WOLFRAM SYSTEM MODELER
Compute QR factorization of square or rectangular matrix A with column pivoting (A(:,p) = Q*R)
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Lapack documentation Purpose ======= This routine is deprecated and has been replaced by routine DGEQP3. DGEQPF computes a QR factorization with column pivoting of a real M-by-N matrix A: A*P = Q*R. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0 A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the upper triangle of the array contains the min(M,N)-by-N upper triangular matrix R; the elements below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT (input/output) INTEGER array, dimension (N) On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A. TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors. WORK (workspace) DOUBLE PRECISION array, dimension (3*N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Details =============== The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n) Each H(i) has the form H = I - tau * v * v' 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). The matrix P is represented in jpvt as follows: If jpvt(j) = i then the jth column of P is the ith canonical unit vector.
Description: Square or rectangular matrix
Default Value: A
Type: Real[size(A, 1),size(A, 2)]
Description: QR factorization in packed format
Type: Real[min(size(A, 1), size(A, 2))]
Description: The scalar factors of the elementary reflectors of Q
Default Value: zeros(size(A, 2))
Type: Integer[size(A, 2)]
Description: Pivot vector