geqrt2(3)

📦
version 3.12.1 · 9 versions
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💅 geqrt2(3) 💅

okay so this is the manual page for geqrt2, and honestly? it's giving "four subroutines, one vibe" ✨

🎀 NAME 🎀

geqrt2 — geqrt2: QR factor, with T, level 2 🦋

🌸 SYNOPSIS 🌸

Functions

  • subroutine cgeqrt2 (m, n, a, lda, t, ldt, info) — CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
  • subroutine dgeqrt2 (m, n, a, lda, t, ldt, info) — DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
  • subroutine sgeqrt2 (m, n, a, lda, t, ldt, info) — SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
  • subroutine zgeqrt2 (m, n, a, lda, t, ldt, info) — ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

✨ Detailed Description ✨

no extra prose up here bestie, the real content lives down in Function Documentation — and there are four whole entries waiting for you 👑

💖 Function Documentation 💖

🌈 cgeqrt2

subroutine cgeqrt2 (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

!>
!> CGEQRT2 computes a QR factorization of a complex M-by-N matrix A,
!> using the compact WY representation of Q.
!>

Parameters

  • M
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= N.
!>
  • N
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>
  • A
!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the complex M-by-N matrix A.  On exit, the elements on and
!>          above the diagonal contain the N-by-N upper triangular matrix R; the
!>          elements below the diagonal are the columns of V.  See below for
!>          further details.
!>
  • LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
  • T
!>          T is COMPLEX array, dimension (LDT,N)
!>          The N-by-N upper triangular factor of the block reflector.
!>          The elements on and above the diagonal contain the block
!>          reflector T; the elements below the diagonal are not used.
!>          See below for further details.
!>
  • LDT
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= max(1,N).
!>
  • INFO
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>

Author

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

Further Details:

!>
!>  The matrix V stores the elementary reflectors H(i) in the i-th column
!>  below the diagonal. For example, if M=5 and N=3, the matrix V is
!>
!>               V = (  1       )
!>                   ( v1  1    )
!>                   ( v1 v2  1 )
!>                   ( v1 v2 v3 )
!>                   ( v1 v2 v3 )
!>
!>  where the vi's represent the vectors which define H(i), which are returned
!>  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
!>  block reflector H is then given by
!>
!>               H = I - V * T * V**H
!>
!>  where V**H is the conjugate transpose of V.
!>

Definition at line 126 of file cgeqrt2.f.

🦋 dgeqrt2

subroutine dgeqrt2 (integer m, integer n, double precision, dimension( lda,
* ) a, integer lda, double precision, dimension( ldt, * ) t, integer
ldt, integer info)

DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

!>
!> DGEQRT2 computes a QR factorization of a real M-by-N matrix A,
!> using the compact WY representation of Q.
!>

Parameters

  • M
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= N.
!>
  • N
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>
  • A
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the real M-by-N matrix A.  On exit, the elements on and
!>          above the diagonal contain the N-by-N upper triangular matrix R; the
!>          elements below the diagonal are the columns of V.  See below for
!>          further details.
!>
  • LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
  • T
!>          T is DOUBLE PRECISION array, dimension (LDT,N)
!>          The N-by-N upper triangular factor of the block reflector.
!>          The elements on and above the diagonal contain the block
!>          reflector T; the elements below the diagonal are not used.
!>          See below for further details.
!>
  • LDT
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= max(1,N).
!>
  • INFO
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>

Author

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

Further Details:

!>
!>  The matrix V stores the elementary reflectors H(i) in the i-th column
!>  below the diagonal. For example, if M=5 and N=3, the matrix V is
!>
!>               V = (  1       )
!>                   ( v1  1    )
!>                   ( v1 v2  1 )
!>                   ( v1 v2 v3 )
!>                   ( v1 v2 v3 )
!>
!>  where the vi's represent the vectors which define H(i), which are returned
!>  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
!>  block reflector H is then given by
!>
!>               H = I - V * T * V**T
!>
!>  where V**T is the transpose of V.
!>

Definition at line 126 of file dgeqrt2.f.

🌟 sgeqrt2

subroutine sgeqrt2 (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

!>
!> SGEQRT2 computes a QR factorization of a real M-by-N matrix A,
!> using the compact WY representation of Q.
!>

Parameters

  • M
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= N.
!>
  • N
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>
  • A
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the real M-by-N matrix A.  On exit, the elements on and
!>          above the diagonal contain the N-by-N upper triangular matrix R; the
!>          elements below the diagonal are the columns of V.  See below for
!>          further details.
!>
  • LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
  • T
!>          T is REAL array, dimension (LDT,N)
!>          The N-by-N upper triangular factor of the block reflector.
!>          The elements on and above the diagonal contain the block
!>          reflector T; the elements below the diagonal are not used.
!>          See below for further details.
!>
  • LDT
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= max(1,N).
!>
  • INFO
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>

Author

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

Further Details:

!>
!>  The matrix V stores the elementary reflectors H(i) in the i-th column
!>  below the diagonal. For example, if M=5 and N=3, the matrix V is
!>
!>               V = (  1       )
!>                   ( v1  1    )
!>                   ( v1 v2  1 )
!>                   ( v1 v2 v3 )
!>                   ( v1 v2 v3 )
!>
!>  where the vi's represent the vectors which define H(i), which are returned
!>  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
!>  block reflector H is then given by
!>
!>               H = I - V * T * V**T
!>
!>  where V**T is the transpose of V.
!>

Definition at line 126 of file sgeqrt2.f.

👑 zgeqrt2

subroutine zgeqrt2 (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer
    info)

ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

!>
!> ZGEQRT2 computes a QR factorization of a complex M-by-N matrix A,
!> using the compact WY representation of Q.
!>

Parameters

  • M
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= N.
!>
  • N
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>
  • A
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the complex M-by-N matrix A.  On exit, the elements on and
!>          above the diagonal contain the N-by-N upper triangular matrix R; the
!>          elements below the diagonal are the columns of V.  See below for
!>          further details.
!>
  • LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
  • T
!>          T is COMPLEX*16 array, dimension (LDT,N)
!>          The N-by-N upper triangular factor of the block reflector.
!>          The elements on and above the diagonal contain the block
!>          reflector T; the elements below the diagonal are not used.
!>          See below for further details.
!>
  • LDT

okay so we're literally mid-parameter-list right here 😭 LDT for zgeqrt2 is where part 1 dips — part 2 picks it right back up, no cap 🫶

  • LDT — is an INTEGER bestie. It’s the leading dimension of the array T, and you must have LDT >= max(1,N). No cap, that’s the rule. 🫶
  • INFO — is an INTEGER too, and it’s the vibe check at the end:
    • = 0: successful exit, slay ✨
    • < 0: if INFO = -i, then the i-th argument had an illegal value 💀

👑 AUTHOR 👑

Okay so this iconic function was brought to you by:

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

🔥 FURTHER DETAILS 🔥

Okay so here’s the tea on how the matrix V works: it stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V looks like this:

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

where the vi’s represent the vectors which define H(i), and those are returned in the matrix A. The 1’s along the diagonal of V are not stored in A. The block reflector H is then given by:

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

where V**H is the conjugate transpose of V. Periodt. 💅

📍 Definition at line 126 of file zgeqrt2.f.

🤖 AUTHOR (auto-generated) 🤖

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okay bye bestie, this was geqrt2(3) from LAPACK Version 3.12.0 — the footer didn’t give a date, but it’s giving timeless icon energy 💖✨

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