SRC/cgeqrfp.f(3)

💖 SRC/cgeqrfp.f 💖

okay so this page comes from the Library Functions Manual, and it's all about the CGEQRFP subroutine, bestie. buckle up, it's giving linear algebra but make it cute. 🎀

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🌸 NAME 🌸

SRC/cgeqrfp.f — literally the page, periodt. home of the CGEQRFP subroutine. 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

here's the call, exactly as it appears:

subroutine cgeqrfp (m, n, a, lda, tau, work, lwork, info)

and the big label is CGEQRFP, iykyk. 🦋

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🦋 Function/Subroutine Documentation 🦋

🫶 subroutine cgeqrfp 🫶

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

label: CGEQRFP. iconic. ✨

🎯 Purpose 🎯

the Purpose block is giving main character energy. it says — and I'm keeping the facts exactly — that CGEQR2P 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. constraint: M >= 0.
• N — N is INTEGER. the number of columns of the matrix A. constraint: N >= 0.
• A — A is COMPLEX 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. constraint: LDA >= max(1,M).
• TAU — TAU is COMPLEX array, dimension (min(M,N)). the scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is COMPLEX 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 cgeqrfp.f. 📍

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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buh-bye bestie! this page is from LAPACK Version 3.12.0, page SRC/cgeqrfp.f(3) — mwah 💋🫶✨