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Update LAPACK to 3.9.0

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Martin Kroeker 2019-12-29 22:25:25 +01:00 committed by GitHub
parent 90f316e888
commit 252b075870
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44 changed files with 306 additions and 276 deletions
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46
lapack-netlib/SRC/cgesvj.f
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@ -89,12 +89,12 @@
*> Specifies whether to compute the right singular vectors, that *> Specifies whether to compute the right singular vectors, that
*> is, the matrix V: *> is, the matrix V:
*> = 'V' or 'J': the matrix V is computed and returned in the array V *> = 'V' or 'J': the matrix V is computed and returned in the array V
*> = 'A' : the Jacobi rotations are applied to the MV-by-N *> = 'A': the Jacobi rotations are applied to the MV-by-N
*> array V. In other words, the right singular vector *> array V. In other words, the right singular vector
*> matrix V is not computed explicitly; instead it is *> matrix V is not computed explicitly; instead it is
*> applied to an MV-by-N matrix initially stored in the *> applied to an MV-by-N matrix initially stored in the
*> first MV rows of V. *> 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 *> referenced
*> \endverbatim *> \endverbatim
*> *>
@ -116,8 +116,8 @@
*> A is COMPLEX array, dimension (LDA,N) *> A is COMPLEX array, dimension (LDA,N)
*> On entry, the M-by-N matrix A. *> On entry, the M-by-N matrix A.
*> On exit, *> On exit,
*> If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C': *> If JOBU = 'U' .OR. JOBU = 'C':
*> If INFO .EQ. 0 : *> If INFO = 0 :
*> RANKA orthonormal columns of U are returned in the *> RANKA orthonormal columns of U are returned in the
*> leading RANKA columns of the array A. Here RANKA <= N *> leading RANKA columns of the array A. Here RANKA <= N
*> is the number of computed singular values of A that are *> is the number of computed singular values of A that are
@ -127,9 +127,9 @@
*> in the array RWORK as RANKA=NINT(RWORK(2)). Also see the *> in the array RWORK as RANKA=NINT(RWORK(2)). Also see the
*> descriptions of SVA and RWORK. The computed columns of U *> descriptions of SVA and RWORK. The computed columns of U
*> are mutually numerically orthogonal up to approximately *> are mutually numerically orthogonal up to approximately
*> TOL=SQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'), *> TOL=SQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU = 'C'),
*> see the description of JOBU. *> see the description of JOBU.
*> If INFO .GT. 0, *> If INFO > 0,
*> the procedure CGESVJ did not converge in the given number *> the procedure CGESVJ did not converge in the given number
*> of iterations (sweeps). In that case, the computed *> of iterations (sweeps). In that case, the computed
*> columns of U may not be orthogonal up to TOL. The output *> columns of U may not be orthogonal up to TOL. The output
@ -137,8 +137,8 @@
*> values in SVA(1:N)) and V is still a decomposition of the *> values in SVA(1:N)) and V is still a decomposition of the
*> input matrix A in the sense that the residual *> input matrix A in the sense that the residual
*> || A - SCALE * U * SIGMA * V^* ||_2 / ||A||_2 is small. *> || A - SCALE * U * SIGMA * V^* ||_2 / ||A||_2 is small.
*> If JOBU .EQ. 'N': *> If JOBU = 'N':
*> If INFO .EQ. 0 : *> If INFO = 0 :
*> Note that the left singular vectors are 'for free' in the *> Note that the left singular vectors are 'for free' in the
*> one-sided Jacobi SVD algorithm. However, if only the *> one-sided Jacobi SVD algorithm. However, if only the
*> singular values are needed, the level of numerical *> singular values are needed, the level of numerical
@ -147,7 +147,7 @@
*> numerically orthogonal up to approximately M*EPS. Thus, *> numerically orthogonal up to approximately M*EPS. Thus,
*> on exit, A contains the columns of U scaled with the *> on exit, A contains the columns of U scaled with the
*> corresponding singular values. *> corresponding singular values.
*> If INFO .GT. 0 : *> If INFO > 0 :
*> the procedure CGESVJ did not converge in the given number *> the procedure CGESVJ did not converge in the given number
*> of iterations (sweeps). *> of iterations (sweeps).
*> \endverbatim *> \endverbatim
@ -162,9 +162,9 @@
*> \verbatim *> \verbatim
*> SVA is REAL array, dimension (N) *> SVA is REAL array, dimension (N)
*> On exit, *> On exit,
*> If INFO .EQ. 0 : *> If INFO = 0 :
*> depending on the value SCALE = RWORK(1), we have: *> depending on the value SCALE = RWORK(1), we have:
*> If SCALE .EQ. ONE: *> If SCALE = ONE:
*> SVA(1:N) contains the computed singular values of A. *> SVA(1:N) contains the computed singular values of A.
*> During the computation SVA contains the Euclidean column *> During the computation SVA contains the Euclidean column
*> norms of the iterated matrices in the array A. *> norms of the iterated matrices in the array A.
@ -173,7 +173,7 @@
*> factored representation is due to the fact that some of the *> factored representation is due to the fact that some of the
*> singular values of A might underflow or overflow. *> singular values of A might underflow or overflow.
*> *>
*> If INFO .GT. 0 : *> If INFO > 0 :
*> the procedure CGESVJ did not converge in the given number of *> the procedure CGESVJ did not converge in the given number of
*> iterations (sweeps) and SCALE*SVA(1:N) may not be accurate. *> iterations (sweeps) and SCALE*SVA(1:N) may not be accurate.
*> \endverbatim *> \endverbatim
@ -181,7 +181,7 @@
*> \param[in] MV *> \param[in] MV
*> \verbatim *> \verbatim
*> MV is INTEGER *> MV is INTEGER
*> If JOBV .EQ. 'A', then the product of Jacobi rotations in CGESVJ *> If JOBV = 'A', then the product of Jacobi rotations in CGESVJ
*> is applied to the first MV rows of V. See the description of JOBV. *> is applied to the first MV rows of V. See the description of JOBV.
*> \endverbatim *> \endverbatim
*> *>
@ -199,16 +199,16 @@
*> \param[in] LDV *> \param[in] LDV
*> \verbatim *> \verbatim
*> LDV is INTEGER *> LDV is INTEGER
*> The leading dimension of the array V, LDV .GE. 1. *> The leading dimension of the array V, LDV >= 1.
*> If JOBV .EQ. 'V', then LDV .GE. max(1,N). *> If JOBV = 'V', then LDV >= max(1,N).
*> If JOBV .EQ. 'A', then LDV .GE. max(1,MV) . *> If JOBV = 'A', then LDV >= max(1,MV) .
*> \endverbatim *> \endverbatim
*> *>
*> \param[in,out] CWORK *> \param[in,out] CWORK
*> \verbatim *> \verbatim
*> CWORK is COMPLEX array, dimension (max(1,LWORK)) *> CWORK is COMPLEX array, dimension (max(1,LWORK))
*> Used as workspace. *> Used as workspace.
*> If on entry LWORK .EQ. -1, then a workspace query is assumed and *> If on entry LWORK = -1, then a workspace query is assumed and
*> no computation is done; CWORK(1) is set to the minial (and optimal) *> no computation is done; CWORK(1) is set to the minial (and optimal)
*> length of CWORK. *> length of CWORK.
*> \endverbatim *> \endverbatim
@ -223,7 +223,7 @@
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (max(6,LRWORK)) *> RWORK is REAL array, dimension (max(6,LRWORK))
*> On entry, *> On entry,
*> If JOBU .EQ. 'C' : *> If JOBU = 'C' :
*> RWORK(1) = CTOL, where CTOL defines the threshold for convergence. *> RWORK(1) = CTOL, where CTOL defines the threshold for convergence.
*> The process stops if all columns of A are mutually *> The process stops if all columns of A are mutually
*> orthogonal up to CTOL*EPS, EPS=SLAMCH('E'). *> orthogonal up to CTOL*EPS, EPS=SLAMCH('E').
@ -243,11 +243,11 @@
*> RWORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep. *> RWORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep.
*> This is useful information in cases when CGESVJ did *> This is useful information in cases when CGESVJ did
*> not converge, as it can be used to estimate whether *> 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.
*> RWORK(6) = the largest absolute value over all sines of the *> RWORK(6) = the largest absolute value over all sines of the
*> Jacobi rotation angles in the last sweep. It can be *> Jacobi rotation angles in the last sweep. It can be
*> useful for a post festum analysis. *> useful for a post festum analysis.
*> If on entry LRWORK .EQ. -1, then a workspace query is assumed and *> If on entry LRWORK = -1, then a workspace query is assumed and
*> no computation is done; RWORK(1) is set to the minial (and optimal) *> no computation is done; RWORK(1) is set to the minial (and optimal)
*> length of RWORK. *> length of RWORK.
*> \endverbatim *> \endverbatim
@ -261,9 +261,9 @@
*> \param[out] INFO *> \param[out] INFO
*> \verbatim *> \verbatim
*> INFO is INTEGER *> INFO is INTEGER
*> = 0 : successful exit. *> = 0: successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value *> < 0: if INFO = -i, then the i-th argument had an illegal value
*> > 0 : CGESVJ did not converge in the maximal allowed number *> > 0: CGESVJ did not converge in the maximal allowed number
*> (NSWEEP=30) of sweeps. The output may still be useful. *> (NSWEEP=30) of sweeps. The output may still be useful.
*> See the description of RWORK. *> See the description of RWORK.
*> \endverbatim *> \endverbatim

