/home/abui.../cgeqrfp.f(3)

💖 NAME 💖

okay bestie, this is the manual page for /home/abui.../cgeqrfp.f(3) from the Library Functions Manual — and the actual source file name it’s serving is:

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

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

   Functions/Subroutines
       subroutine CGEQRFP (m, n, a, lda, tau, work, lwork, info)
           CGEQRFP

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🦋 Function/Subroutine Documentation 🦋

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

🎀 Purpose 🎀

so the docs say 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 🌈

here’s the whole cast, no skips:

• M — M is INTEGER. it’s the number of rows of the matrix A. Constraint: M >= 0.
• N — N is INTEGER. it’s 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. Constraint: LWORK >= max(1,N). 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 148 of file cgeqrfp.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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ok bye bestie, final sign-off from the footer: LAPACK Version 3.12.0, from /home/abui.../cgeqrfp.f(3). 💖✨