laqr3(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

okay bestie, welcome to laqr3(3) from the Library Functions Manual — this is the aggressive-early-deflation group chat, and it's giving main-character energy. 💅✨

✨ NAME ✨

laqr3 — laqr3: step in hseqr.

🌸 SYNOPSIS 🌸

🦋 Functions 🦋

       subroutine claqr3 (wantt, wantz, n, ktop, kbot, nw, h, ldh, iloz, ihiz,
           z, ldz, ns, nd, sh, v, ldv, nh, t, ldt, nv, wv, ldwv, work, lwork)

CLAQR3 is the complex one: it performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix — aggressive early deflation. ✨

       subroutine dlaqr3 (wantt, wantz, n, ktop, kbot, nw, h, ldh, iloz, ihiz,
           z, ldz, ns, nd, sr, si, v, ldv, nh, t, ldt, nv, wv, ldwv, work,
           lwork)

DLAQR3 is the double-precision orthogonal flavor: it performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix — aggressive early deflation. 💅

       subroutine slaqr3 (wantt, wantz, n, ktop, kbot, nw, h, ldh, iloz, ihiz,
           z, ldz, ns, nd, sr, si, v, ldv, nh, t, ldt, nv, wv, ldwv, work,
           lwork)

SLAQR3 is the single-precision orthogonal one: it performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix — aggressive early deflation. 🦋

       subroutine zlaqr3 (wantt, wantz, n, ktop, kbot, nw, h, ldh, iloz, ihiz,
           z, ldz, ns, nd, sh, v, ldv, nh, t, ldt, nv, wv, ldwv, work, lwork)

ZLAQR3 does the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix — aggressive early deflation. 👑

💅 Detailed Description 💅

bestie, the source gives this section no body text — no tea here, just the heading. 💨

🎀 Function Documentation 🎀

💖 `subroutine claqr3` — the complex one 💖

   subroutine claqr3 (logical wantt, logical wantz, integer n, integer ktop,
       integer kbot, integer nw, complex, dimension( ldh, * ) h, integer ldh,
       integer iloz, integer ihiz, complex, dimension( ldz, * ) z, integer ldz,
       integer ns, integer nd, complex, dimension( * ) sh, complex, dimension(
       ldv, * ) v, integer ldv, integer nh, complex, dimension( ldt, * ) t,
       integer ldt, integer nv, complex, dimension( ldwv, * ) wv, integer ldwv,
       complex, dimension( * ) work, integer lwork)

CLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix — aggressive early deflation. Periodt.

🔥 Purpose: 🔥

Aggressive early deflation: 💀 CLAQR3 accepts as input an upper Hessenberg matrix H and performs a unitary similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output H has been over-written by a new Hessenberg matrix that is a perturbation of a unitary similarity transformation of H. It is to be hoped that the final version of H has many zero subdiagonal entries. ✨

