# cgerq2.f(3) [centos man page]

cgerq2.f(3) LAPACK cgerq2.f(3)NAME

cgerq2.f-SYNOPSIS

Functions/Subroutines subroutine cgerq2 (M, N, A, LDA, TAU, WORK, INFO) CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.Function/Subroutine Documentation subroutine cgerq2 (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerINFO) CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. Purpose: CGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R * Q. 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 COMPLEX array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). LDA LDA is INTEGER The leading dimension of the array A. 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 (M) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Further Details: The matrix Q is represented as a product of elementary reflectors Q = H(1)**H H(2)**H . . . H(k)**H, 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). Definition at line 124 of file cgerq2.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 cgerq2.f(3)

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zgeql2.f(3) LAPACK zgeql2.f(3)NAME

zgeql2.f-SYNOPSIS

Functions/Subroutines subroutine zgeql2 (M, N, A, LDA, TAU, WORK, INFO) ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.Function/Subroutine Documentation subroutine zgeql2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO) ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. Purpose: ZGEQL2 computes a QL factorization of a complex m by n matrix A: A = Q * L. 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 COMPLEX*16 array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix L; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK WORK is COMPLEX*16 array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Further Details: The matrix Q is represented as a product of elementary reflectors Q = H(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i). Definition at line 124 of file zgeql2.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 zgeql2.f(3)