SRC/zgeqrfp.f(3)

💅 SRC/zgeqrfp.f 💅

okay so bestie, this is the SRC/zgeqrfp.f(3) page from the Library Functions Manual ✨. It’s giving very “LAPACK routine, but make it group chat.” We are not dropping a single fact. Periodt.

🌸 NAME 🌸

SRC/zgeqrfp.f — that’s the name of the page/file, and yes, it’s short. Iconic.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine zgeqrfp (m, n, a, lda, tau, work, lwork, info) — ZGEQRFP.

subroutine zgeqrfp (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
    work, integer lwork, integer info)

📚 Function/Subroutine Documentation 📚

subroutine zgeqrfp (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info) — label ZGEQRFP.

🎯 Purpose 🎯

The purpose block says: ZGEQR2P computes a QR factorization of a complex M-by-N matrix A:

   A = Q * ( R ),
            ( 0 )

where:

• Q is a M-by-M orthogonal matrix;
• R is an upper-triangular N-by-N matrix with nonnegative diagonal entries;
• 0 is a (M-N)-by-N zero matrix, if M > N.

🎀 Parameters 🎀

• M — M is INTEGER; the number of rows of the matrix A. M >= 0.
• 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 M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are real and nonnegative; the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
• TAU — TAU is COMPLEX*16 array, dimension (min(M,N)); the scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER; the dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• 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 Q is represented as a product of elementary reflectors:

Q = H(1) H(2) . . . H(k), where k = min(m,n).

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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

See Lapack Working Note 203 for details.

Definition at line 149 of file zgeqrfp.f.

🤖 Author 🤖

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byeee bestie, that’s the whole page — LAPACK Version 3.12.0, SRC/zgeqrfp.f(3) 🫶✨