🌸 Parameters 🌸

WANTT — WANTT is LOGICAL. If .TRUE., then the Hessenberg matrix H is fully updated so that the triangular Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then only enough of H is updated to preserve the eigenvalues. 🫶
WANTZ — WANTZ is LOGICAL. If .TRUE., then the unitary matrix Z is updated so that the unitary Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then Z is not referenced. 💅
N — N is INTEGER. The order of the matrix H and (if WANTZ is .TRUE.) the order of the unitary matrix Z.
KTOP — KTOP is INTEGER. It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix.
KBOT — KBOT is INTEGER. It is assumed without a check that either KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix.
NW — NW is INTEGER. Deflation window size. 1 <= NW <= (KBOT-KTOP+1).
H — H is COMPLEX array, dimension (LDH,N). On input the initial N-by-N section of H stores the Hessenberg matrix undergoing aggressive early deflation. On output H has been transformed by a unitary similarity transformation, perturbed, and then returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries. 💀
LDH — LDH is INTEGER. Leading dimension of H just as declared in the calling subroutine. N <= LDH.
ILOZ — ILOZ is INTEGER. That's the whole note in the source, bestie — no extra lore here. 🫶
IHIZ — IHIZ is INTEGER. Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N.
Z — Z is COMPLEX array, dimension (LDZ,N). If WANTZ is .TRUE., then on output, the unitary similarity transformation mentioned above has been accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. If WANTZ is .FALSE., then Z is unreferenced.
LDZ — LDZ is INTEGER. The leading dimension of Z just as declared in the calling subroutine. 1 <= LDZ.
NS — NS is INTEGER. The number of unconverged (ie approximate) eigenvalues returned in SR and SI that may be used as shifts by the calling subroutine.
ND — ND is INTEGER. The number of converged eigenvalues uncovered by this subroutine.
SH — SH is COMPLEX array, dimension (KBOT). On output, approximate eigenvalues that may be used for shifts are stored in SH(KBOT-ND-NS+1) through SR(KBOT-ND). Converged eigenvalues are stored in SH(KBOT-ND+1) through SH(KBOT). (Yes, bestie, the source says SR there — we're keeping it exactly as written. 🙈)
V — V is COMPLEX array, dimension (LDV,NW). An NW-by-NW work array.
LDV — LDV is INTEGER. The leading dimension of V just as declared in the calling subroutine. NW <= LDV.
NH — NH is INTEGER. The number of columns of T. NH >= NW.
T — T is COMPLEX array, dimension (LDT,NW).
LDT — LDT is INTEGER. The leading dimension of T just as declared in the calling subroutine. NW <= LDT.
NV — NV is INTEGER. The number of rows of work array WV available for workspace. NV >= NW.
WV — WV is COMPLEX array, dimension (LDWV,NW).
LDWV — LDWV is INTEGER. The leading dimension of W just as declared in the calling subroutine. NW <= LDV. (Again, exactly as the source has it. 🫠)
WORK — WORK is COMPLEX array, dimension (LWORK). On exit, WORK(1) is set to an estimate of the optimal value of LWORK for the given values of N, NW, KTOP and KBOT.
LWORK — LWORK is INTEGER. The dimension of the work array WORK. LWORK = 2*NW suffices, but greater efficiency may result from larger values of LWORK. If LWORK = -1, then a workspace query is assumed; CLAQR3 only estimates the optimal workspace size for the given values of N, NW, KTOP and KBOT. The estimate is returned in WORK(1). No error message related to LWORK is issued by XERBLA. Neither H nor Z are accessed. 🔥

👑 Author 👑

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

💖 Contributors: 💖

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA.

Definition at line 263 of file claqr3.f.

💜 `subroutine dlaqr3` — the double-precision one 💜

   subroutine dlaqr3 (logical wantt, logical wantz, integer n, integer ktop,
       integer kbot, integer nw, double precision, dimension( ldh, * ) h,
       integer ldh, integer iloz, integer ihiz, double precision, dimension(
       ldz, * ) z, integer ldz, integer ns, integer nd, double precision,
       dimension( * ) sr, double precision, dimension( * ) si, double
       precision, dimension( ldv, * ) v, integer ldv, integer nh, double
       precision, dimension( ldt, * ) t, integer ldt, integer nv, double
       precision, dimension( ldwv, * ) wv, integer ldwv, double precision,
       dimension( * ) work, integer lwork)

DLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix — aggressive early deflation. 💅

🔥 Purpose: 🔥

Aggressive early deflation: 💀 DLAQR3 accepts as input an upper Hessenberg matrix H and performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output H has been over-written by a new Hessenberg matrix that is a perturbation of an orthogonal similarity transformation of H. It is to be hoped that the final version of H has many zero subdiagonal entries. ✨

