diff --git a/lapack-netlib/SRC/dporfsx.f b/lapack-netlib/SRC/dporfsx.f index 53724925e..67cca9ccf 100644 --- a/lapack-netlib/SRC/dporfsx.f +++ b/lapack-netlib/SRC/dporfsx.f @@ -135,7 +135,7 @@ *> \param[in,out] S *> \verbatim *> 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 = *> '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 @@ -263,7 +263,7 @@ *> information as described below. There currently are up to three *> pieces of information returned for each right-hand side. If *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then -*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most +*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. *> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith @@ -299,14 +299,14 @@ *> \param[in] NPARAMS *> \verbatim *> NPARAMS is INTEGER -*> Specifies the number of parameters set in PARAMS. If .LE. 0, the +*> Specifies the number of parameters set in PARAMS. If <= 0, the *> PARAMS array is never referenced and default values are used. *> \endverbatim *> *> \param[in,out] PARAMS *> \verbatim *> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS) -*> Specifies algorithm parameters. If an entry is .LT. 0.0, then +*> Specifies algorithm parameters. If an entry is < 0.0, then *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. @@ -314,9 +314,9 @@ *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 -*> = 0.0 : No refinement is performed, and no error bounds are +*> = 0.0: No refinement is performed, and no error bounds are *> computed. -*> = 1.0 : Use the double-precision refinement algorithm, +*> = 1.0: Use the double-precision refinement algorithm, *> possibly with doubled-single computations if the *> compilation environment does not support DOUBLE *> PRECISION. diff --git a/lapack-netlib/SRC/dposvxx.f b/lapack-netlib/SRC/dposvxx.f index 488e0b15a..b0de44910 100644 --- a/lapack-netlib/SRC/dposvxx.f +++ b/lapack-netlib/SRC/dposvxx.f @@ -366,7 +366,7 @@ *> information as described below. There currently are up to three *> pieces of information returned for each right-hand side. If *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then -*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most +*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. *> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith @@ -402,14 +402,14 @@ *> \param[in] NPARAMS *> \verbatim *> NPARAMS is INTEGER -*> Specifies the number of parameters set in PARAMS. If .LE. 0, the +*> Specifies the number of parameters set in PARAMS. If <= 0, the *> PARAMS array is never referenced and default values are used. *> \endverbatim *> *> \param[in,out] PARAMS *> \verbatim *> PARAMS is DOUBLE PRECISION array, dimension NPARAMS -*> Specifies algorithm parameters. If an entry is .LT. 0.0, then +*> Specifies algorithm parameters. If an entry is < 0.0, then *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. @@ -417,9 +417,9 @@ *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 -*> = 0.0 : No refinement is performed, and no error bounds are +*> = 0.0: No refinement is performed, and no error bounds are *> computed. -*> = 1.0 : Use the extra-precise refinement algorithm. +*> = 1.0: Use the extra-precise refinement algorithm. *> (other values are reserved for future use) *> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual diff --git a/lapack-netlib/SRC/dsb2st_kernels.f b/lapack-netlib/SRC/dsb2st_kernels.f index 3bf126d5b..a9dc6b5ca 100644 --- a/lapack-netlib/SRC/dsb2st_kernels.f +++ b/lapack-netlib/SRC/dsb2st_kernels.f @@ -1,26 +1,26 @@ *> \brief \b DSB2ST_KERNELS * * @generated from zhb2st_kernels.f, fortran z -> d, Wed Dec 7 08:22:39 2016 -* +* * =========== DOCUMENTATION =========== * -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * *> \htmlonly -*> Download DSB2ST_KERNELS + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> +*> Download DSB2ST_KERNELS + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> *> [TXT] -*> \endhtmlonly +*> \endhtmlonly * * Definition: * =========== * -* SUBROUTINE DSB2ST_KERNELS( UPLO, WANTZ, TTYPE, +* SUBROUTINE DSB2ST_KERNELS( UPLO, WANTZ, TTYPE, * ST, ED, SWEEP, N, NB, IB, * A, LDA, V, TAU, LDVT, WORK) * @@ -32,9 +32,9 @@ * INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT * .. * .