SLARFT(3)

💅 SLARFT(3) — Library Functions Manual

Bestie, you're in SLARFT(3) under the Library Functions Manual, and this is the page for slarft.f. The full source path is right below in NAME, because we keep the receipts. 💖

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slarft.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

subroutine SLARFT (direct, storev, n, k, v, ldv, tau, t, ldt)
    SLARFT forms the triangular factor T of a block reflector H = I -
    vtvH

📚 Function/Subroutine Documentation 📚

Here's the full signature, no cap:

subroutine SLARFT (character direct, character storev, integer n, integer k,
    real, dimension( ldv, * ) v, integer ldv, real, dimension( * ) tau,
    real, dimension( ldt, * ) t, integer ldt)

SLARFT forms the triangular factor T of a block reflector H = I - vtvH.

🎯 Purpose

Okay so SLARFT forms the triangular factor T of a real block reflector H of order n, and H is defined as a product of k elementary reflectors. Periodt.

• If DIRECT = 'F', then H = H(1) H(2) . . . H(k) and T is upper triangular.
• If DIRECT = 'B', then H = H(k) . . . H(2) H(1) and T is lower triangular.
• If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and:

H  =  I - V * T * V**T

• If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and:

H  =  I - V**T * T * V

🛠️ Parameters

• DIRECT — CHARACTER*1. Specifies the order in which the elementary reflectors are multiplied to form the block reflector:
  • = 'F': H = H(1) H(2) . . . H(k) (Forward)
  • = 'B': H = H(k) . . . H(2) H(1) (Backward)
• STOREV — CHARACTER*1. Specifies how the vectors which define the elementary reflectors are stored (see also Further Details):
  • = 'C': columnwise
  • = 'R': rowwise
• N — INTEGER. The order of the block reflector H. N >= 0.
• K — INTEGER. The order of the triangular factor T (= the number of elementary reflectors). K >= 1.
• V — REAL array, dimension
  • (LDV,K) if STOREV = 'C'
  • (LDV,N) if STOREV = 'R'

The matrix V. See further details.

• LDV — INTEGER. The leading dimension of the array V. If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
• TAU — REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i).
• T — REAL array, dimension (LDT,K). The k by k triangular factor T of the block reflector. If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is lower triangular. The rest of the array is not used.
• LDT — INTEGER. The leading dimension of the array T. LDT >= K.

👑 Author

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

🦋 Further Details

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. The elements equal to 1 are not stored. Behold the diagram, bestie:

DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

             V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                 ( v1  1    )                     (     1 v2 v2 v2 )
                 ( v1 v2  1 )                     (        1 v3 v3 )
                 ( v1 v2 v3 )
                 ( v1 v2 v3 )

DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

             V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                 ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                 (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                 (     1 v3 )
                 (        1 )

Definition at line 162 of file slarft.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

LAPACK Version 3.12.0 · source footer: /home/abui...RC/slarft.f(3) — that's the wrap, bestie, periodt. 💖✨