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Update LAPACK to 3.9.0

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Martin Kroeker 2019-12-29 22:58:27 +01:00 committed by GitHub
parent 1522f0f7f2
commit 688af253bf
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41 changed files with 1763 additions and 203 deletions
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2
lapack-netlib/SRC/dbdsqr.f
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@ -166,7 +166,7 @@
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (4*N)
*> WORK is DOUBLE PRECISION array, dimension (4*(N-1))
*> \endverbatim
*>
*> \param[out] INFO

2
lapack-netlib/SRC/dbdsvdx.f
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@ -165,7 +165,7 @@
*>
*> \param[out] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension (2*N,K) )
*> Z is DOUBLE PRECISION array, dimension (2*N,K)
*> If JOBZ = 'V', then if INFO = 0 the first NS columns of Z
*> contain the singular vectors of the matrix B corresponding to
*> the selected singular values, with U in rows 1 to N and V

92
lapack-netlib/SRC/dcombssq.f Normal file
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@ -0,0 +1,92 @@
*> \brief \b DCOMBSSQ adds two scaled sum of squares quantities.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*
* Definition:
* ===========
*
* SUBROUTINE DCOMBSSQ( V1, V2 )
*
* .. Array Arguments ..
* DOUBLE PRECISION V1( 2 ), V2( 2 )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCOMBSSQ adds two scaled sum of squares quantities, V1 := V1 + V2.
*> That is,
*>
*> V1_scale**2 * V1_sumsq := V1_scale**2 * V1_sumsq
*> + V2_scale**2 * V2_sumsq
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in,out] V1
*> \verbatim
*> V1 is DOUBLE PRECISION array, dimension (2).
*> The first scaled sum.
*> V1(1) = V1_scale, V1(2) = V1_sumsq.
*> \endverbatim
*>
*> \param[in] V2
*> \verbatim
*> V2 is DOUBLE PRECISION array, dimension (2).
*> The second scaled sum.
*> V2(1) = V2_scale, V2(2) = V2_sumsq.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2018
*
*> \ingroup OTHERauxiliary
*
* =====================================================================
SUBROUTINE DCOMBSSQ( V1, V2 )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2018
*
* .. Array Arguments ..
DOUBLE PRECISION V1( 2 ), V2( 2 )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Executable Statements ..
*
IF( V1( 1 ).GE.V2( 1 ) ) THEN
IF( V1( 1 ).NE.ZERO ) THEN
V1( 2 ) = V1( 2 ) + ( V2( 1 ) / V1( 1 ) )**2 * V2( 2 )
END IF
ELSE
V1( 2 ) = V2( 2 ) + ( V1( 1 ) / V2( 1 ) )**2 * V1( 2 )
V1( 1 ) = V2( 1 )
END IF
RETURN
*
* End of DCOMBSSQ
*
END

10
lapack-netlib/SRC/dgbrfsx.f
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@ -308,7 +308,7 @@
*> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most
*> the first (:,N_ERR_BNDS) entries are returned.
*>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@ -344,14 +344,14 @@
*> \param[in] NPARAMS
*> \verbatim
*> NPARAMS is INTEGER
*> Specifies the number of parameters set in PARAMS. If .LE. 0, the
*> Specifies the number of parameters set in PARAMS. If <= 0, the
*> PARAMS array is never referenced and default values are used.
*> \endverbatim
*>
*> \param[in,out] PARAMS
*> \verbatim
*> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
*> Specifies algorithm parameters. If an entry is .LT. 0.0, then
*> Specifies algorithm parameters. If an entry is < 0.0, then
*> that entry will be filled with default value used for that
*> parameter. Only positions up to NPARAMS are accessed; defaults
*> are used for higher-numbered parameters.
@ -359,9 +359,9 @@
*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
*> refinement or not.
*> Default: 1.0D+0
*> = 0.0 : No refinement is performed, and no error bounds are
*> = 0.0: No refinement is performed, and no error bounds are
*> computed.
*> = 1.0 : Use the double-precision refinement algorithm,
*> = 1.0: Use the double-precision refinement algorithm,
*> possibly with doubled-single computations if the
*> compilation environment does not support DOUBLE
*> PRECISION.

10
lapack-netlib/SRC/dgbsvxx.f
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@ -431,7 +431,7 @@
*> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most
*> the first (:,N_ERR_BNDS) entries are returned.
*>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@ -467,14 +467,14 @@
*> \param[in] NPARAMS
*> \verbatim
*> NPARAMS is INTEGER
*> Specifies the number of parameters set in PARAMS. If .LE. 0, the
*> Specifies the number of parameters set in PARAMS. If <= 0, the
*> PARAMS array is never referenced and default values are used.
*> \endverbatim
*>
*> \param[in,out] PARAMS
*> \verbatim
*> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
*> Specifies algorithm parameters. If an entry is .LT. 0.0, then
*> Specifies algorithm parameters. If an entry is < 0.0, then
*> that entry will be filled with default value used for that
*> parameter. Only positions up to NPARAMS are accessed; defaults
*> are used for higher-numbered parameters.
@ -482,9 +482,9 @@
*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
*> refinement or not.
*> Default: 1.0D+0
*> = 0.0 : No refinement is performed, and no error bounds are
*> = 0.0: No refinement is performed, and no error bounds are
*> computed.
*> = 1.0 : Use the extra-precise refinement algorithm.
*> = 1.0: Use the extra-precise refinement algorithm.
*> (other values are reserved for future use)
*>
*> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

8
lapack-netlib/SRC/dgebak.f
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@ -47,10 +47,10 @@
*> \verbatim
*> JOB is CHARACTER*1
*> Specifies the type of backward transformation required:
*> = 'N', do nothing, return immediately;
*> = 'P', do backward transformation for permutation only;
*> = 'S', do backward transformation for scaling only;
*> = 'B', do backward transformations for both permutation and
*> = 'N': do nothing, return immediately;
*> = 'P': do backward transformation for permutation only;
*> = 'S': do backward transformation for scaling only;
*> = 'B': do backward transformations for both permutation and
*> scaling.
*> JOB must be the same as the argument JOB supplied to DGEBAL.
*> \endverbatim