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), V( * ), +* DOUBLE PRECISION A( LDA, * ), V( * ), * TAU( * ), WORK( * ) -* +* *> \par Purpose: * ============= *> @@ -124,7 +124,7 @@ *> LDVT is INTEGER. *> \endverbatim *> -*> \param[in] WORK +*> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array. Workspace of size nb. *> \endverbatim @@ -147,7 +147,7 @@ *> http://doi.acm.org/10.1145/2063384.2063394 *> *> A. Haidar, J. Kurzak, P. Luszczek, 2013. -*> An improved parallel singular value algorithm and its implementation +*> An improved parallel singular value algorithm and its implementation *> for multicore hardware, In Proceedings of 2013 International Conference *> for High Performance Computing, Networking, Storage and Analysis (SC '13). *> Denver, Colorado, USA, 2013. @@ -155,16 +155,16 @@ *> http://doi.acm.org/10.1145/2503210.2503292 *> *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. -*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure +*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure *> calculations based on fine-grained memory aware tasks. *> International Journal of High Performance Computing Applications. *> Volume 28 Issue 2, Pages 196-209, May 2014. -*> http://hpc.sagepub.com/content/28/2/196 +*> http://hpc.sagepub.com/content/28/2/196 *> *> \endverbatim *> * ===================================================================== - SUBROUTINE DSB2ST_KERNELS( UPLO, WANTZ, TTYPE, + SUBROUTINE DSB2ST_KERNELS( UPLO, WANTZ, TTYPE, $ ST, ED, SWEEP, N, NB, IB, $ A, LDA, V, TAU, LDVT, WORK) * @@ -181,7 +181,7 @@ INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT * .. * .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), V( * ), + DOUBLE PRECISION A( LDA, * ), V( * ), $ TAU( * ), WORK( * ) * .. * @@ -195,8 +195,8 @@ * .. Local Scalars .. LOGICAL UPPER INTEGER I, J1, J2, LM, LN, VPOS, TAUPOS, - $ DPOS, OFDPOS, AJETER - DOUBLE PRECISION CTMP + $ DPOS, OFDPOS, AJETER + DOUBLE PRECISION CTMP * .. * .. External Subroutines .. EXTERNAL DLARFG, DLARFX, DLARFY @@ -209,7 +209,7 @@ * .. * .. * .. Executable Statements .. -* +* AJETER = IB + LDVT UPPER = LSAME( UPLO, 'U' ) @@ -240,10 +240,10 @@ V( VPOS ) = ONE DO 10 I = 1, LM-1 V( VPOS+I ) = ( A( OFDPOS-I, ST+I ) ) - A( OFDPOS-I, ST+I ) = ZERO + A( OFDPOS-I, ST+I ) = ZERO 10 CONTINUE CTMP = ( A( OFDPOS, ST ) ) - CALL DLARFG( LM, CTMP, V( VPOS+1 ), 1, + CALL DLARFG( LM, CTMP, V( VPOS+1 ), 1, $ TAU( TAUPOS ) ) A( OFDPOS, ST ) = CTMP * @@ -281,14 +281,14 @@ * V( VPOS ) = ONE DO 30 I = 1, LM-1 - V( VPOS+I ) = + V( VPOS+I ) = $ ( A( DPOS-NB-I, J1+I ) ) A( DPOS-NB-I, J1+I ) = ZERO 30 CONTINUE CTMP = ( A( DPOS-NB, J1 ) ) CALL DLARFG( LM, CTMP, V( VPOS+1 ), 1, TAU( TAUPOS ) ) A( DPOS-NB, J1 ) = CTMP -* +* CALL DLARFX( 'Right', LN-1, LM, V( VPOS ), $ TAU( TAUPOS ), $ A( DPOS-NB+1, J1 ), LDA-1, WORK) @@ -296,9 +296,9 @@ ENDIF * * Lower case -* +* ELSE -* +* IF( WANTZ ) THEN VPOS = MOD( SWEEP-1, 2 ) * N + ST TAUPOS = MOD( SWEEP-1, 2 ) * N + ST @@ -313,9 +313,9 @@ V( VPOS ) = ONE DO 20 I = 1, LM-1 V( VPOS+I ) = A( OFDPOS+I, ST-1 ) - A( OFDPOS+I, ST-1 ) = ZERO + A( OFDPOS+I, ST-1 ) = ZERO 20 CONTINUE - CALL DLARFG( LM, A( OFDPOS, ST-1 ), V( VPOS+1 ), 1, + CALL DLARFG( LM, A( OFDPOS, ST-1 ), V( VPOS+1 ), 1, $ TAU( TAUPOS ) ) * LM = ED - ST + 1 @@ -342,7 +342,7 @@ LM = J2-J1+1 * IF( LM.GT.0) THEN - CALL DLARFX( 'Right', LM, LN, V( VPOS ), + CALL DLARFX( 'Right', LM, LN, V( VPOS ), $ TAU( TAUPOS ), A( DPOS+NB, ST ), $ LDA-1, WORK) * @@ -359,13 +359,13 @@ V( VPOS+I ) = A( DPOS+NB+I, ST ) A( DPOS+NB+I, ST ) = ZERO 40 CONTINUE - CALL DLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1, + CALL DLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1, $ TAU( TAUPOS ) ) * - CALL DLARFX( 'Left', LM, LN-1, V( VPOS ), + CALL DLARFX( 'Left', LM, LN-1, V( VPOS ), $ ( TAU( TAUPOS ) ), $ A( DPOS+NB-1, ST+1 ), LDA-1, WORK) - + ENDIF ENDIF ENDIF @@ -374,4 +374,4 @@ * * END OF DSB2ST_KERNELS * - END + END diff --git a/lapack-netlib/SRC/dsbgvx.f b/lapack-netlib/SRC/dsbgvx.f index eab5ebcbb..6de1eb89b 100644 --- a/lapack-netlib/SRC/dsbgvx.f +++ b/lapack-netlib/SRC/dsbgvx.f @@ -261,11 +261,11 @@ *> \param[out] INFO *> \verbatim *> INFO is INTEGER -*> = 0 : successful exit -*> < 0 : if INFO = -i, the i-th argument had an illegal value +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value *> <= N: if INFO = i, then i eigenvectors failed to converge. *> 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 *> minor of order i of B is not positive definite. *> The factorization of B could not be completed and diff --git a/lapack-netlib/SRC/dsgesv.f b/lapack-netlib/SRC/dsgesv.f index f47327d00..edbb87e7a 100644 --- a/lapack-netlib/SRC/dsgesv.f +++ b/lapack-netlib/SRC/dsgesv.f @@ -92,9 +92,9 @@ *> dimension (LDA,N) *> On entry, the N-by-N coefficient matrix A. *> 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 -*> (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 *> A = P*L*U; the unit diagonal elements of L are not stored. *> \endverbatim @@ -111,8 +111,8 @@ *> The pivot indices that define the permutation matrix P; *> row i of the matrix was interchanged with row IPIV(i). *> Corresponds either to the single precision factorization -*> (if INFO.EQ.0 and ITER.GE.0) or the double precision -*> factorization (if INFO.EQ.0 and ITER.LT.0). +*> (if INFO = 0 and ITER >= 0) or the double precision +*> factorization (if INFO = 0 and ITER < 0). *> \endverbatim *> *> \param[in] B @@ -406,7 +406,7 @@ 30 CONTINUE * * 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 * on double precision routine. * diff --git a/lapack-netlib/SRC/dsposv.f b/lapack-netlib/SRC/dsposv.f index 4a8575241..6c8baa56b 100644 --- a/lapack-netlib/SRC/dsposv.f +++ b/lapack-netlib/SRC/dsposv.f @@ -106,9 +106,9 @@ *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> 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 -*> (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 *> factorization A = U**T*U or A = L*L**T. *> \endverbatim @@ -413,7 +413,7 @@ 30 CONTINUE * * 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 on double precision routine. * diff --git a/lapack-netlib/SRC/dstemr.f b/lapack-netlib/SRC/dstemr.f index a1a8e3433..16c9d970d 100644 --- a/lapack-netlib/SRC/dstemr.f +++ b/lapack-netlib/SRC/dstemr.f @@ -233,13 +233,13 @@ *> \param[in,out] TRYRAC *> \verbatim *> 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 *> accuracy. If so, the code uses relative-accuracy preserving *> algorithms that might be (a bit) slower depending on the matrix. *> If the matrix does not define its eigenvalues to high relative *> 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 *> techniques. *> On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix diff --git a/lapack-netlib/SRC/dsyconvf.f b/lapack-netlib/SRC/dsyconvf.f index 37c8157ba..60cfd1e65 100644 --- a/lapack-netlib/SRC/dsyconvf.f +++ b/lapack-netlib/SRC/dsyconvf.f @@ -291,7 +291,7 @@ * * 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 * I = N @@ -344,7 +344,7 @@ * * 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 * I = 1 @@ -435,7 +435,7 @@ * * 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 * I = 1 @@ -488,7 +488,7 @@ * * 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 * I = N diff --git a/lapack-netlib/SRC/dsyconvf_rook.f b/lapack-netlib/SRC/dsyconvf_rook.f index 5c774906e..bd683a087 