10
lapack-netlib/SRC/cgesvxx.f
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@ -411,7 +411,7 @@
*> information as described below. There currently are up to three *> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If *> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> 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 (:,N_ERR_BNDS) entries are returned.
*> *>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@ -447,14 +447,14 @@
*> \param[in] NPARAMS *> \param[in] NPARAMS
*> \verbatim *> \verbatim
*> NPARAMS is INTEGER *> 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. *> PARAMS array is never referenced and default values are used.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in,out] PARAMS *> \param[in,out] PARAMS
*> \verbatim *> \verbatim
*> PARAMS is REAL array, dimension NPARAMS *> PARAMS is REAL 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 *> that entry will be filled with default value used for that
*> parameter. Only positions up to NPARAMS are accessed; defaults *> parameter. Only positions up to NPARAMS are accessed; defaults
*> are used for higher-numbered parameters. *> are used for higher-numbered parameters.
@ -462,9 +462,9 @@
*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
*> refinement or not. *> refinement or not.
*> Default: 1.0 *> Default: 1.0
*> = 0.0 : No refinement is performed, and no error bounds are *> = 0.0: No refinement is performed, and no error bounds are
*> computed. *> computed.
*> = 1.0 : Use the double-precision refinement algorithm, *> = 1.0: Use the double-precision refinement algorithm,
*> possibly with doubled-single computations if the *> possibly with doubled-single computations if the
*> compilation environment does not support DOUBLE *> compilation environment does not support DOUBLE
*> PRECISION. *> PRECISION.

2
lapack-netlib/SRC/cgetsls.f
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@ -1,3 +1,5 @@
*> \brief \b CGETSLS
*
* Definition: * Definition:
* =========== * ===========
* *

8
lapack-netlib/SRC/cggesx.f
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@ -120,10 +120,10 @@
*> \verbatim *> \verbatim
*> SENSE is CHARACTER*1 *> SENSE is CHARACTER*1
*> Determines which reciprocal condition numbers are computed. *> Determines which reciprocal condition numbers are computed.
*> = 'N' : None are computed; *> = 'N': None are computed;
*> = 'E' : Computed for average of selected eigenvalues only; *> = 'E': Computed for average of selected eigenvalues only;
*> = 'V' : Computed for selected deflating subspaces only; *> = 'V': Computed for selected deflating subspaces only;
*> = 'B' : Computed for both. *> = 'B': Computed for both.
*> If SENSE = 'E', 'V', or 'B', SORT must equal 'S'. *> If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
*> \endverbatim *> \endverbatim
*> *>

18
lapack-netlib/SRC/cgsvj0.f
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@ -117,7 +117,7 @@
*> \param[in] MV *> \param[in] MV
*> \verbatim *> \verbatim
*> MV is INTEGER *> 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. *> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced. *> If JOBV = 'N', then MV is not referenced.
*> \endverbatim *> \endverbatim
@ -125,9 +125,9 @@
*> \param[in,out] V *> \param[in,out] V
*> \verbatim *> \verbatim
*> V is COMPLEX array, dimension (LDV,N) *> V is COMPLEX 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. *> 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. *> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced. *> If JOBV = 'N', then V is not referenced.
*> \endverbatim *> \endverbatim
@ -136,8 +136,8 @@
*> \verbatim *> \verbatim
*> LDV is INTEGER *> LDV is INTEGER
*> The leading dimension of the array V, LDV >= 1. *> The leading dimension of the array V, LDV >= 1.
*> If JOBV = 'V', LDV .GE. N. *> If JOBV = 'V', LDV >= N.
*> If JOBV = 'A', LDV .GE. MV. *> If JOBV = 'A', LDV >= MV.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] EPS *> \param[in] EPS
@ -157,7 +157,7 @@
*> TOL is REAL *> TOL is REAL
*> TOL is the threshold for Jacobi rotations. For a pair *> TOL is the threshold for Jacobi rotations. For a pair
*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is *> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
*> applied only if ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL. *> applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] NSWEEP *> \param[in] NSWEEP
@ -175,14 +175,14 @@
*> \param[in] LWORK *> \param[in] LWORK
*> \verbatim *> \verbatim
*> LWORK is INTEGER *> LWORK is INTEGER
*> LWORK is the dimension of WORK. LWORK .GE. M. *> LWORK is the dimension of WORK. LWORK >= M.
*> \endverbatim *> \endverbatim
*> *>
*> \param[out] INFO *> \param[out] INFO
*> \verbatim *> \verbatim
*> INFO is INTEGER *> INFO is INTEGER
*> = 0 : successful exit. *> = 0: successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value *> < 0: if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim *> \endverbatim
* *
* Authors: * Authors:

20
lapack-netlib/SRC/cgsvj1.f
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@ -61,7 +61,7 @@
*> In terms of the columns of A, the first N1 columns are rotated 'against' *> 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 *> 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 *> 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 *> The number of sweeps is given in NSWEEP and the orthogonality threshold
*> is given in TOL. *> is given in TOL.
*> \endverbatim *> \endverbatim
@ -147,7 +147,7 @@
*> \param[in] MV *> \param[in] MV
*> \verbatim *> \verbatim
*> MV is INTEGER *> 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. *> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced. *> If JOBV = 'N', then MV is not referenced.
*> \endverbatim *> \endverbatim
@ -155,9 +155,9 @@
*> \param[in,out] V *> \param[in,out] V
*> \verbatim *> \verbatim
*> V is COMPLEX array, dimension (LDV,N) *> V is COMPLEX 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. *> 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. *> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced. *> If JOBV = 'N', then V is not referenced.
*> \endverbatim *> \endverbatim
@ -166,8 +166,8 @@
*> \verbatim *> \verbatim
*> LDV is INTEGER *> LDV is INTEGER
*> The leading dimension of the array V, LDV >= 1. *> The leading dimension of the array V, LDV >= 1.
*> If JOBV = 'V', LDV .GE. N. *> If JOBV = 'V', LDV >= N.
*> If JOBV = 'A', LDV .GE. MV. *> If JOBV = 'A', LDV >= MV.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] EPS *> \param[in] EPS
@ -187,7 +187,7 @@
*> TOL is REAL *> TOL is REAL
*> TOL is the threshold for Jacobi rotations. For a pair *> TOL is the threshold for Jacobi rotations. For a pair
*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is *> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
*> applied only if ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL. *> applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] NSWEEP *> \param[in] NSWEEP
@ -205,14 +205,14 @@
*> \param[in] LWORK *> \param[in] LWORK
*> \verbatim *> \verbatim
*> LWORK is INTEGER *> LWORK is INTEGER
*> LWORK is the dimension of WORK. LWORK .GE. M. *> LWORK is the dimension of WORK. LWORK >= M.
*> \endverbatim *> \endverbatim
*> *>
*> \param[out] INFO *> \param[out] INFO
*> \verbatim *> \verbatim
*> INFO is INTEGER *> INFO is INTEGER
*> = 0 : successful exit. *> = 0: successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value *> < 0: if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim *> \endverbatim
* *
* Authors: * Authors:

2
lapack-netlib/SRC/chb2st_kernels.f
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@ -124,7 +124,7 @@
*> LDVT is INTEGER. *> LDVT is INTEGER.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array. Workspace of size nb. *> WORK is COMPLEX array. Workspace of size nb.
*> \endverbatim *> \endverbatim

9
lapack-netlib/SRC/checon_3.f
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@ -19,7 +19,7 @@
* =========== * ===========
* *
* SUBROUTINE CHECON_3( UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, * SUBROUTINE CHECON_3( UPLO, N, A, LDA, E, IPIV, ANORM, RCOND,
* WORK, IWORK, INFO ) * WORK, INFO )
* *
* .. Scalar Arguments .. * .. Scalar Arguments ..
* CHARACTER UPLO * CHARACTER UPLO
@ -27,7 +27,7 @@
* REAL ANORM, RCOND * REAL ANORM, RCOND
* .. * ..
* .. Array Arguments .. * .. Array Arguments ..
* INTEGER IPIV( * ), IWORK( * ) * INTEGER IPIV( * )
* COMPLEX A( LDA, * ), E ( * ), WORK( * ) * COMPLEX A( LDA, * ), E ( * ), WORK( * )
* .. * ..
* *
@ -129,11 +129,6 @@
*> WORK is COMPLEX array, dimension (2*N) *> WORK is COMPLEX array, dimension (2*N)
*> \endverbatim *> \endverbatim
*> *>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO *> \param[out] INFO
*> \verbatim *> \verbatim
*> INFO is INTEGER *> INFO is INTEGER

2
lapack-netlib/SRC/cheevr.f
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@ -210,7 +210,7 @@
*> eigenvalues are computed to high relative accuracy when *> eigenvalues are computed to high relative accuracy when
*> possible in future releases. The current code does not *> possible in future releases. The current code does not
*> make any guarantees about high relative accuracy, but *> make any guarantees about high relative accuracy, but
*> furutre releases will. See J. Barlow and J. Demmel, *> future releases will. See J. Barlow and J. Demmel,
*> "Computing Accurate Eigensystems of Scaled Diagonally *> "Computing Accurate Eigensystems of Scaled Diagonally
*> Dominant Matrices", LAPACK Working Note #7, for a discussion *> Dominant Matrices", LAPACK Working Note #7, for a discussion
*> of which matrices define their eigenvalues to high relative *> of which matrices define their eigenvalues to high relative

2
lapack-netlib/SRC/cheevr_2stage.f
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@ -217,7 +217,7 @@
*> eigenvalues are computed to high relative accuracy when *> eigenvalues are computed to high relative accuracy when
*> possible in future releases. The current code does not *> possible in future releases. The current code does not
*> make any guarantees about high relative accuracy, but *> make any guarantees about high relative accuracy, but
*> furutre releases will. See J. Barlow and J. Demmel, *> future releases will. See J. Barlow and J. Demmel,
*> "Computing Accurate Eigensystems of Scaled Diagonally *> "Computing Accurate Eigensystems of Scaled Diagonally
*> Dominant Matrices", LAPACK Working Note #7, for a discussion *> Dominant Matrices", LAPACK Working Note #7, for a discussion
*> of which matrices define their eigenvalues to high relative *> of which matrices define their eigenvalues to high relative

1
lapack-netlib/SRC/chegs2.f
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@ -97,6 +97,7 @@
*> B is COMPLEX array, dimension (LDB,N) *> B is COMPLEX array, dimension (LDB,N)
*> The triangular factor from the Cholesky factorization of B, *> The triangular factor from the Cholesky factorization of B,
*> as returned by CPOTRF. *> as returned by CPOTRF.
*> B is modified by the routine but restored on exit.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] LDB *> \param[in] LDB

1
lapack-netlib/SRC/chegst.f
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@ -97,6 +97,7 @@
*> B is COMPLEX array, dimension (LDB,N) *> B is COMPLEX array, dimension (LDB,N)
*> The triangular factor from the Cholesky factorization of B, *> The triangular factor from the Cholesky factorization of B,
*> as returned by CPOTRF. *> as returned by CPOTRF.
*> B is modified by the routine but restored on exit.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] LDB *> \param[in] LDB

12
lapack-netlib/SRC/cherfsx.f
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@ -102,7 +102,7 @@
*> \param[in] A *> \param[in] A
*> \verbatim *> \verbatim
*> A is COMPLEX array, dimension (LDA,N) *> A is COMPLEX array, dimension (LDA,N)
*> The symmetric matrix A. If UPLO = 'U', the leading N-by-N *> The Hermitian matrix A. If UPLO = 'U', the leading N-by-N
*> upper triangular part of A contains the upper triangular *> upper triangular part of A contains the upper triangular
*> part of the matrix A, and the strictly lower triangular *> part of the matrix A, and the strictly lower triangular
*> part of A is not referenced. If UPLO = 'L', the leading *> part of A is not referenced. If UPLO = 'L', the leading
@ -270,7 +270,7 @@
*> information as described below. There currently are up to three *> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If *> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> 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 (:,N_ERR_BNDS) entries are returned.
*> *>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@ -306,14 +306,14 @@
*> \param[in] NPARAMS *> \param[in] NPARAMS
*> \verbatim *> \verbatim
*> NPARAMS is INTEGER *> 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. *> PARAMS array is never referenced and default values are used.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in,out] PARAMS *> \param[in,out] PARAMS
*> \verbatim *> \verbatim
*> PARAMS is REAL array, dimension NPARAMS *> PARAMS is REAL 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 *> that entry will be filled with default value used for that
*> parameter. Only positions up to NPARAMS are accessed; defaults *> parameter. Only positions up to NPARAMS are accessed; defaults
*> are used for higher-numbered parameters. *> are used for higher-numbered parameters.
@ -321,9 +321,9 @@
*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
*> refinement or not. *> refinement or not.
*> Default: 1.0 *> Default: 1.0
*> = 0.0 : No refinement is performed, and no error bounds are *> = 0.0: No refinement is performed, and no error bounds are
*> computed. *> computed.
*> = 1.0 : Use the double-precision refinement algorithm, *> = 1.0: Use the double-precision refinement algorithm,
*> possibly with doubled-single computations if the *> possibly with doubled-single computations if the
*> compilation environment does not support DOUBLE *> compilation environment does not support DOUBLE
*> PRECISION. *> PRECISION.

