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Improve inline documentation of ?GEJSV (Reference-LAPACK PR 750)

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Martin Kroeker 2023-03-20 19:51:07 +01:00 committed by GitHub
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4 changed files with 24 additions and 24 deletions
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6
lapack-netlib/SRC/cgejsv.f
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@ -304,7 +304,7 @@
*> -> the minimal requirement is LWORK >= 3*N. *> -> the minimal requirement is LWORK >= 3*N.
*> -> For optimal performance, *> -> For optimal performance,
*> LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB, *> LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
*> where NB is the optimal block size for CGEQP3, CGEQRF, CGELQ, *> where NB is the optimal block size for CGEQP3, CGEQRF, CGELQF,
*> CUNMLQ. In general, the optimal length LWORK is computed as *> CUNMLQ. In general, the optimal length LWORK is computed as
*> LWORK >= max(N+LWORK(CGEQP3), N+LWORK(CGESVJ), *> LWORK >= max(N+LWORK(CGEQP3), N+LWORK(CGESVJ),
*> N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)). *> N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)).
@ -313,7 +313,7 @@
*> -> the minimal requirement is LWORK >= 3*N. *> -> the minimal requirement is LWORK >= 3*N.
*> -> For optimal performance, *> -> For optimal performance,
*> LWORK >= max(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB, *> LWORK >= max(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB,
*> where NB is the optimal block size for CGEQP3, CGEQRF, CGELQ, *> where NB is the optimal block size for CGEQP3, CGEQRF, CGELQF,
*> CUNMLQ. In general, the optimal length LWORK is computed as *> CUNMLQ. In general, the optimal length LWORK is computed as
*> LWORK >= max(N+LWORK(CGEQP3), LWORK(CPOCON), N+LWORK(CGESVJ), *> LWORK >= max(N+LWORK(CGEQP3), LWORK(CPOCON), N+LWORK(CGESVJ),
*> N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)). *> N+LWORK(CGELQF), 2*N+LWORK(CGEQRF), N+LWORK(CUNMLQ)).
@ -350,7 +350,7 @@
*> *>
*> \param[out] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (MAX(7,LWORK)) *> RWORK is REAL array, dimension (MAX(7,LRWORK))
*> On exit, *> On exit,
*> RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1) *> RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1)
*> such that SCALE*SVA(1:N) are the computed singular values *> such that SCALE*SVA(1:N) are the computed singular values

4
lapack-netlib/SRC/dgejsv.f
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@ -224,7 +224,7 @@
*> *>
*> \param[out] U *> \param[out] U
*> \verbatim *> \verbatim
*> U is DOUBLE PRECISION array, dimension ( LDU, N ) *> U is DOUBLE PRECISION array, dimension ( LDU, N ) or ( LDU, M )
*> If JOBU = 'U', then U contains on exit the M-by-N matrix of *> If JOBU = 'U', then U contains on exit the M-by-N matrix of
*> the left singular vectors. *> the left singular vectors.
*> If JOBU = 'F', then U contains on exit the M-by-M matrix of *> If JOBU = 'F', then U contains on exit the M-by-M matrix of
@ -271,7 +271,7 @@
*> *>
*> \param[out] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK) *> WORK is DOUBLE PRECISION array, dimension (MAX(7,LWORK))
*> On exit, if N > 0 .AND. M > 0 (else not referenced), *> On exit, if N > 0 .AND. M > 0 (else not referenced),
*> WORK(1) = SCALE = WORK(2) / WORK(1) is the scaling factor such *> WORK(1) = SCALE = WORK(2) / WORK(1) is the scaling factor such
*> that SCALE*SVA(1:N) are the computed singular values *> that SCALE*SVA(1:N) are the computed singular values

32
lapack-netlib/SRC/sgejsv.f
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@ -224,7 +224,7 @@
*> *>
*> \param[out] U *> \param[out] U
*> \verbatim *> \verbatim
*> U is REAL array, dimension ( LDU, N ) *> U is REAL array, dimension ( LDU, N ) or ( LDU, M )
*> If JOBU = 'U', then U contains on exit the M-by-N matrix of *> If JOBU = 'U', then U contains on exit the M-by-N matrix of
*> the left singular vectors. *> the left singular vectors.