100644 --- a/lapack-netlib/SRC/dsyconvf_rook.f +++ b/lapack-netlib/SRC/dsyconvf_rook.f @@ -282,7 +282,7 @@ * * 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 * I = N @@ -333,7 +333,7 @@ * * 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 * I = 1 @@ -423,7 +423,7 @@ * * 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 * I = 1 @@ -474,7 +474,7 @@ * * 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 * I = N diff --git a/lapack-netlib/SRC/dsyev_2stage.f b/lapack-netlib/SRC/dsyev_2stage.f index fff0dedbc..9d802905c 100644 --- a/lapack-netlib/SRC/dsyev_2stage.f +++ b/lapack-netlib/SRC/dsyev_2stage.f @@ -317,7 +317,7 @@ IF( .NOT.WANTZ ) THEN CALL DSTERF( N, W, WORK( INDE ), INFO ) 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 RETURN CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), diff --git a/lapack-netlib/SRC/dsyevd_2stage.f b/lapack-netlib/SRC/dsyevd_2stage.f index 75a6da436..ff8e08d71 100644 --- a/lapack-netlib/SRC/dsyevd_2stage.f +++ b/lapack-netlib/SRC/dsyevd_2stage.f @@ -385,7 +385,7 @@ IF( .NOT.WANTZ ) THEN CALL DSTERF( N, W, WORK( INDE ), INFO ) 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 RETURN CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N, diff --git a/lapack-netlib/SRC/dsyrfsx.f b/lapack-netlib/SRC/dsyrfsx.f index e128cd4e0..eb091e720 100644 --- a/lapack-netlib/SRC/dsyrfsx.f +++ b/lapack-netlib/SRC/dsyrfsx.f @@ -271,7 +271,7 @@ *> information as described below. There currently are up to three *> pieces of information returned for each right-hand side. If *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then -*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most +*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. *> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith @@ -307,14 +307,14 @@ *> \param[in] NPARAMS *> \verbatim *> NPARAMS is INTEGER -*> Specifies the number of parameters set in PARAMS. If .LE. 0, the +*> Specifies the number of parameters set in PARAMS. If <= 0, the *> PARAMS array is never referenced and default values are used. *> \endverbatim *> *> \param[in,out] PARAMS *> \verbatim *> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS) -*> Specifies algorithm parameters. If an entry is .LT. 0.0, then +*> Specifies algorithm parameters. If an entry is < 0.0, then *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. @@ -322,9 +322,9 @@ *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 -*> = 0.0 : No refinement is performed, and no error bounds are +*> = 0.0: No refinement is performed, and no error bounds are *> computed. -*> = 1.0 : Use the double-precision refinement algorithm, +*> = 1.0: Use the double-precision refinement algorithm, *> possibly with doubled-single computations if the *> compilation environment does not support DOUBLE *> PRECISION. diff --git a/lapack-netlib/SRC/dsysv_aa.f b/lapack-netlib/SRC/dsysv_aa.f index 7192928c6..4ee474448 100644 --- a/lapack-netlib/SRC/dsysv_aa.f +++ b/lapack-netlib/SRC/dsysv_aa.f @@ -42,7 +42,7 @@ *> matrices. *> *> 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', *> where U (or L) is a product of permutation and unit upper (lower) *> triangular matrices, and T is symmetric tridiagonal. The factored @@ -86,7 +86,7 @@ *> *> On exit, if INFO = 0, the tridiagonal matrix T and 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. *> \endverbatim *> @@ -230,7 +230,7 @@ RETURN 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 ) IF( INFO.EQ.0 ) THEN diff --git a/lapack-netlib/SRC/dsysv_aa_2stage.f b/lapack-netlib/SRC/dsysv_aa_2stage.f index 05e538f0b..ef593bc7e 100644 --- a/lapack-netlib/SRC/dsysv_aa_2stage.f +++ b/lapack-netlib/SRC/dsysv_aa_2stage.f @@ -45,7 +45,7 @@ *> matrices. *> *> 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', *> 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 @@ -259,7 +259,7 @@ 