6
lapack-netlib/SRC/chesv_aa.f
View File

@ -42,7 +42,7 @@
*> matrices. *> matrices.
*> *>
*> Aasen's algorithm is used to factor A as *> Aasen's algorithm is used to factor A as
*> A = U * T * U**H, if UPLO = 'U', or *> A = U**H * T * U, if UPLO = 'U', or
*> A = L * T * L**H, if UPLO = 'L', *> A = L * T * L**H, if UPLO = 'L',
*> where U (or L) is a product of permutation and unit upper (lower) *> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and T is Hermitian and tridiagonal. The factored form *> triangular matrices, and T is Hermitian and tridiagonal. The factored form
@ -86,7 +86,7 @@
*> *>
*> On exit, if INFO = 0, the tridiagonal matrix T and the *> On exit, if INFO = 0, the tridiagonal matrix T and the
*> multipliers used to obtain the factor U or L from the *> multipliers used to obtain the factor U or L from the
*> factorization A = U*T*U**H or A = L*T*L**H as computed by *> factorization A = U**H*T*U or A = L*T*L**H as computed by
*> CHETRF_AA. *> CHETRF_AA.
*> \endverbatim *> \endverbatim
*> *>
@ -230,7 +230,7 @@
RETURN RETURN
END IF END IF
* *
* Compute the factorization A = U*T*U**H or A = L*T*L**H. * Compute the factorization A = U**H*T*U or A = L*T*L**H.
* *
CALL CHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) CALL CHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
IF( INFO.EQ.0 ) THEN IF( INFO.EQ.0 ) THEN

4
lapack-netlib/SRC/chesv_aa_2stage.f
View File

@ -43,7 +43,7 @@
*> matrices. *> matrices.
*> *>
*> Aasen's 2-stage algorithm is used to factor A as *> Aasen's 2-stage algorithm is used to factor A as
*> A = U * T * U**H, if UPLO = 'U', or *> A = U**H * T * U, if UPLO = 'U', or
*> A = L * T * L**H, if UPLO = 'L', *> A = L * T * L**H, if UPLO = 'L',
*> where U (or L) is a product of permutation and unit upper (lower) *> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and T is Hermitian and band. The matrix T is *> triangular matrices, and T is Hermitian and band. The matrix T is
@ -257,7 +257,7 @@
END IF END IF
* *
* *
* Compute the factorization A = U*T*U**H or A = L*T*L**H. * Compute the factorization A = U**H*T*U or A = L*T*L**H.
* *
CALL CHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, CALL CHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,
$ WORK, LWORK, INFO ) $ WORK, LWORK, INFO )

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

@ -46,7 +46,7 @@
*> *>
*> CHESVXX uses the diagonal pivoting factorization to compute the *> CHESVXX uses the diagonal pivoting factorization to compute the
*> solution to a complex system of linear equations A * X = B, where *> solution to a complex system of linear equations A * X = B, where
*> A is an N-by-N symmetric matrix and X and B are N-by-NRHS *> A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
*> matrices. *> matrices.
*> *>
*> If requested, both normwise and maximum componentwise error bounds *> If requested, both normwise and maximum componentwise error bounds
@ -88,7 +88,7 @@
*> A = L * D * L**T, if UPLO = 'L', *> A = L * D * L**T, if UPLO = 'L',
*> *>
*> where U (or L) is a product of permutation and unit upper (lower) *> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is symmetric and block diagonal with *> triangular matrices, and D is Hermitian and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks. *> 1-by-1 and 2-by-2 diagonal blocks.
*> *>
*> 3. If some D(i,i)=0, so that D is exactly singular, then the *> 3. If some D(i,i)=0, so that D is exactly singular, then the
@ -161,7 +161,7 @@
*> \param[in,out] A *> \param[in,out] A
*> \verbatim *> \verbatim
*> A is COMPLEX array, dimension (LDA,N) *> A is COMPLEX array, dimension (LDA,N)
*> The symmetric matrix A. If UPLO = 'U', the leading N-by-N *> The Hermitian matrix A. If UPLO = 'U', the leading N-by-N
*> upper triangular part of A contains the upper triangular *> upper triangular part of A contains the upper triangular
*> part of the matrix A, and the strictly lower triangular *> part of the matrix A, and the strictly lower triangular
*> part of A is not referenced. If UPLO = 'L', the leading *> part of A is not referenced. If UPLO = 'L', the leading
@ -378,7 +378,7 @@
*> information as described below. There currently are up to three *> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If *> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> 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 (:,N_ERR_BNDS) entries are returned.
*> *>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@ -414,14 +414,14 @@
*> \param[in] NPARAMS *> \param[in] NPARAMS
*> \verbatim *> \verbatim
*> NPARAMS is INTEGER *> 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. *> PARAMS array is never referenced and default values are used.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in,out] PARAMS *> \param[in,out] PARAMS
*> \verbatim *> \verbatim
*> PARAMS is REAL array, dimension NPARAMS *> PARAMS is REAL 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 *> that entry will be filled with default value used for that
*> parameter. Only positions up to NPARAMS are accessed; defaults *> parameter. Only positions up to NPARAMS are accessed; defaults
*> are used for higher-numbered parameters. *> are used for higher-numbered parameters.
@ -429,9 +429,9 @@
*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
*> refinement or not. *> refinement or not.
*> Default: 1.0 *> Default: 1.0
*> = 0.0 : No refinement is performed, and no error bounds are *> = 0.0: No refinement is performed, and no error bounds are
*> computed. *> computed.
*> = 1.0 : Use the double-precision refinement algorithm, *> = 1.0: Use the double-precision refinement algorithm,
*> possibly with doubled-single computations if the *> possibly with doubled-single computations if the
*> compilation environment does not support DOUBLE *> compilation environment does not support DOUBLE
*> PRECISION. *> PRECISION.

4
lapack-netlib/SRC/chetf2_rk.f
View File

@ -322,7 +322,7 @@
* *
* Factorize A as U*D*U**H using the upper triangle of A * Factorize A as U*D*U**H using the upper triangle of A
* *
* Initilize the first entry of array E, where superdiagonal * Initialize the first entry of array E, where superdiagonal
* elements of D are stored * elements of D are stored
* *
E( 1 ) = CZERO E( 1 ) = CZERO
@ -676,7 +676,7 @@
* *
* Factorize A as L*D*L**H using the lower triangle of A * Factorize A as L*D*L**H using the lower triangle of A
* *
* Initilize the unused last entry of the subdiagonal array E. * Initialize the unused last entry of the subdiagonal array E.
* *
E( N ) = CZERO E( N ) = CZERO
* *

13
lapack-netlib/SRC/chetrd_2stage.f
View File

@ -123,23 +123,22 @@
*> *>
*> \param[out] HOUS2 *> \param[out] HOUS2
*> \verbatim *> \verbatim
*> HOUS2 is COMPLEX array, dimension LHOUS2, that *> HOUS2 is COMPLEX array, dimension (LHOUS2)
*> store the Householder representation of the stage2 *> Stores the Householder representation of the stage2
*> band to tridiagonal. *> band to tridiagonal.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] LHOUS2 *> \param[in] LHOUS2
*> \verbatim *> \verbatim
*> LHOUS2 is INTEGER *> LHOUS2 is INTEGER
*> The dimension of the array HOUS2. LHOUS2 = MAX(1, dimension) *> The dimension of the array HOUS2.
*> If LWORK = -1, or LHOUS2=-1, *> If LWORK = -1, or LHOUS2=-1,
*> then a query is assumed; the routine *> then a query is assumed; the routine
*> only calculates the optimal size of the HOUS2 array, returns *> only calculates the optimal size of the HOUS2 array, returns
*> this value as the first entry of the HOUS2 array, and no error *> this value as the first entry of the HOUS2 array, and no error
*> message related to LHOUS2 is issued by XERBLA. *> message related to LHOUS2 is issued by XERBLA.
*> LHOUS2 = MAX(1, dimension) where *> If VECT='N', LHOUS2 = max(1, 4*n);
*> dimension = 4*N if VECT='N' *> if VECT='V', option not yet available.
*> not available now if VECT='H'
*> \endverbatim *> \endverbatim
*> *>
*> \param[out] WORK *> \param[out] WORK
@ -151,7 +150,7 @@
*> \verbatim *> \verbatim
*> LWORK is INTEGER *> LWORK is INTEGER
*> The dimension of the array WORK. LWORK = MAX(1, dimension) *> The dimension of the array WORK. LWORK = MAX(1, dimension)
*> If LWORK = -1, or LHOUS2=-1, *> If LWORK = -1, or LHOUS2 = -1,
*> then a workspace query is assumed; the routine *> then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns *> only calculates the optimal size of the WORK array, returns
*> this value as the first entry of the WORK array, and no error *> this value as the first entry of the WORK array, and no error