*> If JOBU = 'F', then U contains on exit the M-by-M matrix of *> If JOBU = 'F', then U contains on exit the M-by-M matrix of
@ -271,7 +271,7 @@
*> *>
*> \param[out] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is REAL array, dimension (LWORK) *> WORK is REAL array, dimension (MAX(7,LWORK))
*> On exit, *> On exit,
*> WORK(1) = SCALE = WORK(2) / WORK(1) is the scaling factor such *> WORK(1) = SCALE = WORK(2) / WORK(1) is the scaling factor such
*> that SCALE*SVA(1:N) are the computed singular values *> that SCALE*SVA(1:N) are the computed singular values
@ -318,36 +318,36 @@
*> LWORK >= max(2*M+N,4*N+1,7). This is the minimal requirement. *> LWORK >= max(2*M+N,4*N+1,7). This is the minimal requirement.
*> ->> For optimal performance (blocked code) the optimal value *> ->> For optimal performance (blocked code) the optimal value
*> is LWORK >= max(2*M+N,3*N+(N+1)*NB,7). Here NB is the optimal *> is LWORK >= max(2*M+N,3*N+(N+1)*NB,7). Here NB is the optimal
*> block size for DGEQP3 and DGEQRF. *> block size for SGEQP3 and SGEQRF.
*> In general, optimal LWORK is computed as *> In general, optimal LWORK is computed as
*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF), 7). *> LWORK >= max(2*M+N,N+LWORK(SGEQP3),N+LWORK(SGEQRF), 7).
*> -> .. an estimate of the scaled condition number of A is *> -> .. an estimate of the scaled condition number of A is
*> required (JOBA='E', 'G'). In this case, LWORK is the maximum *> required (JOBA='E', 'G'). In this case, LWORK is the maximum
*> of the above and N*N+4*N, i.e. LWORK >= max(2*M+N,N*N+4*N,7). *> of the above and N*N+4*N, i.e. LWORK >= max(2*M+N,N*N+4*N,7).
*> ->> For optimal performance (blocked code) the optimal value *> ->> For optimal performance (blocked code) the optimal value
*> is LWORK >= max(2*M+N,3*N+(N+1)*NB, N*N+4*N, 7). *> is LWORK >= max(2*M+N,3*N+(N+1)*NB, N*N+4*N, 7).
*> In general, the optimal length LWORK is computed as *> In general, the optimal length LWORK is computed as
*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF), *> LWORK >= max(2*M+N,N+LWORK(SGEQP3),N+LWORK(SGEQRF),
*> N+N*N+LWORK(DPOCON),7). *> N+N*N+LWORK(SPOCON),7).
*> *>
*> If SIGMA and the right singular vectors are needed (JOBV = 'V'), *> If SIGMA and the right singular vectors are needed (JOBV = 'V'),
*> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7). *> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
*> -> For optimal performance, LWORK >= max(2*M+N,3*N+(N+1)*NB,7), *> -> For optimal performance, LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
*> where NB is the optimal block size for DGEQP3, DGEQRF, DGELQ, *> where NB is the optimal block size for SGEQP3, SGEQRF, SGELQF,
*> DORMLQ. In general, the optimal length LWORK is computed as *> SORMLQ. In general, the optimal length LWORK is computed as
*> LWORK >= max(2*M+N,N+LWORK(DGEQP3), N+LWORK(DPOCON), *> LWORK >= max(2*M+N,N+LWORK(SGEQP3), N+LWORK(SPOCON),
*> N+LWORK(DGELQ), 2*N+LWORK(DGEQRF), N+LWORK(DORMLQ)). *> N+LWORK(SGELQF), 2*N+LWORK(SGEQRF), N+LWORK(SORMLQ)).
