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---
:name: dlahqr
:md5sum: a93986d5c9d574d1cd8150a2f4428399
:category: :subroutine
:arguments:
- wantt:
:type: logical
:intent: input
- wantz:
:type: logical
:intent: input
- n:
:type: integer
:intent: input
- ilo:
:type: integer
:intent: input
- ihi:
:type: integer
:intent: input
- h:
:type: doublereal
:intent: input/output
:dims:
- ldh
- n
- ldh:
:type: integer
:intent: input
- wr:
:type: doublereal
:intent: output
:dims:
- n
- wi:
:type: doublereal
:intent: output
:dims:
- n
- iloz:
:type: integer
:intent: input
- ihiz:
:type: integer
:intent: input
- z:
:type: doublereal
:intent: input/output
:dims:
- "wantz ? ldz : 0"
- "wantz ? n : 0"
- ldz:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAHQR is an auxiliary routine called by DHSEQR to update the\n\
* eigenvalues and Schur decomposition already computed by DHSEQR, by\n\
* dealing with the Hessenberg submatrix in rows and columns ILO to\n\
* IHI.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* WANTT (input) LOGICAL\n\
* = .TRUE. : the full Schur form T is required;\n\
* = .FALSE.: only eigenvalues are required.\n\
*\n\
* WANTZ (input) LOGICAL\n\
* = .TRUE. : the matrix of Schur vectors Z is required;\n\
* = .FALSE.: Schur vectors are not required.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix H. N >= 0.\n\
*\n\
* ILO (input) INTEGER\n\
* IHI (input) INTEGER\n\
* It is assumed that H is already upper quasi-triangular in\n\
* rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless\n\
* ILO = 1). DLAHQR works primarily with the Hessenberg\n\
* submatrix in rows and columns ILO to IHI, but applies\n\
* transformations to all of H if WANTT is .TRUE..\n\
* 1 <= ILO <= max(1,IHI); IHI <= N.\n\
*\n\
* H (input/output) DOUBLE PRECISION array, dimension (LDH,N)\n\
* On entry, the upper Hessenberg matrix H.\n\
* On exit, if INFO is zero and if WANTT is .TRUE., H is upper\n\
* quasi-triangular in rows and columns ILO:IHI, with any\n\
* 2-by-2 diagonal blocks in standard form. If INFO is zero\n\
* and WANTT is .FALSE., the contents of H are unspecified on\n\
* exit. The output state of H if INFO is nonzero is given\n\
* below under the description of INFO.\n\
*\n\
* LDH (input) INTEGER\n\
* The leading dimension of the array H. LDH >= max(1,N).\n\
*\n\
* WR (output) DOUBLE PRECISION array, dimension (N)\n\
* WI (output) DOUBLE PRECISION array, dimension (N)\n\
* The real and imaginary parts, respectively, of the computed\n\
* eigenvalues ILO to IHI are stored in the corresponding\n\
* elements of WR and WI. If two eigenvalues are computed as a\n\
* complex conjugate pair, they are stored in consecutive\n\
* elements of WR and WI, say the i-th and (i+1)th, with\n\
* WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the\n\
* eigenvalues are stored in the same order as on the diagonal\n\
* of the Schur form returned in H, with WR(i) = H(i,i), and, if\n\
* H(i:i+1,i:i+1) is a 2-by-2 diagonal block,\n\
* WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).\n\
*\n\
* ILOZ (input) INTEGER\n\
* IHIZ (input) INTEGER\n\
* Specify the rows of Z to which transformations must be\n\
* applied if WANTZ is .TRUE..\n\
* 1 <= ILOZ <= ILO; IHI <= IHIZ <= N.\n\
*\n\
* Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)\n\
* If WANTZ is .TRUE., on entry Z must contain the current\n\
* matrix Z of transformations accumulated by DHSEQR, and on\n\
* exit Z has been updated; transformations are applied only to\n\
* the submatrix Z(ILOZ:IHIZ,ILO:IHI).\n\
* If WANTZ is .FALSE., Z is not referenced.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= max(1,N).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* .GT. 0: If INFO = i, DLAHQR failed to compute all the\n\
* eigenvalues ILO to IHI in a total of 30 iterations\n\
* per eigenvalue; elements i+1:ihi of WR and WI\n\
* contain those eigenvalues which have been\n\
* successfully computed.\n\
*\n\
* If INFO .GT. 0 and WANTT is .FALSE., then on exit,\n\
* the remaining unconverged eigenvalues are the\n\
* eigenvalues of the upper Hessenberg matrix rows\n\
* and columns ILO thorugh INFO of the final, output\n\
* value of H.\n\
*\n\
* If INFO .GT. 0 and WANTT is .TRUE., then on exit\n\
* (*) (initial value of H)*U = U*(final value of H)\n\
* where U is an orthognal matrix. The final\n\
* value of H is upper Hessenberg and triangular in\n\
* rows and columns INFO+1 through IHI.\n\
*\n\
* If INFO .GT. 0 and WANTZ is .TRUE., then on exit\n\
* (final value of Z) = (initial value of Z)*U\n\
* where U is the orthogonal matrix in (*)\n\
* (regardless of the value of WANTT.)\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* 02-96 Based on modifications by\n\
* David Day, Sandia National Laboratory, USA\n\
*\n\
* 12-04 Further modifications by\n\
* Ralph Byers, University of Kansas, USA\n\
* This is a modified version of DLAHQR from LAPACK version 3.0.\n\
* It is (1) more robust against overflow and underflow and\n\
* (2) adopts the more conservative Ahues & Tisseur stopping\n\
* criterion (LAWN 122, 1997).\n\
*\n\
* =========================================================\n\
*\n"
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