6
lapack-netlib/SRC/chetrd_hb2st.F
View File

@ -50,9 +50,9 @@
* Arguments: * Arguments:
* ========== * ==========
* *
*> \param[in] STAGE *> \param[in] STAGE1
*> \verbatim *> \verbatim
*> STAGE is CHARACTER*1 *> STAGE1 is CHARACTER*1
*> = 'N': "No": to mention that the stage 1 of the reduction *> = 'N': "No": to mention that the stage 1 of the reduction
*> from dense to band using the chetrd_he2hb routine *> from dense to band using the chetrd_he2hb routine
*> was not called before this routine to reproduce AB. *> was not called before this routine to reproduce AB.
@ -512,7 +512,7 @@ C END IF
* *
* Call the kernel * Call the kernel
* *
#if defined(_OPENMP) && _OPENMP >= 201307 #if defined(_OPENMP)
IF( TTYPE.NE.1 ) THEN IF( TTYPE.NE.1 ) THEN
!$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1)) !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1))
!$OMP$ DEPEND(in:WORK(MYID-1)) !$OMP$ DEPEND(in:WORK(MYID-1))

2
lapack-netlib/SRC/chetrd_he2hb.f
View File

@ -363,7 +363,7 @@
* *
* *
* Set the workspace of the triangular matrix T to zero once such a * Set the workspace of the triangular matrix T to zero once such a
* way everytime T is generated the upper/lower portion will be always zero * way every time T is generated the upper/lower portion will be always zero
* *
CALL CLASET( "A", LDT, KD, ZERO, ZERO, WORK( TPOS ), LDT ) CALL CLASET( "A", LDT, KD, ZERO, ZERO, WORK( TPOS ), LDT )
* *

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

@ -37,7 +37,7 @@
*> CHETRF_AA computes the factorization of a complex hermitian matrix A *> CHETRF_AA computes the factorization of a complex hermitian matrix A
*> using the Aasen's algorithm. The form of the factorization is *> using the Aasen's algorithm. The form of the factorization is
*> *>
*> A = U*T*U**H or A = L*T*L**H *> A = U**H*T*U or A = L*T*L**H
*> *>
*> where U (or L) is a product of permutation and unit upper (lower) *> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and T is a hermitian tridiagonal matrix. *> triangular matrices, and T is a hermitian tridiagonal matrix.
@ -223,7 +223,7 @@
IF( UPPER ) THEN IF( UPPER ) THEN
* *
* ..................................................... * .....................................................
* Factorize A as L*D*L**H using the upper triangle of A * Factorize A as U**H*D*U using the upper triangle of A
* ..................................................... * .....................................................
* *
* copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N)) * copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N))
@ -256,7 +256,7 @@
$ A( MAX(1, J), J+1 ), LDA, $ A( MAX(1, J), J+1 ), LDA,
$ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) ) $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) )
* *
* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot) * Adjust IPIV and apply it back (J-th step picks (J+1)-th pivot)
* *
DO J2 = J+2, MIN(N, J+JB+1) DO J2 = J+2, MIN(N, J+JB+1)
IPIV( J2 ) = IPIV( J2 ) + J IPIV( J2 ) = IPIV( J2 ) + J
@ -376,7 +376,7 @@
$ A( J+1, MAX(1, J) ), LDA, $ A( J+1, MAX(1, J) ), LDA,
$ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) ) $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) )
* *
* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot) * Adjust IPIV and apply it back (J-th step picks (J+1)-th pivot)
* *
DO J2 = J+2, MIN(N, J+JB+1) DO J2 = J+2, MIN(N, J+JB+1)
IPIV( J2 ) = IPIV( J2 ) + J IPIV( J2 ) = IPIV( J2 ) + J

30
lapack-netlib/SRC/chetrf_aa_2stage.f
View File

@ -38,7 +38,7 @@
*> CHETRF_AA_2STAGE computes the factorization of a real hermitian matrix A *> CHETRF_AA_2STAGE computes the factorization of a real hermitian matrix A
*> using the Aasen's algorithm. The form of the factorization is *> using the Aasen's algorithm. The form of the factorization is
*> *>
*> A = U*T*U**T or A = L*T*L**T *> A = U**T*T*U or A = L*T*L**T
*> *>
*> where U (or L) is a product of permutation and unit upper (lower) *> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and T is a hermitian band matrix with the *> triangular matrices, and T is a hermitian band matrix with the
@ -277,7 +277,7 @@
IF( UPPER ) THEN IF( UPPER ) THEN
* *
* ..................................................... * .....................................................
* Factorize A as L*D*L**T using the upper triangle of A * Factorize A as U**T*D*U using the upper triangle of A
* ..................................................... * .....................................................
* *
DO J = 0, NT-1 DO J = 0, NT-1
@ -454,13 +454,16 @@ c END IF
CALL CSWAP( K-1, A( (J+1)*NB+1, I1 ), 1, CALL CSWAP( K-1, A( (J+1)*NB+1, I1 ), 1,
$ A( (J+1)*NB+1, I2 ), 1 ) $ A( (J+1)*NB+1, I2 ), 1 )
* > Swap A(I1+1:M, I1) with A(I2, I1+1:M) * > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
CALL CSWAP( I2-I1-1, A( I1, I1+1 ), LDA, IF( I2.GT.(I1+1) ) THEN
$ A( I1+1, I2 ), 1 ) CALL CSWAP( I2-I1-1, A( I1, I1+1 ), LDA,
$ A( I1+1, I2 ), 1 )
CALL CLACGV( I2-I1-1, A( I1+1, I2 ), 1 )
END IF
CALL CLACGV( I2-I1, A( I1, I1+1 ), LDA ) CALL CLACGV( I2-I1, A( I1, I1+1 ), LDA )
CALL CLACGV( I2-I1-1, A( I1+1, I2 ), 1 )
* > Swap A(I2+1:M, I1) with A(I2+1:M, I2) * > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
CALL CSWAP( N-I2, A( I1, I2+1 ), LDA, IF( I2.LT.N )
$ A( I2, I2+1 ), LDA ) $ CALL CSWAP( N-I2, A( I1, I2+1 ), LDA,
$ A( I2, I2+1 ), LDA )
* > Swap A(I1, I1) with A(I2, I2) * > Swap A(I1, I1) with A(I2, I2)
PIV = A( I1, I1 ) PIV = A( I1, I1 )
A( I1, I1 ) = A( I2, I2 ) A( I1, I1 ) = A( I2, I2 )
@ -631,13 +634,16 @@ c END IF
CALL CSWAP( K-1, A( I1, (J+1)*NB+1 ), LDA, CALL CSWAP( K-1, A( I1, (J+1)*NB+1 ), LDA,
$ A( I2, (J+1)*NB+1 ), LDA ) $ A( I2, (J+1)*NB+1 ), LDA )
* > Swap A(I1+1:M, I1) with A(I2, I1+1:M) * > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
CALL CSWAP( I2-I1-1, A( I1+1, I1 ), 1, IF( I2.GT.(I1+1) ) THEN
$ A( I2, I1+1 ), LDA ) CALL CSWAP( I2-I1-1, A( I1+1, I1 ), 1,
$ A( I2, I1+1 ), LDA )
CALL CLACGV( I2-I1-1, A( I2, I1+1 ), LDA )
END IF
CALL CLACGV( I2-I1, A( I1+1, I1 ), 1 ) CALL CLACGV( I2-I1, A( I1+1, I1 ), 1 )
CALL CLACGV( I2-I1-1, A( I2, I1+1 ), LDA )
* > Swap A(I2+1:M, I1) with A(I2+1:M, I2) * > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
CALL CSWAP( N-I2, A( I2+1, I1 ), 1, IF( I2.LT.N )
$ A( I2+1, I2 ), 1 ) $ CALL CSWAP( N-I2, A( I2+1, I1 ), 1,
$ A( I2+1, I2 ), 1 )
* > Swap A(I1, I1) with A(I2, I2) * > Swap A(I1, I1) with A(I2, I2)
PIV = A( I1, I1 ) PIV = A( I1, I1 )
A( I1, I1 ) = A( I2, I2 ) A( I1, I1 ) = A( I2, I2 )

