--- rpl/lapack/lapack/dlaqr0.f 2018/05/29 07:17:58 1.17 +++ rpl/lapack/lapack/dlaqr0.f 2020/05/21 21:45:59 1.18 @@ -67,7 +67,7 @@ *> \param[in] N *> \verbatim *> N is INTEGER -*> The order of the matrix H. N .GE. 0. +*> The order of the matrix H. N >= 0. *> \endverbatim *> *> \param[in] ILO @@ -79,12 +79,12 @@ *> \verbatim *> IHI is INTEGER *> It is assumed that H is already upper triangular in rows -*> and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1, +*> and columns 1:ILO-1 and IHI+1:N and, if ILO > 1, *> H(ILO,ILO-1) is zero. ILO and IHI are normally set by a *> previous call to DGEBAL, and then passed to DGEHRD when the *> matrix output by DGEBAL is reduced to Hessenberg form. *> Otherwise, ILO and IHI should be set to 1 and N, -*> respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N. +*> respectively. If N > 0, then 1 <= ILO <= IHI <= N. *> If N = 0, then ILO = 1 and IHI = 0. *> \endverbatim *> @@ -97,19 +97,19 @@ *> decomposition (the Schur form); 2-by-2 diagonal blocks *> (corresponding to complex conjugate pairs of eigenvalues) *> are returned in standard form, with H(i,i) = H(i+1,i+1) -*> and H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and WANTT is +*> and H(i+1,i)*H(i,i+1) < 0. If INFO = 0 and WANTT is *> .FALSE., then the contents of H are unspecified on exit. -*> (The output value of H when INFO.GT.0 is given under the +*> (The output value of H when INFO > 0 is given under the *> description of INFO below.) *> -*> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and +*> This subroutine may explicitly set H(i,j) = 0 for i > j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER -*> The leading dimension of the array H. LDH .GE. max(1,N). +*> The leading dimension of the array H. LDH >= max(1,N). *> \endverbatim *> *> \param[out] WR @@ -125,7 +125,7 @@ *> and WI(ILO:IHI). If two eigenvalues are computed as a *> complex conjugate pair, they are stored in consecutive *> elements of WR and WI, say the i-th and (i+1)th, with -*> WI(i) .GT. 0 and WI(i+1) .LT. 0. If WANTT is .TRUE., then +*> WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., then *> the eigenvalues are stored in the same order as on the *> diagonal of the Schur form returned in H, with *> WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 diagonal @@ -143,7 +143,7 @@ *> IHIZ is INTEGER *> Specify the rows of Z to which transformations must be *> applied if WANTZ is .TRUE.. -*> 1 .LE. ILOZ .LE. ILO; IHI .LE. IHIZ .LE. N. +*> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. *> \endverbatim *> *> \param[in,out] Z @@ -153,7 +153,7 @@ *> If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is *> replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the *> orthogonal Schur factor of H(ILO:IHI,ILO:IHI). -*> (The output value of Z when INFO.GT.0 is given under +*> (The output value of Z when INFO > 0 is given under *> the description of INFO below.) *> \endverbatim *> @@ -161,7 +161,7 @@ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. if WANTZ is .TRUE. -*> then LDZ.GE.MAX(1,IHIZ). Otherwize, LDZ.GE.1. +*> then LDZ >= MAX(1,IHIZ). Otherwise, LDZ >= 1. *> \endverbatim *> *> \param[out] WORK @@ -174,7 +174,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK .GE. max(1,N) +*> The dimension of the array WORK. LWORK >= max(1,N) *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. @@ -190,19 +190,19 @@ *> \param[out] INFO *> \verbatim *> INFO is INTEGER -*> = 0: successful exit -*> .GT. 0: if INFO = i, DLAQR0 failed to compute all of +*> = 0: successful exit +*> > 0: if INFO = i, DLAQR0 failed to compute all of *> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR *> and WI contain those eigenvalues which have been *> successfully computed. (Failures are rare.) *> -*> If INFO .GT. 0 and WANT is .FALSE., then on exit, +*> If INFO > 0 and WANT is .FALSE., then on exit, *> the remaining unconverged eigenvalues are the eigen- *> values of the upper Hessenberg matrix rows and *> columns ILO through INFO of the final, output *> value of H. *> -*> If INFO .GT. 0 and WANTT is .TRUE., then on exit +*> If INFO > 0 and WANTT is .TRUE., then on exit *> *> (*) (initial value of H)*U = U*(final value of H) *> @@ -210,7 +210,7 @@ *> value of H is upper Hessenberg and quasi-triangular *> in rows and columns INFO+1 through IHI. *> -*> If INFO .GT. 0 and WANTZ is .TRUE., then on exit +*> If INFO > 0 and WANTZ is .TRUE., then on exit *> *> (final value of Z(ILO:IHI,ILOZ:IHIZ) *> = (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U @@ -218,7 +218,7 @@ *> where U is the orthogonal matrix in (*) (regard- *> less of the value of WANTT.) *> -*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not +*> If INFO > 0 and WANTZ is .FALSE., then Z is not *> accessed. *> \endverbatim * @@ -678,7 +678,7 @@ END IF END IF * -* ==== Use up to NS of the the smallest magnatiude +* ==== Use up to NS of the the smallest magnitude * . shifts. If there aren't NS shifts available, * . then use them all, possibly dropping one to * . make the number of shifts even. ====