LAQR5 - 5.2 English - 68552

LAQR5 performs a single small-bulge multi-shift QR sweep.

Purpose:

 LAQR5, called by SLAQR0, performs a
 single small-bulge multi-shift QR sweep.

Parameters:

• WANTT – [in]

  WANTT is LOGICAL

  WANTT = .true. if the quasi-triangular Schur factor is being computed. WANTT is set to .false. otherwise.

• WANTZ – [in]

  WANTZ is LOGICAL

  WANTZ = .true. if the orthogonal Schur factor is being computed. WANTZ is set to .false. otherwise.

• KACC22 – [in]

  KACC22 is INTEGER with value 0, 1, or 2.

  Specifies the computation mode of far-from-diagonal orthogonal updates.

  = 0: SLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries.

  = 1: SLAQR5 accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries.

  = 2: SLAQR5 accumulates reflections, uses matrix-matrix multiply to update the far-from-diagonal matrix entries, and takes advantage of 2-by-2 block structure during matrix multiplies.

• N – [in]

  N is INTEGER

  N is the order of the Hessenberg matrix H upon which this subroutine operates.

• KTOP – [in] KTOP is INTEGER

• KBOT – [in]

  KBOT is INTEGER

  These are the first and last rows and columns of an isolated diagonal block upon which the QR sweep is to be applied. It is assumed without a check that

  either KTOP = 1 or H(KTOP,KTOP-1) = 0

  and

  either KBOT = N or H(KBOT+1,KBOT) = 0.

• NSHFTS – [in]

  NSHFTS is INTEGER

  NSHFTS gives the number of simultaneous shifts. NSHFTS must be positive and even.

• SR – [inout] SR is REAL array, dimension (NSHFTS)

• SI – [inout]

  SI is REAL array, dimension (NSHFTS)

  SR contains the real parts and SI contains the imaginary parts of the NSHFTS shifts of origin that define the multi-shift QR sweep. On output SR and SI may be reordered.

• H – [inout]

  H is REAL array, dimension (LDH,N)

  On input H contains a Hessenberg matrix. On output a multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied to the isolated diagonal block in rows and columns KTOP through KBOT.

• LDH – [in]

  LDH is INTEGER

  LDH is the leading dimension of H just as declared in the calling procedure. LDH >= MAX(1,N).

• ILOZ – [in] ILOZ is INTEGER

• IHIZ – [in]

  IHIZ is INTEGER

  Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N

• Z – [inout]

  Z is REAL array, dimension (LDZ,IHIZ)

  If WANTZ = .TRUE., then the QR Sweep orthogonal similarity transformation is accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right.

  If WANTZ = .FALSE., then Z is unreferenced.

• LDZ – [in]

  LDZ is INTEGER

  LDZ is the leading dimension of Z just as declared in the calling procedure. LDZ >= N.

• V – [out] V is REAL array, dimension (LDV,NSHFTS/2)

• LDV – [in]

  LDV is INTEGER

  LDV is the leading dimension of V as declared in the calling procedure. LDV >= 3.

• U – [out] U is REAL array, dimension (LDU,3*NSHFTS-3)

• LDU – [in]

  LDU is INTEGER

  LDU is the leading dimension of U just as declared in the in the calling subroutine. LDU >= 3*NSHFTS-3.

• NV – [in]

  NV is INTEGER

  NV is the number of rows in WV agailable for workspace. NV >= 1.

• WV – [out] WV is REAL array, dimension (LDWV,3*NSHFTS-3)

• LDWV – [in] LDWV is INTEGER LDWV is the leading dimension of WV as declared in the in the calling subroutine. LDWV >= NV.

• NH – [in] NH is INTEGER NH is the number of columns in array WH available for workspace. NH >= 1.

• WH – [out] WH is REAL array, dimension (LDWH,NH)

• LDWH – [in]

  LDWH is INTEGER

  Leading dimension of WH just as declared in the calling procedure. LDWH >= 3*NSHFTS-3.