4
lapack-netlib/SRC/chetri2.f
View File

@ -62,7 +62,7 @@
*> \param[in,out] A *> \param[in,out] A
*> \verbatim *> \verbatim
*> A is COMPLEX array, dimension (LDA,N) *> A is COMPLEX array, dimension (LDA,N)
*> On entry, the NB diagonal matrix D and the multipliers *> On entry, the block diagonal matrix D and the multipliers
*> used to obtain the factor U or L as computed by CHETRF. *> used to obtain the factor U or L as computed by CHETRF.
*> *>
*> On exit, if INFO = 0, the (symmetric) inverse of the original *> On exit, if INFO = 0, the (symmetric) inverse of the original
@ -82,7 +82,7 @@
*> \param[in] IPIV *> \param[in] IPIV
*> \verbatim *> \verbatim
*> IPIV is INTEGER array, dimension (N) *> IPIV is INTEGER array, dimension (N)
*> Details of the interchanges and the NB structure of D *> Details of the interchanges and the block structure of D
*> as determined by CHETRF. *> as determined by CHETRF.
*> \endverbatim *> \endverbatim
*> *>

132
lapack-netlib/SRC/chetrs_aa.f
View File

@ -37,7 +37,7 @@
*> \verbatim *> \verbatim
*> *>
*> CHETRS_AA solves a system of linear equations A*X = B with a complex *> CHETRS_AA solves a system of linear equations A*X = B with a complex
*> hermitian matrix A using the factorization A = U*T*U**H or *> hermitian matrix A using the factorization A = U**H*T*U or
*> A = L*T*L**H computed by CHETRF_AA. *> A = L*T*L**H computed by CHETRF_AA.
*> \endverbatim *> \endverbatim
* *
@ -49,7 +49,7 @@
*> UPLO is CHARACTER*1 *> UPLO is CHARACTER*1
*> Specifies whether the details of the factorization are stored *> Specifies whether the details of the factorization are stored
*> as an upper or lower triangular matrix. *> as an upper or lower triangular matrix.
*> = 'U': Upper triangular, form is A = U*T*U**H; *> = 'U': Upper triangular, form is A = U**H*T*U;
*> = 'L': Lower triangular, form is A = L*T*L**H. *> = 'L': Lower triangular, form is A = L*T*L**H.
*> \endverbatim *> \endverbatim
*> *>
@ -97,14 +97,16 @@
*> The leading dimension of the array B. LDB >= max(1,N). *> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is DOUBLE array, dimension (MAX(1,LWORK)) *> WORK is COMPLEX array, dimension (MAX(1,LWORK))
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] LWORK *> \param[in] LWORK
*> \verbatim *> \verbatim
*> LWORK is INTEGER, LWORK >= MAX(1,3*N-2). *> LWORK is INTEGER
*> The dimension of the array WORK. LWORK >= max(1,3*N-2).
*> \endverbatim
*> *>
*> \param[out] INFO *> \param[out] INFO
*> \verbatim *> \verbatim
@ -198,24 +200,31 @@
* *
IF( UPPER ) THEN IF( UPPER ) THEN
* *
* Solve A*X = B, where A = U*T*U**T. * Solve A*X = B, where A = U**H*T*U.
* *
* P**T * B * 1) Forward substitution with U**H
* *
K = 1 IF( N.GT.1 ) THEN
DO WHILE ( K.LE.N )
KP = IPIV( K )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
K = K + 1
END DO
* *
* Compute (U \P**T * B) -> B [ (U \P**T * B) ] * Pivot, P**T * B -> B
* *
CALL CTRSM('L', 'U', 'C', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA, K = 1
$ B( 2, 1 ), LDB) DO WHILE ( K.LE.N )
KP = IPIV( K )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
K = K + 1
END DO
* *
* Compute T \ B -> B [ T \ (U \P**T * B) ] * Compute U**H \ B -> B [ (U**H \P**T * B) ]
*
CALL CTRSM( 'L', 'U', 'C', 'U', N-1, NRHS, ONE, A( 1, 2 ),
$ LDA, B( 2, 1 ), LDB)
END IF
*
* 2) Solve with triangular matrix T
*
* Compute T \ B -> B [ T \ (U**H \P**T * B) ]
* *
CALL CLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1) CALL CLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
IF( N.GT.1 ) THEN IF( N.GT.1 ) THEN
@ -226,65 +235,82 @@
CALL CGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB, CALL CGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
$ INFO) $ INFO)
* *
* Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ] * 3) Backward substitution with U
* *
CALL CTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA, IF( N.GT.1 ) THEN
$ B(2, 1), LDB)
* *
* Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ] * Compute U \ B -> B [ U \ (T \ (U**H \P**T * B) ) ]
* *
K = N CALL CTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ),
DO WHILE ( K.GE.1 ) $ LDA, B(2, 1), LDB)
KP = IPIV( K ) *
IF( KP.NE.K ) * Pivot, P * B -> B [ P * (U \ (T \ (U**H \P**T * B) )) ]
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) *
K = K - 1 K = N
END DO DO WHILE ( K.GE.1 )
KP = IPIV( K )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
K = K - 1
END DO
END IF
* *
ELSE ELSE
* *
* Solve A*X = B, where A = L*T*L**T. * Solve A*X = B, where A = L*T*L**H.
* *
* Pivot, P**T * B * 1) Forward substitution with L
* *
K = 1 IF( N.GT.1 ) THEN
DO WHILE ( K.LE.N )
KP = IPIV( K )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
K = K + 1
END DO
* *
* Compute (L \P**T * B) -> B [ (L \P**T * B) ] * Pivot, P**T * B -> B
* *
CALL CTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1), LDA, K = 1
$ B(2, 1), LDB) DO WHILE ( K.LE.N )
KP = IPIV( K )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
K = K + 1
END DO
*
* Compute L \ B -> B [ (L \P**T * B) ]
*
CALL CTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1),
$ LDA, B(2, 1), LDB )
END IF
*
* 2) Solve with triangular matrix T
* *
* Compute T \ B -> B [ T \ (L \P**T * B) ] * Compute T \ B -> B [ T \ (L \P**T * B) ]
* *
CALL CLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1) CALL CLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
IF( N.GT.1 ) THEN IF( N.GT.1 ) THEN
CALL CLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1) CALL CLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1 )
CALL CLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1) CALL CLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1)
CALL CLACGV( N-1, WORK( 2*N ), 1 ) CALL CLACGV( N-1, WORK( 2*N ), 1 )
END IF END IF
CALL CGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB, CALL CGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
$ INFO) $ INFO)
* *
* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ] * 3) Backward substitution with L**H
* *
CALL CTRSM( 'L', 'L', 'C', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA, IF( N.GT.1 ) THEN
$ B( 2, 1 ), LDB)
* *
* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ] * Compute (L**H \ B) -> B [ L**H \ (T \ (L \P**T * B) ) ]
* *
K = N CALL CTRSM( 'L', 'L', 'C', 'U', N-1, NRHS, ONE, A( 2, 1 ),
DO WHILE ( K.GE.1 ) $ LDA, B( 2, 1 ), LDB )
KP = IPIV( K ) *
IF( KP.NE.K ) * Pivot, P * B -> B [ P * (L**H \ (T \ (L \P**T * B) )) ]
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) *
K = K - 1 K = N
END DO DO WHILE ( K.GE.1 )
KP = IPIV( K )
IF( KP.NE.K )
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
K = K - 1
END DO
END IF
* *
END IF END IF
* *

