/home/abui...D/zlahrd.f(3)

💅 NAME 💅

ok so bestie, this page is literally the manual for this one file, and the file is:

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

and it lives inside the Library Functions Manual at /home/abui...D/zlahrd.f(3) — that's the whole vibe, that's the page 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine ZLAHRD (n, k, nb, a, lda, tau, t, ldt, y, ldy) — bestie, what it does is it reduces the first nb columns of a general rectangular matrix A so that everything below the k-th subdiagonal is straight-up zero, and then it hands back the auxiliary matrices you need to apply that transformation to the part of A you haven't reduced yet. iconic behavior honestly 🦋

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🌸 Function/Subroutine Documentation 🌸

subroutine ZLAHRD (integer n, integer k, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( nb ) tau, complex*16, dimension( ldt, nb ) t, integer ldt, complex*16, dimension( ldy, nb ) y, integer ldy)

subroutine ZLAHRD (integer n, integer k, integer nb, complex*16, dimension(
    lda, * ) a, integer lda, complex*16, dimension( nb ) tau, complex*16,
    dimension( ldt, nb ) t, integer ldt, complex*16, dimension( ldy, nb ) y,
    integer ldy)

ZLAHRD reduces the first nb columns of a general rectangular matrix A so that the elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. slay 💜

Purpose:

⚠️ DEPRECATED ALERT ⚠️ This routine is deprecated and has been replaced by routine ZLAHR2. like, it's giving "still here, still working, but please use the new one" 😭

ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero. The reduction is performed by a unitary similarity transformation Q**H * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T. no cap, that's the whole deal ✨

Parameters

• N

N is INTEGER

The order of the matrix A. that's it, that's the girl 🌈

• K

K is INTEGER

The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. lowkey the starting point of the whole thing 💫

• NB

NB is INTEGER

The number of columns to be reduced. count em 🔥

• A

A is COMPLEX*16 array, dimension (LDA,N-K+1)

On entry, the n-by-(n-k+1) general matrix A.

On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix Q as a product of elementary reflectors. The other columns of A are unchanged. See Further Details. bestie pls read Further Details, it's important 🫶

• LDA

LDA is INTEGER

The leading dimension of the array A. LDA >= max(1,N). respect the boundary 👑

• TAU

TAU is COMPLEX*16 array, dimension (NB)

The scalar factors of the elementary reflectors. See Further Details. again — Further Details, go read it 📖

• T

T is COMPLEX*16 array, dimension (LDT,NB)

The upper triangular matrix T. triangle supremacy 🔺

• LDT

LDT is INTEGER

The leading dimension of the array T. LDT >= NB. don't come in under that 💅

• Y

Y is COMPLEX*16 array, dimension (LDY,NB)

The n-by-nb matrix Y. that's her 🌸

• LDY

LDY is INTEGER

The leading dimension of the array Y. LDY >= max(1,N). same energy, different letter ✨

Author

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

the whole squad really said "we built this" 🤝

Further Details:

The matrix Q is represented as a product of nb elementary reflectors

Q = H(1) H(2) . . . H(nb).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in A(i+k+1:n,i), and tau in TAU(i). okay so that's the lore 🧚

The elements of the vectors v together form the (n-k+1)-by-nb matrix V which is needed, with T and Y, to apply the transformation to the unreduced part of the matrix, using an update of the form: A := (I - V*T*V**H) * (A - Y*V**H).

The contents of A on exit are illustrated by the following example with n = 7, k = 3 and nb = 2:

( a   h   a   a   a )
( a   h   a   a   a )
( a   h   a   a   a )
( h   h   a   a   a )
( v1  h   a   a   a )
( v1  v2  a   a   a )
( v1  v2  a   a   a )

where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i). literal legend behavior, the diagram ate 🍓

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📍 Definition at line 166 of file zlahrd.f.

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. not a human, just vibes and a parser 💀

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and that's the page bestie!! 💖 it's LAPACK, Version 3.12.0, signed off from /home/abui...D/zlahrd.f(3) — go reduce some columns, love u, bye 🎀✨