dgeqrt3.f(3) [debian man page]
dgeqrt3.f(3) LAPACK dgeqrt3.f(3) NAME
dgeqrt3.f - SYNOPSIS
Functions/Subroutines recursive subroutine dgeqrt3 (M, N, A, LDA, T, LDT, INFO) DGEQRT3 Function/Subroutine Documentation recursive subroutine dgeqrt3 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldt, * )T, integerLDT, integerINFO) DGEQRT3 Purpose: DGEQRT3 recursively computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000. Parameters: M M is INTEGER The number of rows of the matrix A. M >= N. 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 real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is DOUBLE PRECISION array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). 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. Date: November 2011 Further Details: The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**T where V**T is the transpose of V. For details of the algorithm, see Elmroth and Gustavson (cited above). Definition at line 133 of file dgeqrt3.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dgeqrt3.f(3)
Check Out this Related Man Page
cgeqrt3.f(3) LAPACK cgeqrt3.f(3) NAME
cgeqrt3.f - SYNOPSIS
Functions/Subroutines recursive subroutine cgeqrt3 (M, N, A, LDA, T, LDT, INFO) CGEQRT3 Function/Subroutine Documentation recursive subroutine cgeqrt3 (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldt, * )T, integerLDT, integerINFO) CGEQRT3 Purpose: CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000. Parameters: M M is INTEGER The number of rows of the matrix A. M >= N. 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 complex M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is COMPLEX array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). 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. Date: November 2011 Further Details: The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**H where V**H is the conjugate transpose of V. For details of the algorithm, see Elmroth and Gustavson (cited above). Definition at line 133 of file cgeqrt3.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 cgeqrt3.f(3)