10
lapack-netlib/SRC/chetrs_aa_2stage.f
View File

@ -38,7 +38,7 @@
*> \verbatim *> \verbatim
*> *>
*> CHETRS_AA_2STAGE solves a system of linear equations A*X = B with a real *> CHETRS_AA_2STAGE solves a system of linear equations A*X = B with a real
*> hermitian matrix A using the factorization A = U*T*U**T or *> hermitian matrix A using the factorization A = U**T*T*U or
*> A = L*T*L**T computed by CHETRF_AA_2STAGE. *> A = L*T*L**T computed by CHETRF_AA_2STAGE.
*> \endverbatim *> \endverbatim
* *
@ -50,7 +50,7 @@
*> UPLO is CHARACTER*1 *> UPLO is CHARACTER*1
*> Specifies whether the details of the factorization are stored *> Specifies whether the details of the factorization are stored
*> as an upper or lower triangular matrix. *> as an upper or lower triangular matrix.
*> = 'U': Upper triangular, form is A = U*T*U**T; *> = 'U': Upper triangular, form is A = U**T*T*U;
*> = 'L': Lower triangular, form is A = L*T*L**T. *> = 'L': Lower triangular, form is A = L*T*L**T.
*> \endverbatim *> \endverbatim
*> *>
@ -210,15 +210,15 @@
* *
IF( UPPER ) THEN IF( UPPER ) THEN
* *
* Solve A*X = B, where A = U*T*U**T. * Solve A*X = B, where A = U**T*T*U.
* *
IF( N.GT.NB ) THEN IF( N.GT.NB ) THEN
* *
* Pivot, P**T * B * Pivot, P**T * B -> B
* *
CALL CLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 ) CALL CLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
* *
* Compute (U**T \P**T * B) -> B [ (U**T \P**T * B) ] * Compute (U**T \ B) -> B [ (U**T \P**T * B) ]
* *
CALL CTRSM( 'L', 'U', 'C', 'U', N-NB, NRHS, ONE, A(1, NB+1), CALL CTRSM( 'L', 'U', 'C', 'U', N-NB, NRHS, ONE, A(1, NB+1),
$ LDA, B(NB+1, 1), LDB) $ LDA, B(NB+1, 1), LDB)

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

@ -69,7 +69,7 @@
*> \param[in] N *> \param[in] N
*> \verbatim *> \verbatim
*> N is INTEGER *> N is INTEGER
*> The order of the matrix H. N .GE. 0. *> The order of the matrix H. N >= 0.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] ILO *> \param[in] ILO
@ -86,7 +86,7 @@
*> set by a previous call to CGEBAL, and then passed to ZGEHRD *> set by a previous call to CGEBAL, and then passed to ZGEHRD
*> when the matrix output by CGEBAL is reduced to Hessenberg *> when the matrix output by CGEBAL is reduced to Hessenberg
*> form. Otherwise ILO and IHI should be set to 1 and N *> 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. *> If N = 0, then ILO = 1 and IHI = 0.
*> \endverbatim *> \endverbatim
*> *>
@ -98,17 +98,17 @@
*> triangular matrix T from the Schur decomposition (the *> triangular matrix T from the Schur decomposition (the
*> Schur form). If INFO = 0 and JOB = 'E', the contents of *> Schur form). If INFO = 0 and JOB = 'E', the contents of
*> H are unspecified on exit. (The output value of H when *> H are unspecified on exit. (The output value of H when
*> INFO.GT.0 is given under the description of INFO below.) *> INFO > 0 is given under the description of INFO below.)
*> *>
*> Unlike earlier versions of CHSEQR, this subroutine may *> Unlike earlier versions of CHSEQR, 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. *> or j = IHI+1, IHI+2, ... N.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] LDH *> \param[in] LDH
*> \verbatim *> \verbatim
*> LDH is INTEGER *> 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 *> \endverbatim
*> *>
*> \param[out] W *> \param[out] W
@ -131,7 +131,7 @@
*> if INFO = 0, Z contains Q*Z. *> if INFO = 0, Z contains Q*Z.
*> Normally Q is the unitary matrix generated by CUNGHR *> Normally Q is the unitary matrix generated by CUNGHR
*> after the call to CGEHRD which formed the Hessenberg matrix *> after the call to CGEHRD 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.) *> the description of INFO below.)
*> \endverbatim *> \endverbatim
*> *>
@ -139,7 +139,7 @@
*> \verbatim *> \verbatim
*> LDZ is INTEGER *> LDZ is INTEGER
*> The leading dimension of the array Z. if COMPZ = 'I' or *> 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 *> \endverbatim
*> *>
*> \param[out] WORK *> \param[out] WORK
@ -152,7 +152,7 @@
*> \param[in] LWORK *> \param[in] LWORK
*> \verbatim *> \verbatim
*> LWORK is INTEGER *> 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 *> is sufficient and delivers very good and sometimes
*> optimal performance. However, LWORK as large as 11*N *> optimal performance. However, LWORK as large as 11*N
*> may be required for optimal performance. A workspace *> may be required for optimal performance. A workspace
@ -170,21 +170,21 @@
*> \param[out] INFO *> \param[out] INFO
*> \verbatim *> \verbatim
*> INFO is INTEGER *> INFO is INTEGER
*> = 0: successful exit *> = 0: successful exit
*> .LT. 0: if INFO = -i, the i-th argument had an illegal *> < 0: if INFO = -i, the i-th argument had an illegal
*> value *> value
*> .GT. 0: if INFO = i, CHSEQR failed to compute all of *> > 0: if INFO = i, CHSEQR failed to compute all of
*> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR *> the eigenvalues. Elements 1:ilo-1 and i+1:n of W
*> and WI contain those eigenvalues which have been *> contain those eigenvalues which have been
*> successfully computed. (Failures are rare.) *> 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- *> remaining unconverged eigenvalues are the eigen-
*> values of the upper Hessenberg matrix rows and *> values of the upper Hessenberg matrix rows and
*> columns ILO through INFO of the final, output *> columns ILO through INFO of the final, output
*> value of H. *> 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) *> (*) (initial value of H)*U = U*(final value of H)
*> *>
@ -192,19 +192,19 @@
*> value of H is upper Hessenberg and triangular in *> value of H is upper Hessenberg and triangular in
*> rows and columns INFO+1 through IHI. *> 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 *> (final value of Z) = (initial value of Z)*U
*> *>
*> where U is the unitary matrix in (*) (regard- *> where U is the unitary matrix in (*) (regard-
*> less of the value of JOB.) *> 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 *> (final value of Z) = U
*> where U is the unitary matrix in (*) (regard- *> where U is the unitary matrix in (*) (regard-
*> less of the value of JOB.) *> 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. *> accessed.
*> \endverbatim *> \endverbatim
* *
@ -244,8 +244,8 @@
*> This depends on ILO, IHI and NS. NS is the *> This depends on ILO, IHI and NS. NS is the
*> number of simultaneous shifts returned *> number of simultaneous shifts returned
*> by ILAENV(ISPEC=15). (See ISPEC=15 below.) *> by ILAENV(ISPEC=15). (See ISPEC=15 below.)
*> The default for (IHI-ILO+1).LE.500 is NS. *> The default for (IHI-ILO+1) <= 500 is NS.
*> The default for (IHI-ILO+1).GT.500 is 3*NS/2. *> The default for (IHI-ILO+1) > 500 is 3*NS/2.
*> *>
*> ISPEC=14: Nibble crossover point. (See IPARMQ for *> ISPEC=14: Nibble crossover point. (See IPARMQ for
*> details.) Default: 14% of deflation window *> details.) Default: 14% of deflation window
@ -323,8 +323,8 @@
PARAMETER ( NTINY = 11 ) PARAMETER ( NTINY = 11 )
* *
* ==== NL allocates some local workspace to help small matrices * ==== NL allocates some local workspace to help small matrices
* . through a rare CLAHQR failure. NL .GT. NTINY = 11 is * . through a rare CLAHQR failure. NL > NTINY = 11 is
* . required and NL .LE. NMIN = ILAENV(ISPEC=12,...) is recom- * . required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom-
* . mended. (The default value of NMIN is 75.) Using NL = 49 * . mended. (The default value of NMIN is 75.) Using NL = 49
* . allows up to six simultaneous shifts and a 16-by-16 * . allows up to six simultaneous shifts and a 16-by-16
* . deflation window. ==== * . deflation window. ====

