gelqt3 - gelqt3: LQ factor, with T, recursive

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 gelqt3(3)

recursivesubroutinecgelqt3(integerm,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(ldt,*)t,integerldt,integerinfo)CGELQT3Purpose: CGELQT3 recursively computes a LQ 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. ParametersM 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 below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows 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. FurtherDetails: 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 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). recursivesubroutinedgelqt3(integerm,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldt,*)t,integerldt,integerinfo)DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: DGELQT3 recursively computes a LQ 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. ParametersM 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 below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows 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. FurtherDetails: 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 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). recursivesubroutinesgelqt3(integerm,integern,real,dimension(lda,*)a,integerlda,real,dimension(ldt,*)t,integerldt,integerinfo)SGELQT3Purpose: SGELQT3 recursively computes a LQ 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. ParametersM 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 REAL array, dimension (LDA,N) On entry, the real M-by-N matrix A. On exit, the elements on and below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows 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 REAL 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. FurtherDetails: 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 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). recursivesubroutinezgelqt3(integerm,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldt,*)t,integerldt,integerinfo)ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: ZGELQT3 recursively computes a LQ 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. ParametersM 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*16 array, dimension (LDA,N) On entry, the complex M-by-N matrix A. On exit, the elements on and below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows 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*16 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. FurtherDetails: 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 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).

gelqt3 - gelqt3: LQ factor, with T, recursive

Functions recursive subroutine cgelqt3 (m, n, a, lda, t, ldt, info) CGELQT3 recursive subroutine dgelqt3 (m, n, a, lda, t, ldt, info) DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. recursive subroutine sgelqt3 (m, n, a, lda, t, ldt, info) SGELQT3 recursive subroutine zgelqt3 (m, n, a, lda, t, ldt, info) ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.