4
lapack-netlib/SRC/dgeesx.f
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@ -583,7 +583,9 @@
IF( N.GT.I+1 )
$ CALL DSWAP( N-I-1, A( I, I+2 ), LDA,
$ A( I+1, I+2 ), LDA )
CALL DSWAP( N, VS( 1, I ), 1, VS( 1, I+1 ), 1 )
IF( WANTVS ) THEN
CALL DSWAP( N, VS( 1, I ), 1, VS( 1, I+1 ), 1 )
END IF
A( I, I+1 ) = A( I+1, I )
A( I+1, I ) = ZERO
END IF

56
lapack-netlib/SRC/dgejsv.f
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@ -82,7 +82,7 @@
*> desirable, then this option is advisable. The input matrix A
*> is preprocessed with QR factorization with FULL (row and
*> column) pivoting.
*> = 'G' Computation as with 'F' with an additional estimate of the
*> = 'G': Computation as with 'F' with an additional estimate of the
*> condition number of B, where A=D*B. If A has heavily weighted
*> rows, then using this condition number gives too pessimistic
*> error bound.
@ -133,7 +133,7 @@
*> specified range. If A .NE. 0 is scaled so that the largest singular
*> value of c*A is around DSQRT(BIG), BIG=SLAMCH('O'), then JOBR issues
*> the licence to kill columns of A whose norm in c*A is less than
*> DSQRT(SFMIN) (for JOBR.EQ.'R'), or less than SMALL=SFMIN/EPSLN,
*> DSQRT(SFMIN) (for JOBR = 'R'), or less than SMALL=SFMIN/EPSLN,
*> where SFMIN=SLAMCH('S'), EPSLN=SLAMCH('E').
*> = 'N': Do not kill small columns of c*A. This option assumes that
*> BLAS and QR factorizations and triangular solvers are
@ -230,7 +230,7 @@
*> If JOBU = 'F', then U contains on exit the M-by-M matrix of
*> the left singular vectors, including an ONB
*> of the orthogonal complement of the Range(A).
*> If JOBU = 'W' .AND. (JOBV.EQ.'V' .AND. JOBT.EQ.'T' .AND. M.EQ.N),
*> If JOBU = 'W' .AND. (JOBV = 'V' .AND. JOBT = 'T' .AND. M = N),
*> then U is used as workspace if the procedure
*> replaces A with A^t. In that case, [V] is computed
*> in U as left singular vectors of A^t and then
@ -252,7 +252,7 @@
*> V is DOUBLE PRECISION array, dimension ( LDV, N )
*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
*> the right singular vectors;
*> If JOBV = 'W', AND (JOBU.EQ.'U' AND JOBT.EQ.'T' AND M.EQ.N),
*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
*> then V is used as workspace if the pprocedure
*> replaces A with A^t. In that case, [U] is computed
*> in V as right singular vectors of A^t and then
@ -272,13 +272,13 @@
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> On exit, if N.GT.0 .AND. M.GT.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
*> that SCALE*SVA(1:N) are the computed singular values
*> of A. (See the description of SVA().)
*> WORK(2) = See the description of WORK(1).
*> WORK(3) = SCONDA is an estimate for the condition number of
*> column equilibrated A. (If JOBA .EQ. 'E' or 'G')
*> column equilibrated A. (If JOBA = 'E' or 'G')
*> SCONDA is an estimate of DSQRT(||(R^t * R)^(-1)||_1).
*> It is computed using DPOCON. It holds
*> N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA
@ -297,7 +297,7 @@
*> triangular factor in the first QR factorization.
*> WORK(5) = an estimate of the scaled condition number of the
*> triangular factor in the second QR factorization.
*> The following two parameters are computed if JOBT .EQ. 'T'.
*> The following two parameters are computed if JOBT = 'T'.
*> They are provided for a developer/implementer who is familiar
*> with the details of the method.
*>
@ -313,8 +313,8 @@
*> Length of WORK to confirm proper allocation of work space.
*> LWORK depends on the job:
*>
*> If only SIGMA is needed ( JOBU.EQ.'N', JOBV.EQ.'N' ) and
*> -> .. no scaled condition estimate required (JOBE.EQ.'N'):
*> If only SIGMA is needed (JOBU = 'N', JOBV = 'N') and
*> -> .. no scaled condition estimate required (JOBE = 'N'):
*> LWORK >= max(2*M+N,4*N+1,7). This is the minimal requirement.
*> ->> 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
@ -330,7 +330,7 @@
*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF),
*> N+N*N+LWORK(DPOCON),7).
*>
*> If SIGMA and the right singular vectors are needed (JOBV.EQ.'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).
*> -> For optimal performance, LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
*> where NB is the optimal block size for DGEQP3, DGEQRF, DGELQF,
@ -341,19 +341,19 @@
*> If SIGMA and the left singular vectors are needed
*> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
*> -> For optimal performance:
*> if JOBU.EQ.'U' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
*> if JOBU.EQ.'F' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,N+M*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),
*> where NB is the optimal block size for DGEQP3, DGEQRF, DORMQR.
*> In general, the optimal length LWORK is computed as
*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DPOCON),
*> 2*N+LWORK(DGEQRF), N+LWORK(DORMQR)).
*> Here LWORK(DORMQR) equals N*NB (for JOBU.EQ.'U') or
*> M*NB (for JOBU.EQ.'F').
*> Here LWORK(DORMQR) equals N*NB (for JOBU = 'U') or
*> M*NB (for JOBU = 'F').
*>
*> If the full SVD is needed: (JOBU.EQ.'U' or JOBU.EQ.'F') and
*> -> if JOBV.EQ.'V'
*> If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and
*> -> if JOBV = 'V'
*> the minimal requirement is LWORK >= max(2*M+N,6*N+2*N*N).
*> -> if JOBV.EQ.'J' the minimal requirement is
*> -> if JOBV = 'J' the minimal requirement is
*> LWORK >= max(2*M+N, 4*N+N*N,2*N+N*N+6).
*> -> For optimal performance, LWORK should be additionally
*> larger than N+M*NB, where NB is the optimal block size
@ -369,7 +369,7 @@
*> of JOBA and JOBR.
*> IWORK(2) = the number of the computed nonzero singular values
*> IWORK(3) = if nonzero, a warning message:
*> If IWORK(3).EQ.1 then some of the column norms of A
*> If IWORK(3) = 1 then some of the column norms of A
*> were denormalized floats. The requested high accuracy
*> is not warranted by the data.
*> \endverbatim
@ -377,10 +377,10 @@
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> < 0 : if INFO = -i, then the i-th argument had an illegal value.
*> = 0 : successful exit;
*> > 0 : DGEJSV did not converge in the maximal allowed number
*> of sweeps. The computed values may be inaccurate.
*> < 0: if INFO = -i, then the i-th argument had an illegal value.
*> = 0: successful exit;
*> > 0: DGEJSV did not converge in the maximal allowed number
*> of sweeps. The computed values may be inaccurate.
*> \endverbatim
*
* Authors:
@ -953,7 +953,7 @@
IF ( L2ABER ) THEN
* Standard absolute error bound suffices. All sigma_i with
* sigma_i < N*EPSLN*||A|| are flushed to zero. This is an
* agressive enforcement of lower numerical rank by introducing a
* aggressive enforcement of lower numerical rank by introducing a
* backward error of the order of N*EPSLN*||A||.
TEMP1 = DSQRT(DBLE(N))*EPSLN
DO 3001 p = 2, N
@ -965,7 +965,7 @@
3001 CONTINUE
3002 CONTINUE
ELSE IF ( L2RANK ) THEN
* .. similarly as above, only slightly more gentle (less agressive).
* .. similarly as above, only slightly more gentle (less aggressive).
* Sudden drop on the diagonal of R1 is used as the criterion for
* close-to-rank-deficient.
TEMP1 = DSQRT(SFMIN)
@ -1294,7 +1294,7 @@
CALL DPOCON('Lower',NR,WORK(2*N+1),NR,ONE,TEMP1,
$ WORK(2*N+NR*NR+1),IWORK(M+2*N+1),IERR)
CONDR1 = ONE / DSQRT(TEMP1)
* .. here need a second oppinion on the condition number
* .. here need a second opinion on the condition number
* .. then assume worst case scenario
* R1 is OK for inverse <=> CONDR1 .LT. DBLE(N)
* more conservative <=> CONDR1 .LT. DSQRT(DBLE(N))
@ -1335,7 +1335,7 @@
ELSE
*
* .. ill-conditioned case: second QRF with pivoting
* Note that windowed pivoting would be equaly good
* Note that windowed pivoting would be equally good
* numerically, and more run-time efficient. So, in
* an optimal implementation, the next call to DGEQP3
* should be replaced with eg. CALL SGEQPX (ACM TOMS #782)
@ -1388,7 +1388,7 @@
*
IF ( CONDR2 .GE. COND_OK ) THEN
* .. save the Householder vectors used for Q3
* (this overwrittes the copy of R2, as it will not be
* (this overwrites the copy of R2, as it will not be
* needed in this branch, but it does not overwritte the
* Huseholder vectors of Q2.).
CALL DLACPY( 'U', NR, NR, V, LDV, WORK(2*N+1), N )
@ -1638,7 +1638,7 @@
*
* This branch deploys a preconditioned Jacobi SVD with explicitly
* accumulated rotations. It is included as optional, mainly for
* experimental purposes. It does perfom well, and can also be used.
* experimental purposes. It does perform well, and can also be used.
* In this implementation, this branch will be automatically activated
* if the condition number sigma_max(A) / sigma_min(A) is predicted
* to be greater than the overflow threshold. This is because the

