# sgerq2(3) [centos man page]

sgerq2.f(3) LAPACK sgerq2.f(3)NAME

sgerq2.f-SYNOPSIS

Functions/Subroutines subroutine sgerq2 (M, N, A, LDA, TAU, WORK, INFO) SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.Function/Subroutine Documentation subroutine sgerq2 (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO) SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. Purpose: SGERQ2 computes an RQ factorization of a real 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 REAL 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 orthogonal 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK WORK is REAL 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(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(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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 sgerq2.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 sgerq2.f(3)

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sgeqr2.f(3) LAPACK sgeqr2.f(3)NAME

sgeqr2.f-SYNOPSIS

Functions/Subroutines subroutine sgeqr2 (M, N, A, LDA, TAU, WORK, INFO) SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.Function/Subroutine Documentation subroutine sgeqr2 (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO) SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm. Purpose: SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. 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 elements below the diagonal, with the array TAU, represent the orthogonal 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK WORK is REAL 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(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). Definition at line 122 of file sgeqr2.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 sgeqr2.f(3)