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, $ WORK, LWORK, INFO ) diff --git a/lapack-netlib/SRC/dsysvxx.f b/lapack-netlib/SRC/dsysvxx.f index 6e167d81e..0be50bcd1 100644 --- a/lapack-netlib/SRC/dsysvxx.f +++ b/lapack-netlib/SRC/dsysvxx.f @@ -377,7 +377,7 @@ *> information as described below. There currently are up to three *> pieces of information returned for each right-hand side. If *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then -*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most +*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. *> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith @@ -413,14 +413,14 @@ *> \param[in] NPARAMS *> \verbatim *> NPARAMS is INTEGER -*> Specifies the number of parameters set in PARAMS. If .LE. 0, the +*> Specifies the number of parameters set in PARAMS. If <= 0, the *> PARAMS array is never referenced and default values are used. *> \endverbatim *> *> \param[in,out] PARAMS *> \verbatim *> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS) -*> Specifies algorithm parameters. If an entry is .LT. 0.0, then +*> Specifies algorithm parameters. If an entry is < 0.0, then *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. @@ -428,9 +428,9 @@ *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 -*> = 0.0 : No refinement is performed, and no error bounds are +*> = 0.0: No refinement is performed, and no error bounds are *> computed. -*> = 1.0 : Use the extra-precise refinement algorithm. +*> = 1.0: Use the extra-precise refinement algorithm. *> (other values are reserved for future use) *> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual diff --git a/lapack-netlib/SRC/dsytf2_rk.f b/lapack-netlib/SRC/dsytf2_rk.f index 45cf62ab9..cc9e4616e 100644 --- a/lapack-netlib/SRC/dsytf2_rk.f +++ b/lapack-netlib/SRC/dsytf2_rk.f @@ -312,7 +312,7 @@ * * 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 * E( 1 ) = ZERO @@ -623,7 +623,7 @@ * * 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 * diff --git a/lapack-netlib/SRC/dsytrd_2stage.f b/lapack-netlib/SRC/dsytrd_2stage.f index 522602bb2..fc4b92908 100644 --- a/lapack-netlib/SRC/dsytrd_2stage.f +++ b/lapack-netlib/SRC/dsytrd_2stage.f @@ -123,23 +123,22 @@ *> *> \param[out] HOUS2 *> \verbatim -*> HOUS2 is DOUBLE PRECISION array, dimension LHOUS2, that -*> store the Householder representation of the stage2 +*> HOUS2 is DOUBLE PRECISION array, dimension (LHOUS2) +*> Stores the Householder representation of the stage2 *> band to tridiagonal. *> \endverbatim *> *> \param[in] LHOUS2 *> \verbatim *> LHOUS2 is INTEGER -*> The dimension of the array HOUS2. LHOUS2 = MAX(1, dimension) -*> If LWORK = -1, or LHOUS2=-1, +*> The dimension of the array HOUS2. +*> If LWORK = -1, or LHOUS2 = -1, *> then a query is assumed; the routine *> only calculates the optimal size of the HOUS2 array, returns *> this value as the first entry of the HOUS2 array, and no error *> message related to LHOUS2 is issued by XERBLA. -*> LHOUS2 = MAX(1, dimension) where -*> dimension = 4*N if VECT='N' -*> not available now if VECT='H' +*> If VECT='N', LHOUS2 = max(1, 4*n); +*> if VECT='V', option not yet available. *> \endverbatim *> *> \param[out] WORK diff --git a/lapack-netlib/SRC/dsytrd_sb2st.F b/lapack-netlib/SRC/dsytrd_sb2st.F index 4d81fe226..19f3613e3 100644 --- a/lapack-netlib/SRC/dsytrd_sb2st.F +++ b/lapack-netlib/SRC/dsytrd_sb2st.F @@ -50,9 +50,9 @@ * Arguments: * ========== * -*> \param[in] STAGE +*> \param[in] STAGE1 *> \verbatim -*> STAGE is CHARACTER*1 +*> STAGE1 is CHARACTER*1 *> = 'N': "No": to mention that the stage 1 of the reduction *> from dense to band using the dsytrd_sy2sb routine *> was not called before this routine to reproduce AB. @@ -481,7 +481,7 @@ * * Call the kernel * -#if defined(_OPENMP) && _OPENMP >= 201307 +#if defined(_OPENMP) IF( TTYPE.NE.1 ) THEN !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1)) !