geqrt2(3) Library Functions Manual geqrt2(3) NAME geqrt2 - geqrt2: QR factor, with T, level 2 SYNOPSIS Functions subroutine cgeqrt2 (m, n, a, lda, t, ldt, info) CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. subroutine dgeqrt2 (m, n, a, lda, t, ldt, info) DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. subroutine sgeqrt2 (m, n, a, lda, t, ldt, info) SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. subroutine zgeqrt2 (m, n, a, lda, t, ldt, info) ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Detailed Description Function Documentation subroutine cgeqrt2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info) CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: !> !> CGEQRT2 computes a QR 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 >= 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. 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. !> Definition at line 126 of file cgeqrt2.f. subroutine dgeqrt2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info) DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: !> !> DGEQRT2 computes a QR 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 >= 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. 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. !> Definition at line 126 of file dgeqrt2.f. subroutine sgeqrt2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info) SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: !> !> SGEQRT2 computes a QR 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 >= 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 !> 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 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. 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. !> Definition at line 126 of file sgeqrt2.f. subroutine zgeqrt2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info) ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: !> !> ZGEQRT2 computes a QR 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 >= 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 !> 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*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. 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. !> Definition at line 126 of file zgeqrt2.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 geqrt2(3)