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Update LAPACK to 3.9.0

This commit is contained in:
Martin Kroeker 2019-12-29 23:20:29 +01:00 committed by GitHub
parent a421ab9ce2
commit e3b07ca95d
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GPG Key ID: 4AEE18F83AFDEB23
30 changed files with 227 additions and 198 deletions
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12
lapack-netlib/SRC/dporfsx.f
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@ -135,7 +135,7 @@
*> \param[in,out] S *> \param[in,out] S
*> \verbatim *> \verbatim
*> S is DOUBLE PRECISION array, dimension (N) *> S is DOUBLE PRECISION array, dimension (N)
*> The row scale factors for A. If EQUED = 'Y', A is multiplied on *> The scale factors for A. If EQUED = 'Y', A is multiplied on
*> the left and right by diag(S). S is an input argument if FACT = *> the left and right by diag(S). S is an input argument if FACT =
*> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED *> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
*> = 'Y', each element of S must be positive. If S is output, each *> = 'Y', each element of S must be positive. If S is output, each
@ -263,7 +263,7 @@
*> 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
@ -299,14 +299,14 @@
*> \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 DOUBLE PRECISION array, dimension (NPARAMS) *> 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 *> 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.
@ -314,9 +314,9 @@
*> 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: 1.0D+0 *> 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. *> 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.

10
lapack-netlib/SRC/dposvxx.f
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@ -366,7 +366,7 @@
*> 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
@ -402,14 +402,14 @@
*> \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 DOUBLE PRECISION array, dimension NPARAMS *> 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 *> 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.
@ -417,9 +417,9 @@
*> 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: 1.0D+0 *> 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. *> computed.
*> = 1.0 : Use the extra-precise refinement algorithm. *> = 1.0: Use the extra-precise refinement algorithm.
*> (other values are reserved for future use) *> (other values are reserved for future use)
*> *>
*> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

2
lapack-netlib/SRC/dsb2st_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 DOUBLE PRECISION array. Workspace of size nb. *> WORK is DOUBLE PRECISION array. Workspace of size nb.
*> \endverbatim *> \endverbatim

6
lapack-netlib/SRC/dsbgvx.f
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@ -261,11 +261,11 @@
*> \param[out] INFO *> \param[out] INFO
*> \verbatim *> \verbatim
*> INFO is INTEGER *> INFO is INTEGER
*> = 0 : successful exit *> = 0: successful exit
*> < 0 : if INFO = -i, the i-th argument had an illegal value *> < 0: if INFO = -i, the i-th argument had an illegal value
*> <= N: if INFO = i, then i eigenvectors failed to converge. *> <= N: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in IFAIL. *> Their indices are stored in IFAIL.
*> > N : DPBSTF returned an error code; i.e., *> > N: DPBSTF returned an error code; i.e.,
*> if INFO = N + i, for 1 <= i <= N, then the leading *> if INFO = N + i, for 1 <= i <= N, then the leading
*> minor of order i of B is not positive definite. *> minor of order i of B is not positive definite.
*> The factorization of B could not be completed and *> The factorization of B could not be completed and

10
lapack-netlib/SRC/dsgesv.f
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@ -92,9 +92,9 @@
*> dimension (LDA,N) *> dimension (LDA,N)
*> On entry, the N-by-N coefficient matrix A. *> On entry, the N-by-N coefficient matrix A.
*> On exit, if iterative refinement has been successfully used *> On exit, if iterative refinement has been successfully used
*> (INFO.EQ.0 and ITER.GE.0, see description below), then A is *> (INFO = 0 and ITER >= 0, see description below), then A is
*> unchanged, if double precision factorization has been used *> unchanged, if double precision factorization has been used
*> (INFO.EQ.0 and ITER.LT.0, see description below), then the *> (INFO = 0 and ITER < 0, see description below), then the
*> array A contains the factors L and U from the factorization *> array A contains the factors L and U from the factorization
*> A = P*L*U; the unit diagonal elements of L are not stored. *> A = P*L*U; the unit diagonal elements of L are not stored.
*> \endverbatim *> \endverbatim
@ -111,8 +111,8 @@
*> The pivot indices that define the permutation matrix P; *> The pivot indices that define the permutation matrix P;
*> row i of the matrix was interchanged with row IPIV(i). *> row i of the matrix was interchanged with row IPIV(i).
*> Corresponds either to the single precision factorization *> Corresponds either to the single precision factorization
*> (if INFO.EQ.0 and ITER.GE.0) or the double precision *> (if INFO = 0 and ITER >= 0) or the double precision
*> factorization (if INFO.EQ.0 and ITER.LT.0). *> factorization (if INFO = 0 and ITER < 0).
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] B *> \param[in] B
@ -406,7 +406,7 @@
30 CONTINUE 30 CONTINUE
* *
* If we are at this place of the code, this is because we have * If we are at this place of the code, this is because we have
* performed ITER=ITERMAX iterations and never satisified the * performed ITER=ITERMAX iterations and never satisfied the
* stopping criterion, set up the ITER flag accordingly and follow up * stopping criterion, set up the ITER flag accordingly and follow up
* on double precision routine. * on double precision routine.
* *