$OMP$ DEPEND(in:WORK(MYID-1)) diff --git a/lapack-netlib/SRC/dsytrd_sy2sb.f b/lapack-netlib/SRC/dsytrd_sy2sb.f index e0a5debc5..7f30817b0 100644 --- a/lapack-netlib/SRC/dsytrd_sy2sb.f +++ b/lapack-netlib/SRC/dsytrd_sy2sb.f @@ -363,7 +363,7 @@ * * * 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 ) * diff --git a/lapack-netlib/SRC/dsytrf.f b/lapack-netlib/SRC/dsytrf.f index d8da4f122..a3bd30a2f 100644 --- a/lapack-netlib/SRC/dsytrf.f +++ b/lapack-netlib/SRC/dsytrf.f @@ -39,7 +39,7 @@ *> the Bunch-Kaufman diagonal pivoting method. The form of the *> 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) *> triangular matrices, and D is symmetric and block diagonal with @@ -144,7 +144,7 @@ *> *> \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)* ..., *> 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 @@ -262,7 +262,7 @@ * 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 * KB, where KB is the number of columns factorized by DLASYF; diff --git a/lapack-netlib/SRC/dsytrf_aa.f b/lapack-netlib/SRC/dsytrf_aa.f index 24b3f393b..6df0da2cd 100644 --- a/lapack-netlib/SRC/dsytrf_aa.f +++ b/lapack-netlib/SRC/dsytrf_aa.f @@ -37,7 +37,7 @@ *> DSYTRF_AA computes the factorization of a real symmetric matrix A *> 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) *> triangular matrices, and T is a symmetric tridiagonal matrix. @@ -223,7 +223,7 @@ 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)) @@ -256,7 +256,7 @@ $ A( MAX(1, J), J+1 ), LDA, $ 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) IPIV( J2 ) = IPIV( J2 ) + J @@ -375,7 +375,7 @@ $ A( J+1, MAX(1, J) ), LDA, $ 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) IPIV( J2 ) = IPIV( J2 ) + J diff --git a/lapack-netlib/SRC/dsytrf_aa_2stage.f b/lapack-netlib/SRC/dsytrf_aa_2stage.f index 25fc1a2eb..a37be5bdd 100644 --- a/lapack-netlib/SRC/dsytrf_aa_2stage.f +++ b/lapack-netlib/SRC/dsytrf_aa_2stage.f @@ -38,7 +38,7 @@ *> DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A *> 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) *> 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. *> \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 *> \verbatim *> WORK is DOUBLE PRECISION workspace of size LWORK @@ -120,22 +136,6 @@ *> no error message related to LWORK is issued by XERBLA. *> \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 *> \verbatim *> INFO is INTEGER @@ -275,7 +275,7 @@ 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 @@ -442,12 +442,14 @@ c END IF * > Apply pivots to previous columns of L CALL DSWAP( K-1, A( (J+1)*NB+1, I1 ), 1, $ A( (J+1)*NB+1, I2 ), 1 ) -* > Swap A(I1+1:M, I1) with A(I2, I1+1:M) - CALL DSWAP( I2-I1-1, A( I1, I1+1 ), LDA, - $ A( I1+1, I2 ), 1 ) +* > Swap A(I1+1:M, I1) with A(I2, I1+1:M) + IF( I2.GT.(I1+1) ) + $ CALL DSWAP( I2-I1-1, A( I1, I1+1 ), LDA, + $ A( I1+1, I2 ), 1 ) * > Swap A(I2+1:M, I1) with A(I2+1:M, I2) - CALL DSWAP( N-I2, A( I1, I2+1 ), LDA, - $ A( I2, I2+1 ), LDA ) + IF( I2.LT.N ) + $ CALL DSWAP( N-I2, A( I1, I2+1 ), LDA, + $ A( I2, I2+1 ), LDA ) * > Swap A(I1, I1) with A(I2, I2) PIV = A( I1, I1 ) A( I1, I1 ) = A( I2, I2 ) @@ -616,11 +618,13 @@ c END IF CALL DSWAP( K-1, A( I1, (J+1)*NB+1 ), LDA, $ A( I2, (J+1)*NB+1 ), LDA ) * > Swap A(I1+1:M, I1) with A(I2, I1+1:M) - CALL DSWAP( I2-I1-1, A( I1+1, I1 ), 1, - $ A( I2, I1+1 ), LDA ) + IF( I2.GT.