Merge pull request #3949 from martin-frbg/lapack750
Improve inline documentation of ?GEJSV (Reference-LAPACK PR 750)
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Martin Kroeker
GitHub
commit
2b77f28810
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@ -304,7 +304,7 @@
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*> -> the minimal requirement is LWORK >= 3*N.
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*> -> For optimal performance,
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*> LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
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*> where NB is the optimal block size for CGEQP3, CGEQRF, CGELQ,
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*> where NB is the optimal block size for CGEQP3, CGEQRF, CGELQF,
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*> CUNMLQ. In general, the optimal length LWORK is computed as
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*> LWORK >= max(N+LWORK(CGEQP3), N+LWORK(CGESVJ),
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*> N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)).
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@ -313,7 +313,7 @@
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*> -> the minimal requirement is LWORK >= 3*N.
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*> -> For optimal performance,
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*> LWORK >= max(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB,
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*> where NB is the optimal block size for CGEQP3, CGEQRF, CGELQ,
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*> where NB is the optimal block size for CGEQP3, CGEQRF, CGELQF,
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*> CUNMLQ. In general, the optimal length LWORK is computed as
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*> LWORK >= max(N+LWORK(CGEQP3), LWORK(CPOCON), N+LWORK(CGESVJ),
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*> N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)).
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@ -350,7 +350,7 @@
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (MAX(7,LWORK))
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*> RWORK is REAL array, dimension (MAX(7,LRWORK))
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*> On exit,
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*> RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1)
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*> such that SCALE*SVA(1:N) are the computed singular values
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@ -224,7 +224,7 @@
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*>
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*> \param[out] U
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*> \verbatim
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*> U is DOUBLE PRECISION array, dimension ( LDU, N )
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*> U is DOUBLE PRECISION array, dimension ( LDU, N ) or ( LDU, M )
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*> If JOBU = 'U', then U contains on exit the M-by-N matrix of
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*> the left singular vectors.
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*> If JOBU = 'F', then U contains on exit the M-by-M matrix of
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@ -271,7 +271,7 @@
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (LWORK)
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*> WORK is DOUBLE PRECISION array, dimension (MAX(7,LWORK))
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*> On exit, if N > 0 .AND. M > 0 (else not referenced),
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*> WORK(1) = SCALE = WORK(2) / WORK(1) is the scaling factor such
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*> that SCALE*SVA(1:N) are the computed singular values
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@ -224,7 +224,7 @@
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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 ( LDU, N )
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*> U is REAL array, dimension ( LDU, N ) or ( LDU, M )
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*> If JOBU = 'U', then U contains on exit the M-by-N matrix of
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*> the left singular vectors.
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*> If JOBU = 'F', then U contains on exit the M-by-M matrix of
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@ -271,7 +271,7 @@
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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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*> WORK is REAL array, dimension (MAX(7,LWORK))
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*> On exit,
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*> WORK(1) = SCALE = WORK(2) / WORK(1) is the scaling factor such
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*> that SCALE*SVA(1:N) are the computed singular values
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@ -318,36 +318,36 @@
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*> LWORK >= max(2*M+N,4*N+1,7). This is the minimal requirement.
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*> ->> For optimal performance (blocked code) the optimal value
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*> is LWORK >= max(2*M+N,3*N+(N+1)*NB,7). Here NB is the optimal
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*> block size for DGEQP3 and DGEQRF.
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*> block size for SGEQP3 and SGEQRF.
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*> In general, optimal LWORK is computed as
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*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF), 7).
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*> LWORK >= max(2*M+N,N+LWORK(SGEQP3),N+LWORK(SGEQRF), 7).
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*> -> .. an estimate of the scaled condition number of A is
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*> required (JOBA='E', 'G'). In this case, LWORK is the maximum
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*> of the above and N*N+4*N, i.e. LWORK >= max(2*M+N,N*N+4*N,7).
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*> ->> For optimal performance (blocked code) the optimal value
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*> is LWORK >= max(2*M+N,3*N+(N+1)*NB, N*N+4*N, 7).
