version 1.17, 2018/05/29 07:18:28
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version 1.18, 2020/05/21 21:46:09
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*> \param[in] N |
*> \param[in] N |
*> \verbatim |
*> \verbatim |
*> N is INTEGER |
*> N is INTEGER |
*> The order of the matrix H. N .GE. 0. |
*> The order of the matrix H. N >= 0. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] ILO |
*> \param[in] ILO |
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*> \verbatim |
*> \verbatim |
*> IHI is INTEGER |
*> IHI is INTEGER |
*> It is assumed that H is already upper triangular in rows |
*> 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 |
*> H(ILO,ILO-1) is zero. ILO and IHI are normally set by a |
*> previous call to ZGEBAL, and then passed to ZGEHRD when the |
*> previous call to ZGEBAL, and then passed to ZGEHRD when the |
*> matrix output by ZGEBAL is reduced to Hessenberg form. |
*> matrix output by ZGEBAL is reduced to Hessenberg form. |
*> Otherwise, ILO and IHI should be set to 1 and N, |
*> Otherwise, ILO and IHI should be set to 1 and N, |
*> respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N. |
*> respectively. If N > 0, then 1 <= ILO <= IHI <= N. |
*> If N = 0, then ILO = 1 and IHI = 0. |
*> If N = 0, then ILO = 1 and IHI = 0. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
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*> contains the upper triangular matrix T from the Schur |
*> contains the upper triangular matrix T from the Schur |
*> decomposition (the Schur form). If INFO = 0 and WANT is |
*> decomposition (the Schur form). If INFO = 0 and WANT is |
*> .FALSE., then the contents of H are unspecified on exit. |
*> .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.) |
*> 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. |
*> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDH |
*> \param[in] LDH |
*> \verbatim |
*> \verbatim |
*> LDH is INTEGER |
*> LDH is INTEGER |
*> The leading dimension of the array H. LDH .GE. max(1,N). |
*> The leading dimension of the array H. LDH >= max(1,N). |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] W |
*> \param[out] W |
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*> IHIZ is INTEGER |
*> IHIZ is INTEGER |
*> Specify the rows of Z to which transformations must be |
*> Specify the rows of Z to which transformations must be |
*> applied if WANTZ is .TRUE.. |
*> applied if WANTZ is .TRUE.. |
*> 1 .LE. ILOZ .LE. ILO; IHI .LE. IHIZ .LE. N. |
*> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in,out] Z |
*> \param[in,out] Z |
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*> If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is |
*> If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is |
*> replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the |
*> replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the |
*> orthogonal Schur factor of H(ILO:IHI,ILO:IHI). |
*> 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.) |
*> the description of INFO below.) |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
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*> \verbatim |
*> \verbatim |
*> LDZ is INTEGER |
*> LDZ is INTEGER |
*> The leading dimension of the array Z. if WANTZ is .TRUE. |
*> 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 |
*> \endverbatim |
*> |
*> |
*> \param[out] WORK |
*> \param[out] WORK |
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*> \param[in] LWORK |
*> \param[in] LWORK |
*> \verbatim |
*> \verbatim |
*> LWORK is INTEGER |
*> LWORK is INTEGER |
*> The dimension of the array WORK. LWORK .GE. max(1,N) |
*> The dimension of the array WORK. LWORK >= max(1,N) |
*> is sufficient, but LWORK typically as large as 6*N may |
*> is sufficient, but LWORK typically as large as 6*N may |
*> be required for optimal performance. A workspace query |
*> be required for optimal performance. A workspace query |
*> to determine the optimal workspace size is recommended. |
*> to determine the optimal workspace size is recommended. |
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*> \verbatim |
*> \verbatim |
*> INFO is INTEGER |
*> INFO is INTEGER |
*> = 0: successful exit |
*> = 0: successful exit |
*> .GT. 0: if INFO = i, ZLAQR4 failed to compute all of |
*> > 0: if INFO = i, ZLAQR4 failed to compute all of |
*> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR |
*> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR |
*> and WI contain those eigenvalues which have been |
*> and WI contain those eigenvalues which have been |
*> successfully computed. (Failures are rare.) |
*> 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- |
*> the remaining unconverged eigenvalues are the eigen- |
*> values of the upper Hessenberg matrix rows and |
*> values of the upper Hessenberg matrix rows and |
*> columns ILO through INFO of the final, output |
*> columns ILO through INFO of the final, output |
*> value of H. |
*> value of H. |
*> |
*> |
*> If INFO .GT. 0 and 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) |
*> (*) (initial value of H)*U = U*(final value of H) |
*> |
*> |
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*> value of H is upper Hessenberg and triangular in |
*> value of H is upper Hessenberg and triangular in |
*> rows and columns INFO+1 through IHI. |
*> rows and columns INFO+1 through IHI. |
*> |
*> |
*> If INFO .GT. 0 and WANTZ is .TRUE., then on exit |
*> If INFO > 0 and WANTZ is .TRUE., then on exit |
*> |
*> |
*> (final value of Z(ILO:IHI,ILOZ:IHIZ) |
*> (final value of Z(ILO:IHI,ILOZ:IHIZ) |
*> = (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U |
*> = (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U |
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*> where U is the unitary matrix in (*) (regard- |
*> where U is the unitary matrix in (*) (regard- |
*> less of the value of WANTT.) |
*> 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. |
*> accessed. |
*> \endverbatim |
*> \endverbatim |
* |
* |
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END IF |
END IF |
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, |
* . shifts. If there aren't NS shifts available, |
* . then use them all, possibly dropping one to |
* . then use them all, possibly dropping one to |
* . make the number of shifts even. ==== |
* . make the number of shifts even. ==== |