19
lapack-netlib/SRC/dgelq.f
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@ -1,3 +1,4 @@
*> \brief \b DGELQ
*
* Definition:
* ===========
@ -17,7 +18,17 @@
* =============
*>
*> \verbatim
*> DGELQ computes a LQ factorization of an M-by-N matrix A.
*>
*> DGELQ computes an LQ factorization of a real M-by-N matrix A:
*>
*> A = ( L 0 ) * Q
*>
*> where:
*>
*> Q is a N-by-N orthogonal matrix;
*> L is an lower-triangular M-by-M matrix;
*> 0 is a M-by-(N-M) zero matrix, if M < N.
*>
*> \endverbatim
*
* Arguments:
@ -138,7 +149,7 @@
*> \verbatim
*>
*> These details are particular for this LAPACK implementation. Users should not
*> take them for granted. These details may change in the future, and are unlikely not
*> take them for granted. These details may change in the future, and are not likely
*> true for another LAPACK implementation. These details are relevant if one wants
*> to try to understand the code. They are not part of the interface.
*>
@ -159,10 +170,10 @@
SUBROUTINE DGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
$ INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK computational routine (version 3.9.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
* December 2016
* November 2019
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N, TSIZE, LWORK

18
lapack-netlib/SRC/dgelq2.f
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@ -33,8 +33,16 @@
*>
*> \verbatim
*>
*> DGELQ2 computes an LQ factorization of a real m by n matrix A:
*> A = L * Q.
*> DGELQ2 computes an LQ factorization of a real m-by-n matrix A:
*>
*> A = ( L 0 ) * Q
*>
*> where:
*>
*> Q is a n-by-n orthogonal matrix;
*> L is an lower-triangular m-by-m matrix;
*> 0 is a m-by-(n-m) zero matrix, if m < n.
*>
*> \endverbatim
*
* Arguments:
@ -96,7 +104,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*> \date November 2019
*
*> \ingroup doubleGEcomputational
*
@ -121,10 +129,10 @@
* =====================================================================
SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK computational routine (version 3.9.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
* November 2019
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N

16
lapack-netlib/SRC/dgelqf.f
View File

@ -34,7 +34,15 @@
*> \verbatim
*>
*> DGELQF computes an LQ factorization of a real M-by-N matrix A:
*> A = L * Q.
*>
*> A = ( L 0 ) * Q
*>
*> where:
*>
*> Q is a N-by-N orthogonal matrix;
*> L is an lower-triangular M-by-M matrix;
*> 0 is a M-by-(N-M) zero matrix, if M < N.
*>
*> \endverbatim
*
* Arguments:
@ -110,7 +118,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*> \date November 2019
*
*> \ingroup doubleGEcomputational
*
@ -135,10 +143,10 @@
* =====================================================================
SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK computational routine (version 3.9.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
* November 2019
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LWORK, M, N