(I1+1) ) + $ CALL DSWAP( I2-I1-1, A( I1+1, I1 ), 1, + $ A( I2, I1+1 ), LDA ) * > Swap A(I2+1:M, I1) with A(I2+1:M, I2) - CALL DSWAP( N-I2, A( I2+1, I1 ), 1, - $ A( I2+1, I2 ), 1 ) + IF( I2.LT.N ) + $ CALL DSWAP( N-I2, A( I2+1, I1 ), 1, + $ A( I2+1, I2 ), 1 ) * > Swap A(I1, I1) with A(I2, I2) PIV = A( I1, I1 ) A( I1, I1 ) = A( I2, I2 ) diff --git a/lapack-netlib/SRC/dsytri2.f b/lapack-netlib/SRC/dsytri2.f index 23f8b9fa2..5c3a5ec76 100644 --- a/lapack-netlib/SRC/dsytri2.f +++ b/lapack-netlib/SRC/dsytri2.f @@ -62,7 +62,7 @@ *> \param[in,out] A *> \verbatim *> 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. *> *> On exit, if INFO = 0, the (symmetric) inverse of the original @@ -82,7 +82,7 @@ *> \param[in] IPIV *> \verbatim *> 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. *> \endverbatim *> diff --git a/lapack-netlib/SRC/dsytrs_aa.f b/lapack-netlib/SRC/dsytrs_aa.f index 05ef31ff3..d9dc0a6d1 100644 --- a/lapack-netlib/SRC/dsytrs_aa.f +++ b/lapack-netlib/SRC/dsytrs_aa.f @@ -37,7 +37,7 @@ *> \verbatim *> *> 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. *> \endverbatim * @@ -49,7 +49,7 @@ *> UPLO is CHARACTER*1 *> Specifies whether the details of the factorization are stored *> 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. *> \endverbatim *> @@ -97,14 +97,16 @@ *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> -*> \param[in] WORK +*> \param[out] WORK *> \verbatim -*> WORK is DOUBLE array, dimension (MAX(1,LWORK)) +*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> \endverbatim *> *> \param[in] LWORK *> \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 *> \verbatim @@ -198,22 +200,29 @@ * 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 * - DO K = 1, N - KP = IPIV( K ) - IF( KP.NE.K ) - $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) - END DO + IF( N.GT.1 ) THEN * -* Compute (U \P**T * B) -> B [ (U \P**T * B) ] +* Pivot, P**T * B -> B * - CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA, - $ B( 2, 1 ), LDB) + DO K = 1, N + KP = IPIV( K ) + IF( KP.NE.K ) + $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + END DO * -* Compute T \ B -> B [ T \ (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, B( 2, 1 ), LDB) + END IF +* +* 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) IF( N.GT.1 ) THEN @@ -223,35 +232,47 @@ CALL DGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB, $ 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, - $ B( 2, 1 ), LDB) + IF( N.GT.1 ) THEN * -* Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ] +* Compute U \ B -> B [ U \ (T \ (U**T \P**T * B) ) ] * - DO K = N, 1, -1 - KP = IPIV( K ) - IF( KP.NE.K ) - $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) - END DO + 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 + KP = IPIV( K ) + IF( KP.NE.K ) + $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + END DO + END IF * ELSE * * Solve A*X = B, where A = L*T*L**T. * -* Pivot, P**T * B +* 1) Forward substitution with L * - DO K = 1, N - KP = IPIV( K ) - IF( KP.NE.K ) - $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) - END DO + IF( N.GT.1 ) THEN * -* Compute (L \P**T * B) -> B [ (L \P**T * B) ] +* Pivot, P**T * B -> B * - CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA, - $ B( 2, 1 ), LDB) + DO K = 1, N + KP = IPIV( K ) + IF( KP.NE.K ) + $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + END DO +* +* Compute L \ B -> B [ (L \P**T * B) ] +* + CALL DTRSM( '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) ] * @@ -263,18 +284,23 @@ CALL DGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB, $ INFO) * -* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ] +* 3) Backward substitution with L**T * - CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA, - $ B( 2, 1 ), LDB) + IF( N.GT.1 ) THEN * -* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ] +* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ] * - DO K = N, 1, -1 - KP = IPIV( K ) - IF( KP.NE.K ) - $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) - END DO + CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), + $ LDA, B( 2, 1 ), LDB) +* +* Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ] +* + DO K = N, 1, -1 + KP = IPIV( K ) + IF( KP.NE.K ) + $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + END DO + END IF * END IF * diff --git a/lapack-netlib/SRC/dsytrs_aa_2stage.f