6
lapack-netlib/SRC/dsposv.f
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@ -106,9 +106,9 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> On exit, if iterative refinement has been successfully used *> On exit, if iterative refinement has been successfully used
*> (INFO.EQ.0 and ITER.GE.0, see description below), then A is *> (INFO = 0 and ITER >= 0, see description below), then A is
*> unchanged, if double precision factorization has been used *> unchanged, if double precision factorization has been used
*> (INFO.EQ.0 and ITER.LT.0, see description below), then the *> (INFO = 0 and ITER < 0, see description below), then the
*> array A contains the factor U or L from the Cholesky *> array A contains the factor U or L from the Cholesky
*> factorization A = U**T*U or A = L*L**T. *> factorization A = U**T*U or A = L*L**T.
*> \endverbatim *> \endverbatim
@ -413,7 +413,7 @@
30 CONTINUE 30 CONTINUE
* *
* If we are at this place of the code, this is because we have * If we are at this place of the code, this is because we have
* performed ITER=ITERMAX iterations and never satisified the * performed ITER=ITERMAX iterations and never satisfied the
* stopping criterion, set up the ITER flag accordingly and follow * stopping criterion, set up the ITER flag accordingly and follow
* up on double precision routine. * up on double precision routine.
* *

4
lapack-netlib/SRC/dstemr.f
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@ -233,13 +233,13 @@
*> \param[in,out] TRYRAC *> \param[in,out] TRYRAC
*> \verbatim *> \verbatim
*> TRYRAC is LOGICAL *> TRYRAC is LOGICAL
*> If TRYRAC.EQ..TRUE., indicates that the code should check whether *> If TRYRAC = .TRUE., indicates that the code should check whether
*> the tridiagonal matrix defines its eigenvalues to high relative *> the tridiagonal matrix defines its eigenvalues to high relative
*> accuracy. If so, the code uses relative-accuracy preserving *> accuracy. If so, the code uses relative-accuracy preserving
*> algorithms that might be (a bit) slower depending on the matrix. *> algorithms that might be (a bit) slower depending on the matrix.
*> If the matrix does not define its eigenvalues to high relative *> If the matrix does not define its eigenvalues to high relative
*> accuracy, the code can uses possibly faster algorithms. *> accuracy, the code can uses possibly faster algorithms.
*> If TRYRAC.EQ..FALSE., the code is not required to guarantee *> If TRYRAC = .FALSE., the code is not required to guarantee
*> relatively accurate eigenvalues and can use the fastest possible *> relatively accurate eigenvalues and can use the fastest possible
*> techniques. *> techniques.
*> On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix *> On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix

8
lapack-netlib/SRC/dsyconvf.f
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@ -291,7 +291,7 @@
* *
* Convert PERMUTATIONS and IPIV * Convert PERMUTATIONS and IPIV
* *
* Apply permutaions to submatrices of upper part of A * Apply permutations to submatrices of upper part of A
* in factorization order where i decreases from N to 1 * in factorization order where i decreases from N to 1
* *
I = N I = N
@ -344,7 +344,7 @@
* *
* Revert PERMUTATIONS and IPIV * Revert PERMUTATIONS and IPIV
* *
* Apply permutaions to submatrices of upper part of A * Apply permutations to submatrices of upper part of A
* in reverse factorization order where i increases from 1 to N * in reverse factorization order where i increases from 1 to N
* *
I = 1 I = 1
@ -435,7 +435,7 @@
* *
* Convert PERMUTATIONS and IPIV * Convert PERMUTATIONS and IPIV
* *
* Apply permutaions to submatrices of lower part of A * Apply permutations to submatrices of lower part of A
* in factorization order where k increases from 1 to N * in factorization order where k increases from 1 to N
* *
I = 1 I = 1
@ -488,7 +488,7 @@
* *
* Revert PERMUTATIONS and IPIV * Revert PERMUTATIONS and IPIV
* *
* Apply permutaions to submatrices of lower part of A * Apply permutations to submatrices of lower part of A
* in reverse factorization order where i decreases from N to 1 * in reverse factorization order where i decreases from N to 1
* *
I = N I = N