3
lapack-netlib/SRC/dgemlq.f
View File

@ -1,3 +1,4 @@
*> \brief \b DGEMLQ
*
* Definition:
* ===========
@ -144,7 +145,7 @@
*> \verbatim
*>
*> These details are particular for this LAPACK implementation. Users should not
*> take them for granted. These details may change in the future, and are unlikely not
*> take them for granted. These details may change in the future, and are not likely
*> true for another LAPACK implementation. These details are relevant if one wants
*> to try to understand the code. They are not part of the interface.
*>

3
lapack-netlib/SRC/dgemqr.f
View File

@ -1,3 +1,4 @@
*> \brief \b DGEMQR
*
* Definition:
* ===========
@ -144,7 +145,7 @@
*> \verbatim
*>
*> These details are particular for this LAPACK implementation. Users should not
*> take them for granted. These details may change in the future, and are unlikely not
*> take them for granted. These details may change in the future, and are not likely
*> true for another LAPACK implementation. These details are relevant if one wants
*> to try to understand the code. They are not part of the interface.
*>

20
lapack-netlib/SRC/dgeqr.f
View File

@ -1,3 +1,4 @@
*> \brief \b DGEQR
*
* Definition:
* ===========
@ -17,7 +18,18 @@
* =============
*>
*> \verbatim
*> DGEQR computes a QR factorization of an M-by-N matrix A.
*>
*> DGEQR computes a QR factorization of a real M-by-N matrix A:
*>
*> A = Q * ( R ),
*> ( 0 )
*>
*> where:
*>
*> Q is a M-by-M orthogonal matrix;
*> R is an upper-triangular N-by-N matrix;
*> 0 is a (M-N)-by-N zero matrix, if M > N.
*>
*> \endverbatim
*
* Arguments:
@ -138,7 +150,7 @@
*> \verbatim
*>
*> These details are particular for this LAPACK implementation. Users should not
*> take them for granted. These details may change in the future, and are unlikely not
*> take them for granted. These details may change in the future, and are not likely
*> true for another LAPACK implementation. These details are relevant if one wants
*> to try to understand the code. They are not part of the interface.
*>
@ -160,10 +172,10 @@
SUBROUTINE DGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK,
$ INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK computational routine (version 3.9.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
* December 2016
* November 2019
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N, TSIZE, LWORK

19
lapack-netlib/SRC/dgeqr2.f
View File

@ -33,8 +33,17 @@
*>
*> \verbatim
*>
*> DGEQR2 computes a QR factorization of a real m by n matrix A:
*> A = Q * R.
*> DGEQR2 computes a QR factorization of a real m-by-n matrix A:
*>
*> A = Q * ( R ),
*> ( 0 )
*>
*> where:
*>
*> Q is a m-by-m orthogonal matrix;
*> R is an upper-triangular n-by-n matrix;
*> 0 is a (m-n)-by-n zero matrix, if m > n.
*>
*> \endverbatim
*
* Arguments:
@ -96,7 +105,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*> \date November 2019
*
*> \ingroup doubleGEcomputational
*
@ -121,10 +130,10 @@
* =====================================================================
SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK computational routine (version 3.9.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
* November 2019
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N

20
lapack-netlib/SRC/dgeqr2p.f
View File

@ -33,8 +33,18 @@
*>
*> \verbatim
*>
*> DGEQR2P computes a QR factorization of a real m by n matrix A:
*> A = Q * R. The diagonal entries of R are nonnegative.
*> DGEQR2P computes a QR factorization of a real m-by-n matrix A:
*>
*> A = Q * ( R ),
*> ( 0 )
*>
*> where:
*>
*> Q is a m-by-m orthogonal matrix;
*> R is an upper-triangular n-by-n matrix with nonnegative diagonal
*> entries;
*> 0 is a (m-n)-by-n zero matrix, if m > n.
*>
*> \endverbatim
*
* Arguments:
@ -97,7 +107,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*> \date November 2019
*
*> \ingroup doubleGEcomputational
*
@ -124,10 +134,10 @@
* =====================================================================
SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK computational routine (version 3.9.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
* November 2019
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N

17
lapack-netlib/SRC/dgeqrf.f
View File

@ -34,7 +34,16 @@
*> \verbatim
*>
*> DGEQRF computes a QR factorization of a real M-by-N matrix A:
*> A = Q * R.
*>
*> A = Q * ( R ),
*> ( 0 )
*>
*> where:
*>
*> Q is a M-by-M orthogonal matrix;
*> R is an upper-triangular N-by-N matrix;
*> 0 is a (M-N)-by-N zero matrix, if M > N.
*>
*> \endverbatim
*
* Arguments:
@ -111,7 +120,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*> \date November 2019
*
*> \ingroup doubleGEcomputational
*
@ -136,10 +145,10 @@
* =====================================================================
SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK computational routine (version 3.9.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
* November 2019
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LWORK, M, N

20
lapack-netlib/SRC/dgeqrfp.f
View File

@ -33,8 +33,18 @@
*>
*> \verbatim
*>
*> DGEQRFP computes a QR factorization of a real M-by-N matrix A:
*> A = Q * R. The diagonal entries of R are nonnegative.
*> DGEQR2P computes a QR factorization of a real M-by-N matrix A:
*>
*> A = Q * ( R ),
*> ( 0 )
*>
*> where:
*>
*> Q is a M-by-M orthogonal matrix;
*> R is an upper-triangular N-by-N matrix with nonnegative diagonal
*> entries;
*> 0 is a (M-N)-by-N zero matrix, if M > N.
*>
*> \endverbatim
*
* Arguments:
@ -112,7 +122,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*> \date November 2019
*
*> \ingroup doubleGEcomputational
*
@ -139,10 +149,10 @@
* =====================================================================
SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK computational routine (version 3.9.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
* November 2019
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LWORK, M, N

10
lapack-netlib/SRC/dgerfsx.f
View File

@ -283,7 +283,7 @@
*> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most
*> the first (:,N_ERR_BNDS) entries are returned.
*>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@ -319,14 +319,14 @@
*> \param[in] NPARAMS
*> \verbatim
*> NPARAMS is INTEGER
*> Specifies the number of parameters set in PARAMS. If .LE. 0, the
*> Specifies the number of parameters set in PARAMS. If <= 0, the
*> PARAMS array is never referenced and default values are used.
*> \endverbatim
*>
*> \param[in,out] PARAMS
*> \verbatim
*> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
*> Specifies algorithm parameters. If an entry is .LT. 0.0, then
*> Specifies algorithm parameters. If an entry is < 0.0, then
*> that entry will be filled with default value used for that
*> parameter. Only positions up to NPARAMS are accessed; defaults
*> are used for higher-numbered parameters.
@ -334,9 +334,9 @@
*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
*> refinement or not.
*> Default: 1.0D+0
*> = 0.0 : No refinement is performed, and no error bounds are
*> = 0.0: No refinement is performed, and no error bounds are
*> computed.
*> = 1.0 : Use the double-precision refinement algorithm,
*> = 1.0: Use the double-precision refinement algorithm,
*> possibly with doubled-single computations if the
*> compilation environment does not support DOUBLE
*> PRECISION.