*> *>
*> If SIGMA and the left singular vectors are needed *> If SIGMA and the left singular vectors are needed
*> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7). *> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
*> -> For optimal performance: *> -> For optimal performance:
*> if JOBU = 'U' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,7), *> if JOBU = 'U' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
*> if JOBU = 'F' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,N+M*NB,7), *> if JOBU = 'F' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,N+M*NB,7),
*> where NB is the optimal block size for DGEQP3, DGEQRF, DORMQR. *> where NB is the optimal block size for SGEQP3, SGEQRF, SORMQR.
*> In general, the optimal length LWORK is computed as *> In general, the optimal length LWORK is computed as
*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DPOCON), *> LWORK >= max(2*M+N,N+LWORK(SGEQP3),N+LWORK(SPOCON),
*> 2*N+LWORK(DGEQRF), N+LWORK(DORMQR)). *> 2*N+LWORK(SGEQRF), N+LWORK(SORMQR)).
*> Here LWORK(DORMQR) equals N*NB (for JOBU = 'U') or *> Here LWORK(SORMQR) equals N*NB (for JOBU = 'U') or
*> M*NB (for JOBU = 'F'). *> M*NB (for JOBU = 'F').
*> *>
*> If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and *> If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and
@ -357,12 +357,12 @@
*> LWORK >= max(2*M+N, 4*N+N*N,2*N+N*N+6). *> LWORK >= max(2*M+N, 4*N+N*N,2*N+N*N+6).
*> -> For optimal performance, LWORK should be additionally *> -> For optimal performance, LWORK should be additionally
*> larger than N+M*NB, where NB is the optimal block size *> larger than N+M*NB, where NB is the optimal block size
*> for DORMQR. *> for SORMQR.
*> \endverbatim *> \endverbatim
*> *>
*> \param[out] IWORK *> \param[out] IWORK
*> \verbatim *> \verbatim
*> IWORK is INTEGER array, dimension (M+3*N). *> IWORK is INTEGER array, dimension (MAX(3,M+3*N)).
*> On exit, *> On exit,
*> IWORK(1) = the numerical rank determined after the initial *> IWORK(1) = the numerical rank determined after the initial
*> QR factorization with pivoting. See the descriptions *> QR factorization with pivoting. See the descriptions

6
lapack-netlib/SRC/zgejsv.f
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@ -304,7 +304,7 @@
*> -> the minimal requirement is LWORK >= 3*N. *> -> the minimal requirement is LWORK >= 3*N.
*> -> For optimal performance, *> -> For optimal performance,
*> LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB, *> LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
*> where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQ, *> where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQF,
*> ZUNMLQ. In general, the optimal length LWORK is computed as *> ZUNMLQ. In general, the optimal length LWORK is computed as
*> LWORK >= max(N+LWORK(ZGEQP3), N+LWORK(ZGESVJ), *> LWORK >= max(N+LWORK(ZGEQP3), N+LWORK(ZGESVJ),
*> N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)). *> N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)).
@ -313,7 +313,7 @@
*> -> the minimal requirement is LWORK >= 3*N. *> -> the minimal requirement is LWORK >= 3*N.
*> -> For optimal performance, *> -> For optimal performance,
*> LWORK >= max(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB, *> LWORK >= max(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB,
*> where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQ, *> where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQF,
*> ZUNMLQ. In general, the optimal length LWORK is computed as *> ZUNMLQ. In general, the optimal length LWORK is computed as
*> LWORK >= max(N+LWORK(ZGEQP3), LWORK(ZPOCON), N+LWORK(ZGESVJ), *> LWORK >= max(N+LWORK(ZGEQP3), LWORK(ZPOCON), N+LWORK(ZGESVJ),
*> N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)). *> N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)).
@ -349,7 +349,7 @@
*> *>
*> \param[out] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (MAX(7,LWORK)) *> RWORK is DOUBLE PRECISION array, dimension (MAX(7,LRWORK))
*> On exit, *> On exit,
*> RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1) *> RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1)
*> such that SCALE*SVA(1:N) are the computed singular values *> such that SCALE*SVA(1:N) are the computed singular values