8
lapack-netlib/SRC/dsyconvf_rook.f
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@ -282,7 +282,7 @@
* *
* Convert PERMUTATIONS * Convert PERMUTATIONS
* *
* Apply permutaions to submatrices of upper part of A * Apply permutations to submatrices of upper part of A
* in factorization order where i decreases from N to 1 * in factorization order where i decreases from N to 1
* *
I = N I = N
@ -333,7 +333,7 @@
* *
* Revert PERMUTATIONS * Revert PERMUTATIONS
* *
* Apply permutaions to submatrices of upper part of A * Apply permutations to submatrices of upper part of A
* in reverse factorization order where i increases from 1 to N * in reverse factorization order where i increases from 1 to N
* *
I = 1 I = 1
@ -423,7 +423,7 @@
* *
* Convert PERMUTATIONS * Convert PERMUTATIONS
* *
* Apply permutaions to submatrices of lower part of A * Apply permutations to submatrices of lower part of A
* in factorization order where i increases from 1 to N * in factorization order where i increases from 1 to N
* *
I = 1 I = 1
@ -474,7 +474,7 @@
* *
* Revert PERMUTATIONS * Revert PERMUTATIONS
* *
* Apply permutaions to submatrices of lower part of A * Apply permutations to submatrices of lower part of A
* in reverse factorization order where i decreases from N to 1 * in reverse factorization order where i decreases from N to 1
* *
I = N I = N

2
lapack-netlib/SRC/dsyev_2stage.f
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@ -317,7 +317,7 @@
IF( .NOT.WANTZ ) THEN IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, WORK( INDE ), INFO ) CALL DSTERF( N, W, WORK( INDE ), INFO )
ELSE ELSE
* Not available in this release, and agrument checking should not * Not available in this release, and argument checking should not
* let it getting here * let it getting here
RETURN RETURN
CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),

2
lapack-netlib/SRC/dsyevd_2stage.f
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@ -385,7 +385,7 @@
IF( .NOT.WANTZ ) THEN IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, WORK( INDE ), INFO ) CALL DSTERF( N, W, WORK( INDE ), INFO )
ELSE ELSE
* Not available in this release, and agrument checking should not * Not available in this release, and argument checking should not
* let it getting here * let it getting here
RETURN RETURN
CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N, CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,

10
lapack-netlib/SRC/dsyrfsx.f
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@ -271,7 +271,7 @@
*> 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
@ -307,14 +307,14 @@
*> \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 DOUBLE PRECISION array, dimension (NPARAMS) *> 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 *> 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.
@ -322,9 +322,9 @@
*> 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: 1.0D+0 *> 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. *> 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/dsysv_aa.f
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@ -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**T, if UPLO = 'U', or *> A = U**T * T * U, if UPLO = 'U', or
*> A = L * T * L**T, if UPLO = 'L', *> A = L * T * 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 T is symmetric tridiagonal. The factored *> triangular matrices, and T is symmetric tridiagonal. The factored
@ -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**T or A = L*T*L**T as computed by *> factorization A = U**T*T*U or A = L*T*L**T as computed by
*> DSYTRF. *> DSYTRF.
*> \endverbatim *> \endverbatim
*> *>
@ -230,7 +230,7 @@
RETURN RETURN
END IF END IF
* *
* Compute the factorization A = U*T*U**T or A = L*T*L**T. * Compute the factorization A = U**T*T*U or A = L*T*L**T.
* *
CALL DSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) CALL DSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
IF( INFO.EQ.0 ) THEN IF( INFO.EQ.0 ) THEN