4
lapack-netlib/SRC/dgesc2.f
View File

@ -90,7 +90,7 @@
*> \verbatim
*> SCALE is DOUBLE PRECISION
*> On exit, SCALE contains the scale factor. SCALE is chosen
*> 0 <= SCALE <= 1 to prevent owerflow in the solution.
*> 0 <= SCALE <= 1 to prevent overflow in the solution.
*> \endverbatim
*
* Authors:
@ -151,7 +151,7 @@
* ..
* .. Executable Statements ..
*
* Set constant to control owerflow
* Set constant to control overflow
*
EPS = DLAMCH( 'P' )
SMLNUM = DLAMCH( 'S' ) / EPS

4
lapack-netlib/SRC/dgesdd.f
View File

@ -322,7 +322,7 @@
*
IF( WNTQN ) THEN
* dbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6)
* keep 7*N for backwards compatability.
* keep 7*N for backwards compatibility.
BDSPAC = 7*N
ELSE
BDSPAC = 3*N*N + 4*N
@ -448,7 +448,7 @@
*
IF( WNTQN ) THEN
* dbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6)
* keep 7*N for backwards compatability.
* keep 7*N for backwards compatibility.
BDSPAC = 7*M
ELSE
BDSPAC = 3*M*M + 4*M

1385
lapack-netlib/SRC/dgesvdq.f Normal file
View File

File diff suppressed because it is too large Load Diff

44
lapack-netlib/SRC/dgesvj.f
View File

@ -90,13 +90,13 @@
*> JOBV is CHARACTER*1
*> Specifies whether to compute the right singular vectors, that
*> is, the matrix V:
*> = 'V' : the matrix V is computed and returned in the array V
*> = 'A' : the Jacobi rotations are applied to the MV-by-N
*> = 'V': the matrix V is computed and returned in the array V
*> = 'A': the Jacobi rotations are applied to the MV-by-N
*> array V. In other words, the right singular vector
*> matrix V is not computed explicitly, instead it is
*> applied to an MV-by-N matrix initially stored in the
*> first MV rows of V.
*> = 'N' : the matrix V is not computed and the array V is not
*> = 'N': the matrix V is not computed and the array V is not
*> referenced
*> \endverbatim
*>
@ -118,8 +118,8 @@
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, the M-by-N matrix A.
*> On exit :
*> If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C' :
*> If INFO .EQ. 0 :
*> If JOBU = 'U' .OR. JOBU = 'C' :
*> If INFO = 0 :
*> RANKA orthonormal columns of U are returned in the
*> leading RANKA columns of the array A. Here RANKA <= N
*> is the number of computed singular values of A that are
@ -129,9 +129,9 @@
*> in the array WORK as RANKA=NINT(WORK(2)). Also see the
*> descriptions of SVA and WORK. The computed columns of U
*> are mutually numerically orthogonal up to approximately
*> TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'),
*> TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU = 'C'),
*> see the description of JOBU.
*> If INFO .GT. 0 :
*> If INFO > 0 :
*> the procedure DGESVJ did not converge in the given number
*> of iterations (sweeps). In that case, the computed
*> columns of U may not be orthogonal up to TOL. The output
@ -140,8 +140,8 @@
*> input matrix A in the sense that the residual
*> ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small.
*>
*> If JOBU .EQ. 'N' :
*> If INFO .EQ. 0 :
*> If JOBU = 'N' :
*> If INFO = 0 :
*> Note that the left singular vectors are 'for free' in the
*> one-sided Jacobi SVD algorithm. However, if only the
*> singular values are needed, the level of numerical
@ -150,7 +150,7 @@
*> numerically orthogonal up to approximately M*EPS. Thus,
*> on exit, A contains the columns of U scaled with the
*> corresponding singular values.
*> If INFO .GT. 0 :
*> If INFO > 0 :
*> the procedure DGESVJ did not converge in the given number
*> of iterations (sweeps).
*> \endverbatim
@ -165,9 +165,9 @@
*> \verbatim
*> SVA is DOUBLE PRECISION array, dimension (N)
*> On exit :
*> If INFO .EQ. 0 :
*> If INFO = 0 :
*> depending on the value SCALE = WORK(1), we have:
*> If SCALE .EQ. ONE :
*> If SCALE = ONE :
*> SVA(1:N) contains the computed singular values of A.
*> During the computation SVA contains the Euclidean column
*> norms of the iterated matrices in the array A.
@ -175,7 +175,7 @@
*> The singular values of A are SCALE*SVA(1:N), and this
*> factored representation is due to the fact that some of the
*> singular values of A might underflow or overflow.
*> If INFO .GT. 0 :
*> If INFO > 0 :
*> the procedure DGESVJ did not converge in the given number of
*> iterations (sweeps) and SCALE*SVA(1:N) may not be accurate.
*> \endverbatim
@ -183,7 +183,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV .EQ. 'A', then the product of Jacobi rotations in DGESVJ
*> If JOBV = 'A', then the product of Jacobi rotations in DGESVJ
*> is applied to the first MV rows of V. See the description of JOBV.
*> \endverbatim
*>
@ -201,16 +201,16 @@
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V, LDV .GE. 1.
*> If JOBV .EQ. 'V', then LDV .GE. max(1,N).
*> If JOBV .EQ. 'A', then LDV .GE. max(1,MV) .
*> The leading dimension of the array V, LDV >= 1.
*> If JOBV = 'V', then LDV >= max(1,N).
*> If JOBV = 'A', then LDV >= max(1,MV) .
*> \endverbatim
*>
*> \param[in,out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> On entry :
*> If JOBU .EQ. 'C' :
*> If JOBU = 'C' :
*> WORK(1) = CTOL, where CTOL defines the threshold for convergence.
*> The process stops if all columns of A are mutually
*> orthogonal up to CTOL*EPS, EPS=DLAMCH('E').
@ -230,7 +230,7 @@
*> WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep.
*> This is useful information in cases when DGESVJ did
*> not converge, as it can be used to estimate whether
*> the output is stil useful and for post festum analysis.
*> the output is still useful and for post festum analysis.
*> WORK(6) = the largest absolute value over all sines of the
*> Jacobi rotation angles in the last sweep. It can be
*> useful for a post festum analysis.
@ -245,9 +245,9 @@
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0 : successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value
*> > 0 : DGESVJ did not converge in the maximal allowed number (30)
*> = 0: successful exit.
*> < 0: if INFO = -i, then the i-th argument had an illegal value
*> > 0: DGESVJ did not converge in the maximal allowed number (30)
*> of sweeps. The output may still be useful. See the
*> description of WORK.
*> \endverbatim

