.TH "gelqt3" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gelqt3 \- gelqt3: LQ factor, with T, recursive .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "recursive subroutine \fBcgelqt3\fP (m, n, a, lda, t, ldt, info)" .br .RI "\fBCGELQT3\fP " .ti -1c .RI "recursive subroutine \fBdgelqt3\fP (m, n, a, lda, t, ldt, info)" .br .RI "\fBDGELQT3\fP recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q\&. " .ti -1c .RI "recursive subroutine \fBsgelqt3\fP (m, n, a, lda, t, ldt, info)" .br .RI "\fBSGELQT3\fP " .ti -1c .RI "recursive subroutine \fBzgelqt3\fP (m, n, a, lda, t, ldt, info)" .br .RI "\fBZGELQT3\fP recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "recursive subroutine cgelqt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)" .PP \fBCGELQT3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M =< N\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf 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\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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)\&. .fi .PP .RE .PP .SS "recursive subroutine dgelqt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)" .PP \fBDGELQT3\fP recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M =< N\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf 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\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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)\&. .fi .PP .RE .PP .SS "recursive subroutine sgelqt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)" .PP \fBSGELQT3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M =< N\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf 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\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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)\&. .fi .PP .RE .PP .SS "recursive subroutine zgelqt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)" .PP \fBZGELQT3\fP recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M =< N\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf 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\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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)\&. .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.