4
lapack-netlib/SRC/dsysv_aa_2stage.f
View File

@ -45,7 +45,7 @@
*> 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**T, if UPLO = 'U', or *> A = U**T * T * U, if UPLO = 'U', or
*> A = L * T * L**T, if UPLO = 'L', *> A = L * T * 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 T is symmetric and band. The matrix T is *> triangular matrices, and T is symmetric and band. The matrix T is
@ -259,7 +259,7 @@
END IF END IF
* *
* *
* Compute the factorization A = U*T*U**T or A = L*T*L**T. * Compute the factorization A = U**T*T*U or A = L*T*L**T.
* *
CALL DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, CALL DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,
$ WORK, LWORK, INFO ) $ WORK, LWORK, INFO )

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

@ -377,7 +377,7 @@
*> 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
@ -413,14 +413,14 @@
*> \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 DOUBLE PRECISION array, dimension (NPARAMS) *> 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 *> 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.
@ -428,9 +428,9 @@
*> 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: 1.0D+0 *> 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. *> computed.
*> = 1.0 : Use the extra-precise refinement algorithm. *> = 1.0: Use the extra-precise refinement algorithm.
*> (other values are reserved for future use) *> (other values are reserved for future use)
*> *>
*> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

4
lapack-netlib/SRC/dsytf2_rk.f
View File

@ -312,7 +312,7 @@
* *
* Factorize A as U*D*U**T using the upper triangle of A * Factorize A as U*D*U**T 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 ) = ZERO E( 1 ) = ZERO
@ -623,7 +623,7 @@
* *
* Factorize A as L*D*L**T using the lower triangle of A * Factorize A as L*D*L**T 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 ) = ZERO E( N ) = ZERO
* *

13
lapack-netlib/SRC/dsytrd_2stage.f
View File

@ -123,23 +123,22 @@
*> *>
*> \param[out] HOUS2 *> \param[out] HOUS2
*> \verbatim *> \verbatim
*> HOUS2 is DOUBLE PRECISION array, dimension LHOUS2, that *> HOUS2 is DOUBLE PRECISION 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

6
lapack-netlib/SRC/dsytrd_sb2st.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 dsytrd_sy2sb routine *> from dense to band using the dsytrd_sy2sb routine
*> was not called before this routine to reproduce AB. *> was not called before this routine to reproduce AB.
@ -481,7 +481,7 @@
* *
* 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/dsytrd_sy2sb.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 DLASET( "A", LDT, KD, ZERO, ZERO, WORK( TPOS ), LDT ) CALL DLASET( "A", LDT, KD, ZERO, ZERO, WORK( TPOS ), LDT )
* *

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

@ -39,7 +39,7 @@
*> the Bunch-Kaufman diagonal pivoting method. The form of the *> the Bunch-Kaufman diagonal pivoting method. The form of the
*> factorization is *> factorization is
*> *>
*> A = U*D*U**T or A = L*D*L**T *> A = U**T*D*U or A = L*D*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 D is symmetric and block diagonal with *> triangular matrices, and D is symmetric and block diagonal with
@ -144,7 +144,7 @@
*> *>
*> \verbatim *> \verbatim
*> *>
*> If UPLO = 'U', then A = U*D*U**T, where *> If UPLO = 'U', then A = U**T*D*U, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ..., *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> i.e., U is a product of terms P(k)*U(k), where k decreases from n to *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
*> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@ -262,7 +262,7 @@
* *
IF( UPPER ) THEN IF( UPPER ) THEN
* *
* Factorize A as U*D*U**T using the upper triangle of A * Factorize A as U**T*D*U using the upper triangle of A
* *
* K is the main loop index, decreasing from N to 1 in steps of * K is the main loop index, decreasing from N to 1 in steps of
* KB, where KB is the number of columns factorized by DLASYF; * KB, where KB is the number of columns factorized by DLASYF;

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

@ -37,7 +37,7 @@
*> DSYTRF_AA computes the factorization of a real symmetric matrix A *> DSYTRF_AA computes the factorization of a real symmetric 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 symmetric tridiagonal matrix. *> triangular matrices, and T is a symmetric tridiagonal matrix.
@ -223,7 +223,7 @@
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
* ..................................................... * .....................................................
* *
* 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
@ -375,7 +375,7 @@
$ 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