10
lapack-netlib/SRC/dgesvxx.f
View File

@ -411,7 +411,7 @@
*> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most
*> the first (:,N_ERR_BNDS) entries are returned.
*>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@ -447,14 +447,14 @@
*> \param[in] NPARAMS
*> \verbatim
*> NPARAMS is INTEGER
*> Specifies the number of parameters set in PARAMS. If .LE. 0, the
*> Specifies the number of parameters set in PARAMS. If <= 0, the
*> PARAMS array is never referenced and default values are used.
*> \endverbatim
*>
*> \param[in,out] PARAMS
*> \verbatim
*> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
*> Specifies algorithm parameters. If an entry is .LT. 0.0, then
*> Specifies algorithm parameters. If an entry is < 0.0, then
*> that entry will be filled with default value used for that
*> parameter. Only positions up to NPARAMS are accessed; defaults
*> are used for higher-numbered parameters.
@ -462,9 +462,9 @@
*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
*> refinement or not.
*> Default: 1.0D+0
*> = 0.0 : No refinement is performed, and no error bounds are
*> = 0.0: No refinement is performed, and no error bounds are
*> computed.
*> = 1.0 : Use the extra-precise refinement algorithm.
*> = 1.0: Use the extra-precise refinement algorithm.
*> (other values are reserved for future use)
*>
*> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

2
lapack-netlib/SRC/dgetc2.f
View File

@ -85,7 +85,7 @@
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> > 0: if INFO = k, U(k, k) is likely to produce owerflow if
*> > 0: if INFO = k, U(k, k) is likely to produce overflow if
*> we try to solve for x in Ax = b. So U is perturbed to
*> avoid the overflow.
*> \endverbatim

2
lapack-netlib/SRC/dgetsls.f
View File

@ -1,3 +1,5 @@
*> \brief \b DGETSLS
*
* Definition:
* ===========
*

8
lapack-netlib/SRC/dggesx.f
View File

@ -131,10 +131,10 @@
*> \verbatim
*> SENSE is CHARACTER*1
*> Determines which reciprocal condition numbers are computed.
*> = 'N' : None are computed;
*> = 'E' : Computed for average of selected eigenvalues only;
*> = 'V' : Computed for selected deflating subspaces only;
*> = 'B' : Computed for both.
*> = 'N': None are computed;
*> = 'E': Computed for average of selected eigenvalues only;
*> = 'V': Computed for selected deflating subspaces only;
*> = 'B': Computed for both.
*> If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
*> \endverbatim
*>

20
lapack-netlib/SRC/dgsvj0.f
View File

@ -117,7 +117,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -125,9 +125,9 @@
*> \param[in,out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV,N)
*> If JOBV .EQ. 'V' then N rows of V are post-multipled by a
*> If JOBV = 'V' then N rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim
@ -136,8 +136,8 @@
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V, LDV >= 1.
*> If JOBV = 'V', LDV .GE. N.
*> If JOBV = 'A', LDV .GE. MV.
*> If JOBV = 'V', LDV >= N.
*> If JOBV = 'A', LDV >= MV.
*> \endverbatim
*>
*> \param[in] EPS
@ -157,7 +157,7 @@
*> TOL is DOUBLE PRECISION
*> TOL is the threshold for Jacobi rotations. For a pair
*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
*> applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
*> applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL.
*> \endverbatim
*>
*> \param[in] NSWEEP
@ -175,14 +175,14 @@
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> LWORK is the dimension of WORK. LWORK .GE. M.
*> LWORK is the dimension of WORK. LWORK >= M.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0 : successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value
*> = 0: successful exit.
*> < 0: if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
@ -1045,7 +1045,7 @@
1993 CONTINUE
* end i=1:NSWEEP loop
* #:) Reaching this point means that the procedure has comleted the given
* #:) Reaching this point means that the procedure has completed the given
* number of iterations.
INFO = NSWEEP - 1
GO TO 1995

30
lapack-netlib/SRC/dgsvj1.f
View File

@ -61,7 +61,7 @@
*> In terms of the columns of A, the first N1 columns are rotated 'against'
*> the remaining N-N1 columns, trying to increase the angle between the
*> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is
*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter.
*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parameter.
*> The number of sweeps is given in NSWEEP and the orthogonality threshold
*> is given in TOL.
*> \endverbatim
@ -147,27 +147,27 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
*>
*> \param[in,out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV,N)
*> If JOBV .EQ. 'V' then N rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> If JOBV = 'V', then N rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V, LDV >= 1.
*> If JOBV = 'V', LDV .GE. N.
*> If JOBV = 'A', LDV .GE. MV.
*> If JOBV = 'V', LDV >= N.
*> If JOBV = 'A', LDV >= MV.
*> \endverbatim
*>
*> \param[in] EPS
@ -187,7 +187,7 @@
*> TOL is DOUBLE PRECISION
*> TOL is the threshold for Jacobi rotations. For a pair
*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
*> applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
*> applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL.
*> \endverbatim
*>
*> \param[in] NSWEEP
@ -205,14 +205,14 @@
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> LWORK is the dimension of WORK. LWORK .GE. M.
*> LWORK is the dimension of WORK. LWORK >= M.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0 : successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value
*> = 0: successful exit.
*> < 0: if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim
*
* Authors:

46
lapack-netlib/SRC/dhseqr.f
View File

@ -70,7 +70,7 @@
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix H. N .GE. 0.
*> The order of the matrix H. N >= 0.
*> \endverbatim
*>
*> \param[in] ILO
@ -87,7 +87,7 @@
*> set by a previous call to DGEBAL, and then passed to ZGEHRD
*> when the matrix output by DGEBAL is reduced to Hessenberg
*> form. Otherwise ILO and IHI should be set to 1 and N
*> respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.
*> respectively. If N > 0, then 1 <= ILO <= IHI <= N.
*> If N = 0, then ILO = 1 and IHI = 0.
*> \endverbatim
*>
@ -100,20 +100,20 @@
*> (the Schur form); 2-by-2 diagonal blocks (corresponding to
*> complex conjugate pairs of eigenvalues) are returned in
*> standard form, with H(i,i) = H(i+1,i+1) and
*> H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and JOB = 'E', the
*> H(i+1,i)*H(i,i+1) < 0. If INFO = 0 and JOB = 'E', the
*> contents of H are unspecified on exit. (The output value of
*> H when INFO.GT.0 is given under the description of INFO
*> H when INFO > 0 is given under the description of INFO
*> below.)
*>
*> Unlike earlier versions of DHSEQR, this subroutine may
*> explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1
*> explicitly H(i,j) = 0 for i > j and j = 1, 2, ... ILO-1
*> or j = IHI+1, IHI+2, ... N.
*> \endverbatim
*>
*> \param[in] LDH
*> \verbatim
*> LDH is INTEGER
*> The leading dimension of the array H. LDH .GE. max(1,N).
*> The leading dimension of the array H. LDH >= max(1,N).
*> \endverbatim
*>
*> \param[out] WR
@ -128,8 +128,8 @@
*> The real and imaginary parts, respectively, of the computed
*> eigenvalues. If two eigenvalues are computed as a complex
*> conjugate pair, they are stored in consecutive elements of
*> WR and WI, say the i-th and (i+1)th, with WI(i) .GT. 0 and
*> WI(i+1) .LT. 0. If JOB = 'S', the eigenvalues are stored in
*> WR and WI, say the i-th and (i+1)th, with WI(i) > 0 and
*> WI(i+1) < 0. If JOB = 'S', the eigenvalues are stored in
*> the same order as on the diagonal of the Schur form returned
*> in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2
*> diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and
@ -148,7 +148,7 @@
*> if INFO = 0, Z contains Q*Z.
*> Normally Q is the orthogonal matrix generated by DORGHR
*> after the call to DGEHRD which formed the Hessenberg matrix
*> H. (The output value of Z when INFO.GT.0 is given under
*> H. (The output value of Z when INFO > 0 is given under
*> the description of INFO below.)
*> \endverbatim
*>
@ -156,7 +156,7 @@
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of the array Z. if COMPZ = 'I' or
*> COMPZ = 'V', then LDZ.GE.MAX(1,N). Otherwize, LDZ.GE.1.
*> COMPZ = 'V', then LDZ >= MAX(1,N). Otherwise, LDZ >= 1.
*> \endverbatim
*>
*> \param[out] WORK
@ -169,7 +169,7 @@
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK. LWORK .GE. max(1,N)
*> The dimension of the array WORK. LWORK >= max(1,N)
*> is sufficient and delivers very good and sometimes
*> optimal performance. However, LWORK as large as 11*N
*> may be required for optimal performance. A workspace
@ -187,21 +187,21 @@
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> .LT. 0: if INFO = -i, the i-th argument had an illegal
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal
*> value
*> .GT. 0: if INFO = i, DHSEQR failed to compute all of
*> > 0: if INFO = i, DHSEQR failed to compute all of
*> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR
*> and WI contain those eigenvalues which have been
*> successfully computed. (Failures are rare.)
*>
*> If INFO .GT. 0 and JOB = 'E', then on exit, the
*> If INFO > 0 and JOB = 'E', then on exit, the
*> remaining unconverged eigenvalues are the eigen-
*> values of the upper Hessenberg matrix rows and
*> columns ILO through INFO of the final, output
*> value of H.
*>
*> If INFO .GT. 0 and JOB = 'S', then on exit
*> If INFO > 0 and JOB = 'S', then on exit
*>
*> (*) (initial value of H)*U = U*(final value of H)
*>
@ -209,19 +209,19 @@
*> value of H is upper Hessenberg and quasi-triangular
*> in rows and columns INFO+1 through IHI.
*>
*> If INFO .GT. 0 and COMPZ = 'V', then on exit
*> If INFO > 0 and COMPZ = 'V', then on exit
*>
*> (final value of Z) = (initial value of Z)*U
*>
*> where U is the orthogonal matrix in (*) (regard-
*> less of the value of JOB.)
*>
*> If INFO .GT. 0 and COMPZ = 'I', then on exit
*> If INFO > 0 and COMPZ = 'I', then on exit
*> (final value of Z) = U
*> where U is the orthogonal matrix in (*) (regard-
*> less of the value of JOB.)
*>
*> If INFO .GT. 0 and COMPZ = 'N', then Z is not
*> If INFO > 0 and COMPZ = 'N', then Z is not
*> accessed.
*> \endverbatim
*
@ -261,8 +261,8 @@
*> This depends on ILO, IHI and NS. NS is the
*> number of simultaneous shifts returned
*> by ILAENV(ISPEC=15). (See ISPEC=15 below.)
*> The default for (IHI-ILO+1).LE.500 is NS.
*> The default for (IHI-ILO+1).GT.500 is 3*NS/2.
*> The default for (IHI-ILO+1) <= 500 is NS.
*> The default for (IHI-ILO+1) > 500 is 3*NS/2.
*>
*> ISPEC=14: Nibble crossover point. (See IPARMQ for
*> details.) Default: 14% of deflation window
@ -341,8 +341,8 @@
PARAMETER ( NTINY = 11 )
*
* ==== NL allocates some local workspace to help small matrices
* . through a rare DLAHQR failure. NL .GT. NTINY = 11 is
* . required and NL .LE. NMIN = ILAENV(ISPEC=12,...) is recom-
* . through a rare DLAHQR failure. NL > NTINY = 11 is
* . required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom-
* . mended. (The default value of NMIN is 75.) Using NL = 49
* . allows up to six simultaneous shifts and a 16-by-16
* . deflation window. ====

4
lapack-netlib/SRC/dla_gbrcond.f
View File

@ -141,13 +141,13 @@
*> i > 0: The ith argument is invalid.
*> \endverbatim
*>
*> \param[in] WORK
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (5*N).
*> Workspace.
*> \endverbatim
*>
*> \param[in] IWORK
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.

