gelqt(3) Library Functions Manual gelqt(3) NAME gelqt - gelqt: LQ factor, with T SYNOPSIS Functions subroutine cgelqt (m, n, mb, a, lda, t, ldt, work, info) CGELQT subroutine dgelqt (m, n, mb, a, lda, t, ldt, work, info) DGELQT subroutine sgelqt (m, n, mb, a, lda, t, ldt, work, info) SGELQT subroutine zgelqt (m, n, mb, a, lda, t, ldt, work, info) ZGELQT Detailed Description Function Documentation subroutine cgelqt (integer m, integer n, integer mb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer info) CGELQT Purpose: CGELQT computes a blocked LQ factorization of a complex M-by-N matrix A using the compact WY representation of 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. MB MB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1. 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 are the rows of V. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is COMPLEX array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. WORK WORK is COMPLEX array, dimension (MB*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. Further Details: The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as T = (T1 T2 ... TB). Definition at line 123 of file cgelqt.f. subroutine dgelqt (integer m, integer n, integer mb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info) DGELQT Purpose: DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of 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. MB MB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1. 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 are the rows of V. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. WORK WORK is DOUBLE PRECISION array, dimension (MB*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. Further Details: The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as T = (T1 T2 ... TB). Definition at line 138 of file dgelqt.f. subroutine sgelqt (integer m, integer n, integer mb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info) SGELQT Purpose: DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of 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. MB MB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1. 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 are the rows of V. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is REAL array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. WORK WORK is REAL array, dimension (MB*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. Further Details: The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as T = (T1 T2 ... TB). Definition at line 123 of file sgelqt.f. subroutine zgelqt (integer m, integer n, integer mb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info) ZGELQT Purpose: ZGELQT computes a blocked LQ factorization of a complex M-by-N matrix A using the compact WY representation of 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. MB MB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1. 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 are the rows of V. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is COMPLEX*16 array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. WORK WORK is COMPLEX*16 array, dimension (MB*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. Further Details: The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as T = (T1 T2 ... TB). Definition at line 138 of file zgelqt.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 gelqt(3)