48
lapack-netlib/SRC/dsytrf_aa_2stage.f
View File

@ -38,7 +38,7 @@
*> DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A *> DSYTRF_AA_2STAGE computes the factorization of a real symmetric 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 symmetric band matrix with the *> triangular matrices, and T is a symmetric band matrix with the
@ -103,6 +103,22 @@
*> no error message related to LTB is issued by XERBLA. *> no error message related to LTB is issued by XERBLA.
*> \endverbatim *> \endverbatim
*> *>
*> \param[out] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> On exit, it contains the details of the interchanges, i.e.,
*> the row and column k of A were interchanged with the
*> row and column IPIV(k).
*> \endverbatim
*>
*> \param[out] IPIV2
*> \verbatim
*> IPIV2 is INTEGER array, dimension (N)
*> On exit, it contains the details of the interchanges, i.e.,
*> the row and column k of T were interchanged with the
*> row and column IPIV2(k).
*> \endverbatim
*>
*> \param[out] WORK *> \param[out] WORK
*> \verbatim *> \verbatim
*> WORK is DOUBLE PRECISION workspace of size LWORK *> WORK is DOUBLE PRECISION workspace of size LWORK
@ -120,22 +136,6 @@
*> no error message related to LWORK is issued by XERBLA. *> no error message related to LWORK is issued by XERBLA.
*> \endverbatim *> \endverbatim
*> *>
*> \param[out] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> On exit, it contains the details of the interchanges, i.e.,
*> the row and column k of A were interchanged with the
*> row and column IPIV(k).
*> \endverbatim
*>
*> \param[out] IPIV2
*> \verbatim
*> IPIV2 is INTEGER array, dimension (N)
*> On exit, it contains the details of the interchanges, i.e.,
*> the row and column k of T were interchanged with the
*> row and column IPIV2(k).
*> \endverbatim
*>
*> \param[out] INFO *> \param[out] INFO
*> \verbatim *> \verbatim
*> INFO is INTEGER *> INFO is INTEGER
@ -275,7 +275,7 @@
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
@ -443,10 +443,12 @@ c END IF
CALL DSWAP( K-1, A( (J+1)*NB+1, I1 ), 1, CALL DSWAP( 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 DSWAP( I2-I1-1, A( I1, I1+1 ), LDA, IF( I2.GT.(I1+1) )
$ CALL DSWAP( I2-I1-1, A( I1, I1+1 ), LDA,
$ A( I1+1, I2 ), 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 DSWAP( N-I2, A( I1, I2+1 ), LDA, IF( I2.LT.N )
$ CALL DSWAP( N-I2, A( I1, I2+1 ), LDA,
$ A( I2, 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 )
@ -616,10 +618,12 @@ c END IF
CALL DSWAP( K-1, A( I1, (J+1)*NB+1 ), LDA, CALL DSWAP( 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 DSWAP( I2-I1-1, A( I1+1, I1 ), 1, IF( I2.GT.(I1+1) )
$ CALL DSWAP( I2-I1-1, A( I1+1, I1 ), 1,
$ A( I2, I1+1 ), LDA ) $ 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 DSWAP( N-I2, A( I2+1, I1 ), 1, IF( I2.LT.N )
$ CALL DSWAP( N-I2, A( I2+1, I1 ), 1,
$ A( I2+1, I2 ), 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 )

4
lapack-netlib/SRC/dsytri2.f
View File

@ -62,7 +62,7 @@
*> \param[in,out] A *> \param[in,out] A
*> \verbatim *> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N) *> A is DOUBLE PRECISION 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 DSYTRF. *> used to obtain the factor U or L as computed by DSYTRF.
*> *>
*> 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 DSYTRF. *> as determined by DSYTRF.
*> \endverbatim *> \endverbatim
*> *>