🌸 Parameters 🌸

WANTT — WANTT is LOGICAL. If .TRUE., then the Hessenberg matrix H is fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then only enough of H is updated to preserve the eigenvalues.
WANTZ
WANTZ — LOGICAL. If .TRUE., then the orthogonal matrix Z is updated so that the orthogonal Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then Z is not referenced. 🫶
N — INTEGER. The order of the matrix H and (if WANTZ is .TRUE.) the order of the orthogonal matrix Z. 💅
KTOP — INTEGER. It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix. 🦋
KBOT — INTEGER. It is assumed without a check that either KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix. 👑
NW — INTEGER. Deflation window size. 1 <= NW <= (KBOT-KTOP+1). ✨
H — DOUBLE PRECISION array, dimension (LDH,N). On input the initial N-by-N section of H stores the Hessenberg matrix undergoing aggressive early deflation. On output H has been transformed by an orthogonal similarity transformation, perturbed, and returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries. 🔥
LDH — INTEGER. Leading dimension of H just as declared in the calling subroutine. N <= LDH. 💜
ILOZ — INTEGER. 🦋
IHIZ — INTEGER. Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N. 🌸
Z — DOUBLE PRECISION array, dimension (LDZ,N). If WANTZ is .TRUE., then on output, the orthogonal similarity transformation mentioned above has been accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. If WANTZ is .FALSE., then Z is unreferenced. 🎀
LDZ — INTEGER. The leading dimension of Z just as declared in the calling subroutine. 1 <= LDZ. ⭐
NS — INTEGER. The number of unconverged (ie approximate) eigenvalues returned in SR and SI that may be used as shifts by the calling subroutine. 🍓
ND — INTEGER. The number of converged eigenvalues uncovered by this subroutine. 👑
SR — DOUBLE PRECISION array, dimension (KBOT). 💖
SI — DOUBLE PRECISION array, dimension (KBOT). On output, the real and imaginary parts of approximate eigenvalues that may be used for shifts are stored in SR(KBOT-ND-NS+1) through SR(KBOT-ND) and SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively. The real and imaginary parts of converged eigenvalues are stored in SR(KBOT-ND+1) through SR(KBOT) and SI(KBOT-ND+1) through SI(KBOT), respectively. ✨
V — DOUBLE PRECISION array, dimension (LDV,NW). An NW-by-NW work array. 🎀
LDV — INTEGER. The leading dimension of V just as declared in the calling subroutine. NW <= LDV. 🌈
NH — INTEGER. The number of columns of T. NH >= NW. 🦋
T — DOUBLE PRECISION array, dimension (LDT,NW). 🍓
LDT — INTEGER. The leading dimension of T just as declared in the calling subroutine. NW <= LDT. 💜
NV — INTEGER. The number of rows of work array WV available for workspace. NV >= NW. ✨
WV — DOUBLE PRECISION array, dimension (LDWV,NW). 🎀
LDWV — INTEGER. The leading dimension of W just as declared in the calling subroutine. NW <= LDV. 🌸
WORK — DOUBLE PRECISION array, dimension (LWORK). On exit, WORK(1) is set to an estimate of the optimal value of LWORK for the given values of N, NW, KTOP and KBOT. 🔥
LWORK — INTEGER. The dimension of the work array WORK. LWORK = 2*NW suffices, but greater efficiency may result from larger values of LWORK. If LWORK = -1, then a workspace query is assumed; DLAQR3 only estimates the optimal workspace size for the given values of N, NW, KTOP and KBOT. The estimate is returned in WORK(1). No error message related to LWORK is issued by XERBLA. Neither H nor Z are accessed. 💅

Author 💖

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Contributors 🎀

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line 272 of file dlaqr3.f. ⭐

✨ `slaqr3` ✨

subroutine slaqr3 (logical wantt, logical wantz, integer n, integer ktop,
     integer kbot, integer nw, real, dimension( ldh, * ) h, integer ldh,
     integer iloz, integer ihiz, real, dimension( ldz, * ) z, integer ldz,
     integer ns, integer nd, real, dimension( * ) sr, real, dimension( * )
     si, real, dimension( ldv, * ) v, integer ldv, integer nh, real,
     dimension( ldt, * ) t, integer ldt, integer nv, real, dimension( ldwv, *
     ) wv, integer ldwv, real, dimension( * ) work, integer lwork)

SLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). 🦋

Purpose ✨

Aggressive early deflation: SLAQR3 accepts as input an upper Hessenberg matrix H and performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output H has been over-written by a new Hessenberg matrix that is a perturbation of an orthogonal similarity transformation of H. It is to be hoped that the final version of H has many zero subdiagonal entries. 🔥