b/lapack-netlib/SRC/dsytrs_aa_2stage.f index bb283cb95..69c702f8a 100644 --- a/lapack-netlib/SRC/dsytrs_aa_2stage.f +++ b/lapack-netlib/SRC/dsytrs_aa_2stage.f @@ -36,7 +36,7 @@ *> \verbatim *> *> 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. *> \endverbatim * @@ -48,7 +48,7 @@ *> UPLO is CHARACTER*1 *> Specifies whether the details of the factorization are stored *> 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. *> \endverbatim *> @@ -208,15 +208,15 @@ * 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 * -* Pivot, P**T * B +* Pivot, P**T * B -> B * 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), $ LDA, B(NB+1, 1), LDB) @@ -234,7 +234,7 @@ CALL DTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1), $ 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 ) * @@ -246,11 +246,11 @@ * IF( N.GT.NB ) THEN * -* Pivot, P**T * B +* Pivot, P**T * B -> B * 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), $ LDA, B(NB+1, 1), LDB) @@ -268,7 +268,7 @@ CALL DTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1), $ 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 ) * diff --git a/lapack-netlib/SRC/dtgsy2.f b/lapack-netlib/SRC/dtgsy2.f index 1c687b15e..e8c9b4001 100644 --- a/lapack-netlib/SRC/dtgsy2.f +++ b/lapack-netlib/SRC/dtgsy2.f @@ -71,7 +71,7 @@ *> R * B**T + L * E**T = scale * -F *> *> 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 *> of an upper bound on the separation between to matrix pairs. Then @@ -85,7 +85,7 @@ *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 -*> = 'N', solve the generalized Sylvester equation (1). +*> = 'N': solve the generalized Sylvester equation (1). *> = 'T': solve the 'transposed' system (3). *> \endverbatim *> diff --git a/lapack-netlib/SRC/dtgsyl.f b/lapack-netlib/SRC/dtgsyl.f index 1cc3a1bf8..bb0751794 100644 --- a/lapack-netlib/SRC/dtgsyl.f +++ b/lapack-netlib/SRC/dtgsyl.f @@ -88,20 +88,20 @@ *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 -*> = 'N', solve the generalized Sylvester equation (1). -*> = 'T', solve the 'transposed' system (3). +*> = 'N': solve the generalized Sylvester equation (1). +*> = 'T': solve the 'transposed' system (3). *> \endverbatim *> *> \param[in] IJOB *> \verbatim *> IJOB is INTEGER *> Specifies what kind of functionality to be performed. -*> =0: solve (1) only. -*> =1: The functionality of 0 and 3. -*> =2: The functionality of 0 and 4. -*> =3: Only an estimate of Dif[(A,D), (B,E)] is computed. +*> = 0: solve (1) only. +*> = 1: The functionality of 0 and 3. +*> = 2: The functionality of 0 and 4. +*> = 3: Only an estimate of Dif[(A,D), (B,E)] is computed. *> (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 ). *> Not referenced if TRANS = 'T'. *> \endverbatim diff --git a/lapack-netlib/SRC/dtpmlqt.f b/lapack-netlib/SRC/dtpmlqt.f index 3782d0c71..975ebdc27 100644 --- a/lapack-netlib/SRC/dtpmlqt.f +++ b/lapack-netlib/SRC/dtpmlqt.f @@ -94,7 +94,7 @@ *> *> \param[in] V *> \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 *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> DTPLQT in B. See Further Details. diff --git a/lapack-netlib/SRC/dtpmqrt.f b/lapack-netlib/SRC/dtpmqrt.f index 44985a80d..a7888e192 100644 --- a/lapack-netlib/SRC/dtpmqrt.f +++ b/lapack-netlib/SRC/dtpmqrt.f @@ -94,7 +94,7 @@ *> *> \param[in] V *> \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 *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> CTPQRT in B. See Further Details. diff --git a/lapack-netlib/SRC/dtprfb.f b/lapack-netlib/SRC/dtprfb.f index 6ae8fad8c..6d3b4dae1 100644 --- a/lapack-netlib/SRC/dtprfb.f +++ b/lapack-netlib/SRC/dtprfb.f @@ -152,8 +152,8 @@ *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. -*> If SIDE = 'L', LDC >= max(1,K); -*> If SIDE = 'R', LDC >= max(1,M). +*> If SIDE = 'L', LDA >= max(1,K); +*> If SIDE = 'R', LDA >= max(1,M). *> \endverbatim *> *> \param[in,out] B