70
lapack-netlib/SRC/dsytrs_aa.f
View File

@ -37,7 +37,7 @@
*> \verbatim *> \verbatim
*> *>
*> DSYTRS_AA solves a system of linear equations A*X = B with a real *> DSYTRS_AA solves a system of linear equations A*X = B with a real
*> symmetric matrix A using the factorization A = U*T*U**T or *> symmetric matrix A using the factorization A = U**T*T*U or
*> A = L*T*L**T computed by DSYTRF_AA. *> A = L*T*L**T computed by DSYTRF_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**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
*> *>
@ -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 DOUBLE PRECISION 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
@ -198,9 +200,13 @@
* *
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.
* *
* Pivot, P**T * B * 1) Forward substitution with U**T
*
IF( N.GT.1 ) THEN
*
* Pivot, P**T * B -> B
* *
DO K = 1, N DO K = 1, N
KP = IPIV( K ) KP = IPIV( K )
@ -208,12 +214,15 @@
$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
END DO END DO
* *
* Compute (U \P**T * B) -> B [ (U \P**T * B) ] * Compute U**T \ B -> B [ (U**T \P**T * B) ]
* *
CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA, CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ),
$ B( 2, 1 ), LDB) $ LDA, B( 2, 1 ), LDB)
END IF
* *
* Compute T \ B -> B [ T \ (U \P**T * B) ] * 2) Solve with triangular matrix T
*
* Compute T \ B -> B [ T \ (U**T \P**T * B) ]
* *
CALL DLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1) CALL DLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1)
IF( N.GT.1 ) THEN IF( N.GT.1 ) THEN
@ -223,24 +232,33 @@
CALL DGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB, CALL DGTSV( 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 DTRSM( '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**T \P**T * B) ) ]
*
CALL DTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ),
$ LDA, B( 2, 1 ), LDB)
*
* Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
* *
DO K = N, 1, -1 DO K = N, 1, -1
KP = IPIV( K ) KP = IPIV( K )
IF( KP.NE.K ) IF( KP.NE.K )
$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
END DO 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**T.
* *
* Pivot, P**T * B * 1) Forward substitution with L
*
IF( N.GT.1 ) THEN
*
* Pivot, P**T * B -> B
* *
DO K = 1, N DO K = 1, N
KP = IPIV( K ) KP = IPIV( K )
@ -248,10 +266,13 @@
$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
END DO END DO
* *
* Compute (L \P**T * B) -> B [ (L \P**T * B) ] * Compute L \ B -> B [ (L \P**T * B) ]
* *
CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA, CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ),
$ B( 2, 1 ), LDB) $ 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) ]
* *
@ -263,18 +284,23 @@
CALL DGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB, CALL DGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB,
$ INFO) $ INFO)
* *
* 3) Backward substitution with L**T
*
IF( N.GT.1 ) THEN
*
* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ] * Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
* *
CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA, CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ),
$ B( 2, 1 ), LDB) $ LDA, B( 2, 1 ), LDB)
* *
* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ] * Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
* *
DO K = N, 1, -1 DO K = N, 1, -1
KP = IPIV( K ) KP = IPIV( K )
IF( KP.NE.K ) IF( KP.NE.K )
$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
END DO END DO
END IF
* *
END IF END IF
* *

18
lapack-netlib/SRC/dsytrs_aa_2stage.f
View File

@ -36,7 +36,7 @@
*> \verbatim *> \verbatim
*> *>
*> DSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a real *> DSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a real
*> symmetric matrix A using the factorization A = U*T*U**T or *> symmetric matrix A using the factorization A = U**T*T*U or
*> A = L*T*L**T computed by DSYTRF_AA_2STAGE. *> A = L*T*L**T computed by DSYTRF_AA_2STAGE.
*> \endverbatim *> \endverbatim
* *
@ -48,7 +48,7 @@
*> 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
*> *>
@ -208,15 +208,15 @@
* *
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 DLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 ) CALL DLASWP( 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 DTRSM( 'L', 'U', 'T', 'U', N-NB, NRHS, ONE, A(1, NB+1), CALL DTRSM( 'L', 'U', 'T', 'U', N-NB, NRHS, ONE, A(1, NB+1),
$ LDA, B(NB+1, 1), LDB) $ LDA, B(NB+1, 1), LDB)
@ -234,7 +234,7 @@
CALL DTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1), CALL DTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1),
$ LDA, B(NB+1, 1), LDB) $ LDA, B(NB+1, 1), LDB)
* *
* Pivot, P * B [ P * (U \ (T \ (U**T \P**T * B) )) ] * Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
* *
CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 ) CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
* *
@ -246,11 +246,11 @@
* *
IF( N.GT.NB ) THEN IF( N.GT.NB ) THEN
* *
* Pivot, P**T * B * Pivot, P**T * B -> B
* *
CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 ) CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
* *
* Compute (L \P**T * B) -> B [ (L \P**T * B) ] * Compute (L \ B) -> B [ (L \P**T * B) ]
* *
CALL DTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1), CALL DTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
$ LDA, B(NB+1, 1), LDB) $ LDA, B(NB+1, 1), LDB)
@ -268,7 +268,7 @@
CALL DTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1), CALL DTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
$ LDA, B(NB+1, 1), LDB) $ LDA, B(NB+1, 1), LDB)
* *
* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ] * Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
* *
CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 ) CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
* *