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*> In general, the optimal length LWORK is computed as
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*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF),
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*> N+N*N+LWORK(DPOCON),7).
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*> LWORK >= max(2*M+N,N+LWORK(SGEQP3),N+LWORK(SGEQRF),
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*> N+N*N+LWORK(SPOCON),7).
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*>
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*> If SIGMA and the right singular vectors are needed (JOBV = 'V'),
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*> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
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*> -> For optimal performance, LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
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*> where NB is the optimal block size for DGEQP3, DGEQRF, DGELQ,
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*> DORMLQ. In general, the optimal length LWORK is computed as
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*> LWORK >= max(2*M+N,N+LWORK(DGEQP3), N+LWORK(DPOCON),
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*> N+LWORK(DGELQ), 2*N+LWORK(DGEQRF), N+LWORK(DORMLQ)).
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*> where NB is the optimal block size for SGEQP3, SGEQRF, SGELQF,
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*> SORMLQ. In general, the optimal length LWORK is computed as
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*> LWORK >= max(2*M+N,N+LWORK(SGEQP3), N+LWORK(SPOCON),
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*> N+LWORK(SGELQF), 2*N+LWORK(SGEQRF), N+LWORK(SORMLQ)).
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*>
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*> If SIGMA and the left singular vectors are needed
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*> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
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*> -> For optimal performance:
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*> if JOBU = 'U' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
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*> if JOBU = 'F' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,N+M*NB,7),
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*> where NB is the optimal block size for DGEQP3, DGEQRF, DORMQR.
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*> where NB is the optimal block size for SGEQP3, SGEQRF, SORMQR.
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*> In general, the optimal length LWORK is computed as
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*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DPOCON),
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*> 2*N+LWORK(DGEQRF), N+LWORK(DORMQR)).
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*> Here LWORK(DORMQR) equals N*NB (for JOBU = 'U') or
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*> LWORK >= max(2*M+N,N+LWORK(SGEQP3),N+LWORK(SPOCON),
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*> 2*N+LWORK(SGEQRF), N+LWORK(SORMQR)).
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*> Here LWORK(SORMQR) equals N*NB (for JOBU = 'U') or
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*> M*NB (for JOBU = 'F').
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*>
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*> If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and
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@ -357,12 +357,12 @@
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*> LWORK >= max(2*M+N, 4*N+N*N,2*N+N*N+6).
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*> -> For optimal performance, LWORK should be additionally
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*> larger than N+M*NB, where NB is the optimal block size
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*> for DORMQR.
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*> for SORMQR.
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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 (M+3*N).
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*> IWORK is INTEGER array, dimension (MAX(3,M+3*N)).
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*> On exit,
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*> IWORK(1) = the numerical rank determined after the initial
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*> QR factorization with pivoting. See the descriptions
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@ -304,7 +304,7 @@
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*> -> the minimal requirement is LWORK >= 3*N.
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*> -> For optimal performance,
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*> LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
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*> where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQ,
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*> where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQF,
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*> ZUNMLQ. In general, the optimal length LWORK is computed as
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*> LWORK >= max(N+LWORK(ZGEQP3), N+LWORK(ZGESVJ),
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*> N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)).
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@ -313,7 +313,7 @@
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*> -> the minimal requirement is LWORK >= 3*N.
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*> -> For optimal performance,
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*> LWORK >= max(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB,
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*> where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQ,
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*> where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQF,
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*> ZUNMLQ. In general, the optimal length LWORK is computed as
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*> LWORK >= max(N+LWORK(ZGEQP3), LWORK(ZPOCON), N+LWORK(ZGESVJ),
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*> N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)).
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@ -349,7 +349,7 @@
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension (MAX(7,LWORK))
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*> RWORK is DOUBLE PRECISION array, dimension (MAX(7,LRWORK))
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*> On exit,
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*> RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1)
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*> such that SCALE*SVA(1:N) are the computed singular values
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