SRC/dgeqrfp.f(3)

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🌸 NAME 🌸

SRC/dgeqrfp.f

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✨ SYNOPSIS ✨

Functions/Subroutines

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

DGEQRFP

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💖 Function/Subroutine Documentation 💖

   subroutine dgeqrfp (integer m, integer n, double precision, dimension( lda,
       * ) a, integer lda, double precision, dimension( * ) tau, double
       precision, dimension( * ) work, integer lwork, integer info)

DGEQRFP

🎯 Purpose 🎯

Okay so the purpose section says — and I am quoting with my whole chest — that DGEQR2P computes a QR factorization of a real 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).

WORK

WORK is DOUBLE PRECISION 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**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 149 of file dgeqrfp.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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