SRC/zgebd2.f(3)

💖 NAME 💖

SRC/zgebd2.f — bestie, this is the page for zgebd2 from the LAPACK Library Functions Manual, and it's literally the name section, so we're keeping it cute and iconic 👑.

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine zgebd2 (m, n, a, lda, d, e, tauq, taup, work, info)
    ZGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm.

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💅 Function/Subroutine Documentation 💅

   subroutine zgebd2 (integer m, integer n, complex*16, dimension( lda, * ) a,
       integer lda, double precision, dimension( * ) d, double precision,
       dimension( * ) e, complex*16, dimension( * ) tauq, complex*16,
       dimension( * ) taup, complex*16, dimension( * ) work, integer info)

ZGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm. No cap, that's the whole vibe 😌.

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🎯 Purpose 🎯

okay so ZGEBD2 takes a complex general m by n matrix A and reduces it to upper or lower real bidiagonal form B by a unitary transformation:

Q**H * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. periodt 🌈.

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🌸 Parameters 🌸

• M — M is INTEGER. The number of rows in the matrix A. M >= 0.
• N — N is INTEGER. The number of columns in the matrix A. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the m by n general matrix to be reduced. On exit:
  • if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors;
  • if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors.
  • See Further Details.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• D — D is DOUBLE PRECISION array, dimension (min(M,N)). The diagonal elements of the bidiagonal matrix B: D(i) = A(i,i).
• E — E is DOUBLE PRECISION array, dimension (min(M,N)-1). The off-diagonal elements of the bidiagonal matrix B: if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
• TAUQ — TAUQ is COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors which represent the unitary matrix Q. See Further Details.
• TAUP — TAUP is COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors which represent the unitary matrix P. See Further Details.
• WORK — WORK is COMPLEX*16 array, dimension (max(M,N)).
• INFO — INFO is INTEGER.
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.

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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 matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>  If m >= n,
!>
!>     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
!>  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
!>  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  If m < n,
!>
!>     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, v and u are complex vectors;
!>  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
!>  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
!>  tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  The contents of A on exit are illustrated by the following examples:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
!>    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
!>    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
!>    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
!>    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
!>    (  v1  v2  v3  v4  v5 )
!>
!>  where d and e denote diagonal and off-diagonal elements of B, vi
!>  denotes an element of the vector defining H(i), and ui an element of
!>  the vector defining G(i).
!>

Definition at line 188 of file zgebd2.f.

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🖋️ Author 🖋️

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the page, bestie — made with LAPACK Version 3.12.0 energy from SRC/zgebd2.f(3), mwah 💜