SRC/clarfg.f(3)

🌸 SRC/clarfg.f(3) 🌸

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🎀 NAME 🎀

SRC/clarfg.f

✨ SYNOPSIS ✨

🫶 Functions/Subroutines

• subroutine clarfg (n, alpha, x, incx, tau) — CLARFG generates an elementary reflector (Householder matrix).

💖 Function/Subroutine Documentation 💖

🌈 subroutine clarfg (integer n, complex alpha, complex, dimension( * ) x, integer incx, complex tau)

CLARFG generates an elementary reflector (Householder matrix).

🔥 Purpose:

okay so CLARFG generates a complex elementary reflector H of order n, such that:

      H**H * ( alpha ) = ( beta ),   H**H * H = I.
             (   x   )   (   0  )

where alpha and beta are scalars, with beta real, and x is an (n-1)-element complex vector. H is represented in the form:

      H = I - tau * ( 1 ) * ( 1 v**H ) ,
                    ( v )

where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian.

If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix.

Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1.

🎀 Parameters

• N — N is INTEGER. The order of the elementary reflector.
• ALPHA — ALPHA is COMPLEX. On entry, the value alpha. On exit, it is overwritten with the value beta.
• X — X is COMPLEX array, dimension (1+(N-2)*abs(INCX)). On entry, the vector x. On exit, it is overwritten with the vector v.
• INCX — INCX is INTEGER. The increment between elements of X. INCX > 0.
• TAU — TAU is COMPLEX. The value tau.

👑 Author

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

Definition at line 105 of file clarfg.f.

🧚 Author 🧚

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