CLARFT(3)

💅 CLARFT(3) — Library Functions Manual 💅

okay bestie, manual vibes: Library Functions Manual, page /home/abui...RC/clarft.f(3). buckle up, we're doing Fortran linear algebra and we're doing it fabulously ✨

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/clarft.f — yes, the whole path is the name here. no cap, that's just how this page rolls 💖

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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🎀 Function/Subroutine Documentation 🎀

💫 subroutine CLARFT 💫

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

CLARFT forms the triangular factor T of a block reflector H = I - vtvH — that's the whole main-character mission, bestie 👑

🫶 Purpose 🫶

CLARFT forms the triangular factor T of a complex block reflector H of order n, which 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**H

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**H * T * V

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🌸 Parameters 🌸

• DIRECT — DIRECT is 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). choose your fighter 💅
• STOREV — STOREV is CHARACTER*1. Specifies how the vectors which define the elementary reflectors are stored (see also Further Details): = 'C': columnwise; = 'R': rowwise.
• N — N is INTEGER. The order of the block reflector H. N >= 0.
• K — K is INTEGER. The order of the triangular factor T (= the number of elementary reflectors). K >= 1.
• V — V is COMPLEX array, dimension (LDV,K) if STOREV = 'C', or (LDV,N) if STOREV = 'R'. The matrix V. See further details. she's got range 💖
• LDV — LDV is INTEGER. The leading dimension of the array V. If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
• TAU — TAU is COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i).
• T — T is COMPLEX 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 — LDT is INTEGER. The leading dimension of the array T. LDT >= K.

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💖 Author 💖

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

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🦋 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. iconic diagram moment 🎀

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 clarft.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 and that's the whole page, bestie — signed off from LAPACK Version 3.12.0, footer page /home/abui...RC/clarft.f(3), with no date listed so I'm not out here inventing one 💅✨