPLO, MNMIN, MNMIN, MNMIN, NRHS, S1, WORK, VT,
|
|
$ LDPT, U, LDPT, Z, LDX, WORK( MNMIN+1 ), IINFO )
|
|
*
|
|
* Check error code from SBDSQR.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'SBDSQR(vects)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 4 ) = ULPINV
|
|
GO TO 170
|
|
END IF
|
|
END IF
|
|
*
|
|
* Use SBDSQR 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, WORK, 1 )
|
|
*
|
|
CALL SBDSQR( UPLO, MNMIN, 0, 0, 0, S2, WORK, VT, LDPT, U,
|
|
$ LDPT, Z, LDX, WORK( MNMIN+1 ), IINFO )
|
|
*
|
|
* Check error code from SBDSQR.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'SBDSQR(values)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 9 ) = ULPINV
|
|
GO TO 170
|
|
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 SBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT,
|
|
$ WORK, RESULT( 4 ) )
|
|
CALL SBDT02( MNMIN, NRHS, Y, LDX, Z, LDX, U, LDPT, WORK,
|
|
$ RESULT( 5 ) )
|
|
CALL SORT01( 'Columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK,
|
|
$ RESULT( 6 ) )
|
|
CALL SORT01( 'Rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK,
|
|
$ 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 SBDSQR 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 )
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IF( IINFO.EQ.0 )
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$ GO TO 140
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TEMP1 = TEMP1*TWO
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|
130 CONTINUE
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*
|
|
140 CONTINUE
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RESULT( 10 ) = TEMP1
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*
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* Use SBDSQR to form the decomposition A := (QU) S (VT PT)
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|
* from the bidiagonal form A := Q B PT.
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|
*
|
|
IF( .NOT.BIDIAG ) THEN
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|
CALL SCOPY( MNMIN, BD, 1, S2, 1 )
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|
IF( MNMIN.GT.0 )
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$ CALL SCOPY( MNMIN-1, BE, 1, WORK, 1 )
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*
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|
CALL SBDSQR( UPLO, MNMIN, N, M, NRHS, S2, WORK, PT, LDPT,
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$ Q, LDQ, Y, LDX, WORK( MNMIN+1 ), IINFO )
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|
*
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* Test 11: Check the decomposition A := Q*U * S2 * VT*PT
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|
* 12: Check the computation Z := U' * Q' * X
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* 13: Check the orthogonality of Q*U
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|
* 14: Check the orthogonality of VT*PT
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|
*
|
|
CALL SBDT01( M, N, 0, A, LDA, Q, LDQ, S2, DUMMA, PT,
|
|
$ LDPT, WORK, RESULT( 11 ) )
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|
CALL SBDT02( M, NRHS, X, LDX, Y, LDX, Q, LDQ, WORK,
|
|
$ RESULT( 12 ) )
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|
CALL SORT01( 'Columns', M, MQ, Q, LDQ, WORK, LWORK,
|
|
$ RESULT( 13 ) )
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|
CALL SORT01( 'Rows', MNMIN, N, PT, LDPT, WORK, LWORK,
|
|
$ RESULT( 14 ) )
|
|
END IF
|
|
*
|
|
* Use SBDSDC to form the SVD of the bidiagonal matrix B:
|
|
* B := U * S1 * VT
|
|
*
|
|
CALL SCOPY( MNMIN, BD, 1, S1, 1 )
|
|
IF( MNMIN.GT.0 )
|
|
$ CALL SCOPY( MNMIN-1, BE, 1, WORK, 1 )
|
|
CALL SLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, U, LDPT )
|
|
CALL SLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, VT, LDPT )
|
|
*
|
|
CALL SBDSDC( UPLO, 'I', MNMIN, S1, WORK, U, LDPT, VT, LDPT,
|
|
$ DUM, IDUM, WORK( MNMIN+1 ), IWORK, IINFO )
|
|
*
|
|
* Check error code from SBDSDC.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'SBDSDC(vects)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 15 ) = ULPINV
|
|
GO TO 170
|
|
END IF
|
|
END IF
|
|
*
|
|
* Use SBDSDC to compute only the singular values of the
|
|
* bidiagonal matrix B; U and VT should not be modified.
|
|
*
|
|
CALL SCOPY( MNMIN, BD, 1, S2, 1 )
|
|
IF( MNMIN.GT.0 )
|
|
$ CALL SCOPY( MNMIN-1, BE, 1, WORK, 1 )
|
|
*
|
|
CALL SBDSDC( UPLO, 'N', MNMIN, S2, WORK, DUM, 1, DUM, 1,
|
|
$ DUM, IDUM, WORK( MNMIN+1 ), IWORK, IINFO )
|
|
*
|
|
* Check error code from SBDSDC.
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9998 )'SBDSDC(values)', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
IF( IINFO.LT.0 ) THEN
|
|
RETURN
|
|
ELSE
|
|
RESULT( 18 ) = ULPINV
|
|
GO TO 170
|
|
END IF
|
|
END IF
|
|
*
|
|
* Test 15: Check the decomposition B := U * S1 * VT
|
|
* 16: Check the orthogonality of U
|
|
* 17: Check the orthogonality of VT
|
|
*
|
|
CALL SBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT,
|
|
$ WORK, RESULT( 15 ) )
|
|
CALL SORT01( 'Columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK,
|
|
$ RESULT( 16 ) )
|
|
CALL SORT01( 'Rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK,
|
|
$ RESULT( 17 ) )
|
|
*
|
|
* Test 18: Check that the singular values are sorted in
|
|
* non-increasing order and are non-negative
|
|
*
|
|
RESULT( 18 ) = ZERO
|
|
DO 150 I = 1, MNMIN - 1
|
|
IF( S1( I ).LT.S1( I+1 ) )
|
|
$ RESULT( 18 ) = ULPINV
|
|
IF( S1( I ).LT.ZERO )
|
|
$ RESULT( 18 ) = ULPINV
|
|
150 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( S1( MNMIN ).LT.ZERO )
|
|
$ RESULT( 18 ) = ULPINV
|
|
END IF
|
|
*
|
|
* Test 19: Compare SBDSQR with and without singular vectors
|
|
*
|
|
TEMP2 = ZERO
|
|
*
|
|
DO 160 J = 1, MNMIN
|
|
TEMP1 = ABS( S1( J )-S2( J ) ) /
|
|
$ MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
|
|
$ ULP*MAX( ABS( S1( 1 ) ), ABS( S2( 1 ) ) ) )
|
|
TEMP2 = MAX( TEMP1, TEMP2 )
|
|
160 CONTINUE
|
|
*
|
|
RESULT( 19 ) = TEMP2
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
170 CONTINUE
|
|
DO 180 J = 1, 19
|
|
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
|
|
180 CONTINUE
|
|
IF( .NOT.BIDIAG ) THEN
|
|
NTEST = NTEST + 19
|
|
ELSE
|
|
NTEST = NTEST + 5
|
|
END IF
|
|
*
|
|
190 CONTINUE
|
|
200 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NTEST, 0 )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SCHKBD
|
|
*
|
|
9999 FORMAT( ' M=', I5, ', N=', I5, ', type ', I2, ', seed=',
|
|
$ 4( I4, ',' ), ' test(', I2, ')=', G11.4 )
|
|
9998 FORMAT( ' SCHKBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
|
|
$ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
|
|
$ I5, ')' )
|
|
*
|
|
END
|