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

@ -132,13 +132,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

@ -125,13 +125,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

@ -65,19 +65,19 @@
*> \verbatim *> \verbatim
*> PREC_TYPE is INTEGER *> PREC_TYPE is INTEGER
*> Specifies the intermediate precision to be used in refinement. *> Specifies the intermediate precision to be used in refinement.
*> The value is defined by ILAPREC(P) where P is a CHARACTER and *> The value is defined by ILAPREC(P) where P is a CHARACTER and P
*> P = 'S': Single *> = 'S': Single
*> = 'D': Double *> = 'D': Double
*> = 'I': Indigenous *> = 'I': Indigenous
*> = 'X', 'E': Extra *> = 'X' or 'E': Extra
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] TRANS_TYPE *> \param[in] TRANS_TYPE
*> \verbatim *> \verbatim
*> TRANS_TYPE is INTEGER *> TRANS_TYPE is INTEGER
*> Specifies the transposition operation on A. *> Specifies the transposition operation on A.
*> The value is defined by ILATRANS(T) where T is a CHARACTER and *> The value is defined by ILATRANS(T) where T is a CHARACTER and T
*> T = 'N': No transpose *> = 'N': No transpose
*> = 'T': Transpose *> = 'T': Transpose
*> = 'C': Conjugate transpose *> = 'C': Conjugate transpose
*> \endverbatim *> \endverbatim
@ -269,7 +269,7 @@
*> information as described below. There currently are up to three *> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If *> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> 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 (:,N_ERR_BNDS) entries are returned.
*> *>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

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

@ -21,7 +21,7 @@
* REAL FUNCTION CLA_GERCOND_C( TRANS, N, A, LDA, AF, LDAF, IPIV, C, * REAL FUNCTION CLA_GERCOND_C( TRANS, N, A, LDA, AF, LDAF, IPIV, C,
* CAPPLY, INFO, WORK, RWORK ) * CAPPLY, INFO, WORK, RWORK )
* *
* .. Scalar Aguments .. * .. Scalar Arguments ..
* CHARACTER TRANS * CHARACTER TRANS
* LOGICAL CAPPLY * LOGICAL CAPPLY
* INTEGER N, LDA, LDAF, INFO * INTEGER N, LDA, LDAF, INFO
@ -114,13 +114,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.
@ -147,7 +147,7 @@
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016 * December 2016
* *
* .. Scalar Aguments .. * .. Scalar Arguments ..
CHARACTER TRANS CHARACTER TRANS
LOGICAL CAPPLY LOGICAL CAPPLY
INTEGER N, LDA, LDAF, INFO INTEGER N, LDA, LDAF, INFO

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

@ -107,13 +107,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

@ -65,19 +65,19 @@
*> \verbatim *> \verbatim
*> PREC_TYPE is INTEGER *> PREC_TYPE is INTEGER
*> Specifies the intermediate precision to be used in refinement. *> Specifies the intermediate precision to be used in refinement.
*> The value is defined by ILAPREC(P) where P is a CHARACTER and *> The value is defined by ILAPREC(P) where P is a CHARACTER and P
*> P = 'S': Single *> = 'S': Single
*> = 'D': Double *> = 'D': Double
*> = 'I': Indigenous *> = 'I': Indigenous
*> = 'X', 'E': Extra *> = 'X' or 'E': Extra
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] TRANS_TYPE *> \param[in] TRANS_TYPE
*> \verbatim *> \verbatim
*> TRANS_TYPE is INTEGER *> TRANS_TYPE is INTEGER
*> Specifies the transposition operation on A. *> Specifies the transposition operation on A.
*> The value is defined by ILATRANS(T) where T is a CHARACTER and *> The value is defined by ILATRANS(T) where T is a CHARACTER and T
*> T = 'N': No transpose *> = 'N': No transpose
*> = 'T': Transpose *> = 'T': Transpose
*> = 'C': Conjugate transpose *> = 'C': Conjugate transpose
*> \endverbatim *> \endverbatim
@ -257,7 +257,7 @@
*> information as described below. There currently are up to three *> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If *> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> 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 (:,N_ERR_BNDS) entries are returned.
*> *>
*> The first index in ERRS_C(i,:) corresponds to the ith *> The first index in ERRS_C(i,:) corresponds to the ith

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

@ -110,13 +110,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

@ -103,13 +103,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

@ -66,11 +66,11 @@
*> \verbatim *> \verbatim
*> PREC_TYPE is INTEGER *> PREC_TYPE is INTEGER
*> Specifies the intermediate precision to be used in refinement. *> Specifies the intermediate precision to be used in refinement.
*> The value is defined by ILAPREC(P) where P is a CHARACTER and *> The value is defined by ILAPREC(P) where P is a CHARACTER and P
*> P = 'S': Single *> = 'S': Single
*> = 'D': Double *> = 'D': Double
*> = 'I': Indigenous *> = 'I': Indigenous
*> = 'X', 'E': Extra *> = 'X' or 'E': Extra
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] UPLO *> \param[in] UPLO
@ -254,7 +254,7 @@
*> information as described below. There currently are up to three *> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If *> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> 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 (:,N_ERR_BNDS) entries are returned.
*> *>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

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

@ -102,13 +102,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

@ -95,13 +95,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

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

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

@ -85,7 +85,7 @@
*> The leading dimension of the array AF. LDAF >= max(1,N). *> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is REAL array, dimension (2*N) *> WORK is REAL array, dimension (2*N)
*> \endverbatim *> \endverbatim

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

@ -110,13 +110,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

@ -103,13 +103,13 @@
*> i > 0: The ith argument is invalid. *> i > 0: The ith argument is invalid.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is COMPLEX array, dimension (2*N). *> WORK is COMPLEX array, dimension (2*N).
*> Workspace. *> Workspace.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] RWORK *> \param[out] RWORK
*> \verbatim *> \verbatim
*> RWORK is REAL array, dimension (N). *> RWORK is REAL array, dimension (N).
*> Workspace. *> Workspace.

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

@ -66,11 +66,11 @@
*> \verbatim *> \verbatim
*> PREC_TYPE is INTEGER *> PREC_TYPE is INTEGER
*> Specifies the intermediate precision to be used in refinement. *> Specifies the intermediate precision to be used in refinement.
*> The value is defined by ILAPREC(P) where P is a CHARACTER and *> The value is defined by ILAPREC(P) where P is a CHARACTER and P
*> P = 'S': Single *> = 'S': Single
*> = 'D': Double *> = 'D': Double
*> = 'I': Indigenous *> = 'I': Indigenous
*> = 'X', 'E': Extra *> = 'X' or 'E': Extra
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] UPLO *> \param[in] UPLO
@ -254,7 +254,7 @@
*> information as described below. There currently are up to three *> information as described below. There currently are up to three
*> pieces of information returned for each right-hand side. If *> pieces of information returned for each right-hand side. If
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> 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 (:,N_ERR_BNDS) entries are returned.
*> *>
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

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

@ -102,7 +102,7 @@
*> as determined by CSYTRF. *> as determined by CSYTRF.
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is REAL array, dimension (2*N) *> WORK is REAL array, dimension (2*N)
*> \endverbatim *> \endverbatim

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

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