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

💅 NAME 💅

okay bestie, this is the Library Functions Manual glow-up for /home/abui.../sgeqrfp.f(3) — yes, the LAPACK page, but make it cute. The actual file path is:

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

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines

• subroutine SGEQRFP (m, n, a, lda, tau, work, lwork, info) — SGEQRFP

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📚 Function/Subroutine Documentation 📚

🧬 subroutine SGEQRFP

subroutine SGEQRFP (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) tau, real, dimension( * ) work,
    integer lwork, integer info)

SGEQRFP

🎯 Purpose

okay so the Purpose block literally says SGEQR2P computes a QR factorization of a real M-by-N matrix A — keep that energy exactly as written, bestie:

    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 REAL 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 nonnegative; the elements below the diagonal, with the array TAU, represent the orthogonal 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 REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is REAL 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 >= 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**T

where tau is a real scalar, and v is a real 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 sgeqrfp.f.

🪄 Author

Generated automatically by Doxygen for LAPACK from the source code.

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