Parameters 💅

WANTT — LOGICAL. If .TRUE., then the Hessenberg matrix H is fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then only enough of H is updated to preserve the eigenvalues. 🔥
WANTZ — LOGICAL. If .TRUE., then the orthogonal matrix Z is updated so that the orthogonal Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then Z is not referenced. 🫶
N — INTEGER. The order of the matrix H and (if WANTZ is .TRUE.) the order of the orthogonal matrix Z. 💅
KTOP — INTEGER. It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix. 🦋
KBOT — INTEGER. It is assumed without a check that either KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix. 👑
NW — INTEGER. Deflation window size. 1 <= NW <= (KBOT-KTOP+1). ✨
H — REAL array, dimension (LDH,N). On input the initial N-by-N section of H stores the Hessenberg matrix undergoing aggressive early deflation. On output H has been transformed by an orthogonal similarity transformation, perturbed, and returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries. 🔥
LDH — INTEGER. Leading dimension of H just as declared in the calling subroutine. N <= LDH. 💜
ILOZ — INTEGER. 🦋
IHIZ — INTEGER. Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N. 🌸
Z — REAL array, dimension (LDZ,N). If WANTZ is .TRUE., then on output, the orthogonal similarity transformation mentioned above has been accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. If WANTZ is .FALSE., then Z is unreferenced. 🎀
LDZ — INTEGER. The leading dimension of Z just as declared in the calling subroutine. 1 <= LDZ. ⭐
NS — INTEGER. The number of unconverged (ie approximate) eigenvalues returned in SR and SI that may be used as shifts by the calling subroutine. 🍓
ND — INTEGER. The number of converged eigenvalues uncovered by this subroutine. 👑
SR — REAL array, dimension (KBOT). 🌸
SI — 🌈
SI — SI is a REAL array, dimension (KBOT). On output, the real and imaginary parts of approximate eigenvalues that may be used for shifts are stored in SR(KBOT-ND-NS+1) through SR(KBOT-ND) and SI(KBOT-ND-NS+1) through SI(KBOT), respectively. The real and imaginary parts of converged eigenvalues are stored in SR(KBOT-ND+1) through SR(KBOT) and SI(KBOT-ND+1) through SI(KBOT), respectively.
V — V is a REAL array, dimension (LDV,NW). It’s an NW-by-NW work array.
LDV — LDV is INTEGER. The leading dimension of V just as declared in the calling subroutine. NW <= LDV.
NH — NH is INTEGER. The number of columns of T. NH >= NW.
T — T is a REAL array, dimension (LDT,NW).
LDT — LDT is INTEGER. The leading dimension of T just as declared in the calling subroutine. NW <= LDT.
NV — NV is INTEGER. The number of rows of work array WV available for workspace. NV >= NW.
WV — WV is a REAL array, dimension (LDWV,NW).
LDWV — LDWV is INTEGER. The leading dimension of W just as declared in the calling subroutine. NW <= LDV.
WORK — WORK is a REAL array, dimension (LWORK). On exit, WORK(1) is set to an estimate of the optimal value of LWORK for the given values of N, NW, KTOP and KBOT.
LWORK — LWORK is INTEGER. The dimension of the work array WORK. LWORK = 2*NW suffices, but greater efficiency may result from larger values of LWORK.

If LWORK = -1, then a workspace query is assumed; SLAQR3 only estimates the optimal workspace size for the given values of N, NW, KTOP and KBOT. The estimate is returned in WORK(1). No error message related to LWORK is issued by XERBLA. Neither H nor Z are accessed.

👑 Author 👑

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Contributors: Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line 272 of file slaqr3.f.

🦋 `zlaqr3` — the complex*16 version 🦋

   subroutine zlaqr3 (logical wantt, logical wantz, integer n, integer ktop,
       integer kbot, integer nw, complex*16, dimension( ldh, * ) h, integer
       ldh, integer iloz, integer ihiz, complex*16, dimension( ldz, * ) z,
       integer ldz, integer ns, integer nd, complex*16, dimension( * ) sh,
       complex*16, dimension( ldv, * ) v, integer ldv, integer nh, complex*16,
       dimension( ldt, * ) t, integer ldt, integer nv, complex*16, dimension(
       ldwv, * ) wv, integer ldwv, complex*16, dimension( * ) work, integer
       lwork)

ZLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).

🎯 Purpose 🎯

Aggressive early deflation, bestie. ZLAQR3 accepts as input an upper Hessenberg matrix H and performs an unitary similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output H has been over-written by a new Hessenberg matrix that is a perturbation of an unitary similarity transformation of H. It is to be hoped that the final version of H has many zero subdiagonal entries.

✨ Parameters ✨

WANTT — WANTT is LOGICAL. If .TRUE., then the Hessenberg matrix H is fully updated so that the triangular Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then only enough of H is updated to preserve the eigenvalues.
WANTZ — WANTZ is LOGICAL. If .TRUE., then the unitary matrix Z is updated so that the unitary Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then Z is not referenced.
N — N is INTEGER. The order of the matrix H and (if WANTZ is .TRUE.) the order of the unitary matrix Z.
KTOP — KTOP is INTEGER. It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix.
KBOT — KBOT is INTEGER. It is assumed without a check that either KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix.
NW — NW is INTEGER. Deflation window size. 1 <= NW <= (KBOT-KTOP+1).
H — H is COMPLEX*16 array, dimension (LDH,N). On input the initial N-by-N section of H stores the Hessenberg matrix undergoing aggressive early deflation. On output H has been transformed by a unitary similarity transformation, perturbed, and the returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries.
LDH — LDH is INTEGER. Leading dimension of H just as declared in the calling subroutine. N <= LDH.
ILOZ — ILOZ is INTEGER.
IHIZ — IHIZ is INTEGER. Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N.
Z — Z is COMPLEX*16 array, dimension (LDZ,N). If WANTZ is .TRUE., then on output, the unitary similarity transformation mentioned above has been accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. If WANTZ is .FALSE., then Z is unreferenced.
LDZ — LDZ is INTEGER. The leading dimension of Z just as declared in the calling subroutine. 1 <= LDZ.
NS — NS is INTEGER. The number of unconverged (ie approximate) eigenvalues returned in SR and SI that may be used as shifts by the calling subroutine.
ND — ND is INTEGER. The number of converged eigenvalues uncovered by this subroutine.
SH — SH is COMPLEX*16 array, dimension (KBOT). On output, approximate eigenvalues that may be used for shifts are stored in SH(KBOT-ND-NS+1) through SR(KBOT-ND). Converged eigenvalues are stored in SH(KBOT-ND+1) through SH(KBOT).
V — V is COMPLEX*16 array, dimension (LDV,NW). An NW-by-NW work array.
LDV — LDV is INTEGER. The leading dimension of V just as declared in the calling subroutine. NW <= LDV.
NH — NH is INTEGER. The number of columns of T. NH >= NW.
T — T is COMPLEX*16 array, dimension (LDT,NW).
LDT — LDT is INTEGER. The leading dimension of T just as declared in the calling subroutine. NW <= LDT.
NV — NV is INTEGER. The number of rows of work array WV available for workspace. NV >= NW.
WV — WV is COMPLEX*16 array, dimension (LDWV,NW).
LDWV — LDWV is INTEGER. The leading dimension of W just as declared in the calling subroutine. NW <= LDV.
WORK — WORK is COMPLEX*16 array, dimension (LWORK). On exit, WORK(1) is set to an estimate of the optimal value of LWORK for the given values of N, NW, KTOP and KBOT.
LWORK — LWORK is INTEGER. The dimension of the work array WORK. LWORK = 2*NW suffices, but greater efficiency may result from larger values of LWORK.

If LWORK = -1, then a workspace query is assumed; ZLAQR3 only estimates the optimal workspace size for the given values of N, NW, KTOP and KBOT. The estimate is returned in WORK(1). No error message related to LWORK is issued by XERBLA. Neither H nor Z are accessed.

👑 Author 👑

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Contributors: Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line 264 of file zlaqr3.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

That’s the whole laqr3(3) situation, bestie 💖 — footer tea: LAPACK Version 3.12.0, laqr3(3), and the date slot is not listed on this page. Slay. 💅✨

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

laqr3(3)

✨ NAME ✨

🌸 SYNOPSIS 🌸

🦋 Functions 🦋

💅 Detailed Description 💅

🎀 Function Documentation 🎀

💖 subroutine claqr3 — the complex one 💖

🔥 Purpose: 🔥

🌸 Parameters 🌸

👑 Author 👑

💖 Contributors: 💖

💜 subroutine dlaqr3 — the double-precision one 💜

🔥 Purpose: 🔥

🌸 Parameters 🌸

Author 💖

Contributors 🎀

✨ slaqr3 ✨

Purpose ✨

Parameters 💅

👑 Author 👑

🦋 zlaqr3 — the complex*16 version 🦋

🎯 Purpose 🎯

✨ Parameters ✨

👑 Author 👑

🪄 Author 🪄

💖 `subroutine claqr3` — the complex one 💖

💜 `subroutine dlaqr3` — the double-precision one 💜

✨ `slaqr3` ✨

🦋 `zlaqr3` — the complex*16 version 🦋