4
lapack-netlib/SRC/dtgsy2.f
View File

@ -71,7 +71,7 @@
*> R * B**T + L * E**T = scale * -F *> R * B**T + L * E**T = scale * -F
*> *>
*> This case is used to compute an estimate of Dif[(A, D), (B, E)] = *> This case is used to compute an estimate of Dif[(A, D), (B, E)] =
*> sigma_min(Z) using reverse communicaton with DLACON. *> sigma_min(Z) using reverse communication with DLACON.
*> *>
*> DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL *> DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL
*> of an upper bound on the separation between to matrix pairs. Then *> of an upper bound on the separation between to matrix pairs. Then
@ -85,7 +85,7 @@
*> \param[in] TRANS *> \param[in] TRANS
*> \verbatim *> \verbatim
*> TRANS is CHARACTER*1 *> TRANS is CHARACTER*1
*> = 'N', solve the generalized Sylvester equation (1). *> = 'N': solve the generalized Sylvester equation (1).
*> = 'T': solve the 'transposed' system (3). *> = 'T': solve the 'transposed' system (3).
*> \endverbatim *> \endverbatim
*> *>

14
lapack-netlib/SRC/dtgsyl.f
View File

@ -88,20 +88,20 @@
*> \param[in] TRANS *> \param[in] TRANS
*> \verbatim *> \verbatim
*> TRANS is CHARACTER*1 *> TRANS is CHARACTER*1
*> = 'N', solve the generalized Sylvester equation (1). *> = 'N': solve the generalized Sylvester equation (1).
*> = 'T', solve the 'transposed' system (3). *> = 'T': solve the 'transposed' system (3).
*> \endverbatim *> \endverbatim
*> *>
*> \param[in] IJOB *> \param[in] IJOB
*> \verbatim *> \verbatim
*> IJOB is INTEGER *> IJOB is INTEGER
*> Specifies what kind of functionality to be performed. *> Specifies what kind of functionality to be performed.
*> =0: solve (1) only. *> = 0: solve (1) only.
*> =1: The functionality of 0 and 3. *> = 1: The functionality of 0 and 3.
*> =2: The functionality of 0 and 4. *> = 2: The functionality of 0 and 4.
*> =3: Only an estimate of Dif[(A,D), (B,E)] is computed. *> = 3: Only an estimate of Dif[(A,D), (B,E)] is computed.
*> (look ahead strategy IJOB = 1 is used). *> (look ahead strategy IJOB = 1 is used).
*> =4: Only an estimate of Dif[(A,D), (B,E)] is computed. *> = 4: Only an estimate of Dif[(A,D), (B,E)] is computed.
*> ( DGECON on sub-systems is used ). *> ( DGECON on sub-systems is used ).
*> Not referenced if TRANS = 'T'. *> Not referenced if TRANS = 'T'.
*> \endverbatim *> \endverbatim

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

@ -94,7 +94,7 @@
*> *>
*> \param[in] V *> \param[in] V
*> \verbatim *> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDA,K) *> V is DOUBLE PRECISION array, dimension (LDV,K)
*> The i-th row must contain the vector which defines the *> The i-th row must contain the vector which defines the
*> elementary reflector H(i), for i = 1,2,...,k, as returned by *> elementary reflector H(i), for i = 1,2,...,k, as returned by
*> DTPLQT in B. See Further Details. *> DTPLQT in B. See Further Details.

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

@ -94,7 +94,7 @@
*> *>
*> \param[in] V *> \param[in] V
*> \verbatim *> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDA,K) *> V is DOUBLE PRECISION array, dimension (LDV,K)
*> The i-th column must contain the vector which defines the *> The i-th column must contain the vector which defines the
*> elementary reflector H(i), for i = 1,2,...,k, as returned by *> elementary reflector H(i), for i = 1,2,...,k, as returned by
*> CTPQRT in B. See Further Details. *> CTPQRT in B. See Further Details.

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

@ -152,8 +152,8 @@
*> \verbatim *> \verbatim
*> LDA is INTEGER *> LDA is INTEGER
*> The leading dimension of the array A. *> The leading dimension of the array A.
*> If SIDE = 'L', LDC >= max(1,K); *> If SIDE = 'L', LDA >= max(1,K);
*> If SIDE = 'R', LDC >= max(1,M). *> If SIDE = 'R', LDA >= max(1,M).
*> \endverbatim *> \endverbatim
*> *>
*> \param[in,out] B *> \param[in,out] B