gelqf(3) Library Functions Manual gelqf(3) NAME gelqf - gelqf: LQ factor SYNOPSIS Functions subroutine cgelqf (m, n, a, lda, tau, work, lwork, info) CGELQF subroutine dgelqf (m, n, a, lda, tau, work, lwork, info) DGELQF subroutine sgelqf (m, n, a, lda, tau, work, lwork, info) SGELQF subroutine zgelqf (m, n, a, lda, tau, work, lwork, info) ZGELQF Detailed Description Function Documentation subroutine cgelqf (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info) CGELQF Purpose: CGELQF computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) 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 COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, 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 (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,M). For optimum performance LWORK >= M*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(k)**H . . . H(2)**H H(1)**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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i). Definition at line 142 of file cgelqf.f. subroutine dgelqf (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info) DGELQF Purpose: DGELQF computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) 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 below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above 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 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 >= max(1,M). For optimum performance LWORK >= M*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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), and tau in TAU(i). Definition at line 142 of file dgelqf.f. subroutine sgelqf (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info) SGELQF Purpose: SGELQF computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) 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 below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above 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 (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,M). For optimum performance LWORK >= M*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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), and tau in TAU(i). Definition at line 142 of file sgelqf.f. subroutine zgelqf (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info) ZGELQF Purpose: ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) 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 COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, 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 (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,M). For optimum performance LWORK >= M*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(k)**H . . . H(2)**H H(1)**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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i). Definition at line 142 of file zgelqf.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 gelqf(3)