12
lapack-netlib/SRC/dla_gbrfsx_extended.f
View File

@ -66,19 +66,19 @@
*> \verbatim
*> PREC_TYPE is INTEGER
*> Specifies the intermediate precision to be used in refinement.
*> The value is defined by ILAPREC(P) where P is a CHARACTER and
*> P = 'S': Single
*> The value is defined by ILAPREC(P) where P is a CHARACTER and P
*> = 'S': Single
*> = 'D': Double
*> = 'I': Indigenous
*> = 'X', 'E': Extra
*> = 'X' or 'E': Extra
*> \endverbatim
*>
*> \param[in] TRANS_TYPE
*> \verbatim
*> TRANS_TYPE is INTEGER
*> Specifies the transposition operation on A.
*> The value is defined by ILATRANS(T) where T is a CHARACTER and
*> T = 'N': No transpose
*> The value is defined by ILATRANS(T) where T is a CHARACTER and T
*> = 'N': No transpose
*> = 'T': Transpose
*> = 'C': Conjugate transpose
*> \endverbatim
@ -270,7 +270,7 @@
*> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most
*> the first (:,N_ERR_BNDS) entries are returned.
*>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

4
lapack-netlib/SRC/dla_gercond.f
View File

@ -123,13 +123,13 @@
*> i > 0: The ith argument is invalid.
*> \endverbatim
*>
*> \param[in] WORK
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (3*N).
*> Workspace.
*> \endverbatim
*>
*> \param[in] IWORK
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.

12
lapack-netlib/SRC/dla_gerfsx_extended.f
View File

@ -64,19 +64,19 @@
*> \verbatim
*> PREC_TYPE is INTEGER
*> Specifies the intermediate precision to be used in refinement.
*> The value is defined by ILAPREC(P) where P is a CHARACTER and
*> P = 'S': Single
*> The value is defined by ILAPREC(P) where P is a CHARACTER and P
*> = 'S': Single
*> = 'D': Double
*> = 'I': Indigenous
*> = 'X', 'E': Extra
*> = 'X' or 'E': Extra
*> \endverbatim
*>
*> \param[in] TRANS_TYPE
*> \verbatim
*> TRANS_TYPE is INTEGER
*> Specifies the transposition operation on A.
*> The value is defined by ILATRANS(T) where T is a CHARACTER and
*> T = 'N': No transpose
*> The value is defined by ILATRANS(T) where T is a CHARACTER and T
*> = 'N': No transpose
*> = 'T': Transpose
*> = 'C': Conjugate transpose
*> \endverbatim
@ -256,7 +256,7 @@
*> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
*> ERRS_C is not accessed. If N_ERR_BNDS .LT. 3, then at most
*> ERRS_C is not accessed. If N_ERR_BNDS < 3, then at most
*> the first (:,N_ERR_BNDS) entries are returned.
*>
*> The first index in ERRS_C(i,:) corresponds to the ith

4
lapack-netlib/SRC/dla_porcond.f
View File

@ -113,13 +113,13 @@
*> i > 0: The ith argument is invalid.
*> \endverbatim
*>
*> \param[in] WORK
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (3*N).
*> Workspace.
*> \endverbatim
*>
*> \param[in] IWORK
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.

8
lapack-netlib/SRC/dla_porfsx_extended.f
View File

@ -65,11 +65,11 @@
*> \verbatim
*> PREC_TYPE is INTEGER
*> Specifies the intermediate precision to be used in refinement.
*> The value is defined by ILAPREC(P) where P is a CHARACTER and
*> P = 'S': Single
*> The value is defined by ILAPREC(P) where P is a CHARACTER and P
*> = 'S': Single
*> = 'D': Double
*> = 'I': Indigenous
*> = 'X', 'E': Extra
*> = 'X' or 'E': Extra
*> \endverbatim
*>
*> \param[in] UPLO
@ -246,7 +246,7 @@
*> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most
*> the first (:,N_ERR_BNDS) entries are returned.
*>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

2
lapack-netlib/SRC/dla_porpvgrw.f
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@ -85,7 +85,7 @@
*> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim
*>
*> \param[in] WORK
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (2*N)
*> \endverbatim

4
lapack-netlib/SRC/dla_syrcond.f
View File

@ -119,13 +119,13 @@
*> i > 0: The ith argument is invalid.
*> \endverbatim
*>
*> \param[in] WORK
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (3*N).
*> Workspace.
*> \endverbatim
*>
*> \param[in] IWORK
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.

8
lapack-netlib/SRC/dla_syrfsx_extended.f
View File

@ -67,11 +67,11 @@
*> \verbatim
*> PREC_TYPE is INTEGER
*> Specifies the intermediate precision to be used in refinement.
*> The value is defined by ILAPREC(P) where P is a CHARACTER and
*> P = 'S': Single
*> The value is defined by ILAPREC(P) where P is a CHARACTER and P
*> = 'S': Single
*> = 'D': Double
*> = 'I': Indigenous
*> = 'X', 'E': Extra
*> = 'X' or 'E': Extra
*> \endverbatim
*>
*> \param[in] UPLO
@ -255,7 +255,7 @@
*> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most
*> the first (:,N_ERR_BNDS) entries are returned.
*>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

2
lapack-netlib/SRC/dla_syrpvgrw.f
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@ -101,7 +101,7 @@
*> as determined by DSYTRF.
*> \endverbatim
*>
*> \param[in] WORK
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (2*N)
*> \endverbatim

2
lapack-netlib/SRC/dla_wwaddw.f
View File

@ -36,7 +36,7 @@
*> DLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
*>
*> This works for all extant IBM's hex and binary floating point
*> arithmetics, but not for decimal.
*> arithmetic, but not for decimal.
*> \endverbatim
*
* Arguments: