ctzrqf(3) [debian man page]
ctzrqf.f(3) LAPACK ctzrqf.f(3) NAME
ctzrqf.f - SYNOPSIS
Functions/Subroutines subroutine ctzrqf (M, N, A, LDA, TAU, INFO) CTZRQF Function/Subroutine Documentation subroutine ctzrqf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, integerINFO) CTZRQF Purpose: This routine is deprecated and has been replaced by routine CTZRZF. CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix. 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 >= M. A A is COMPLEX array, dimension (LDA,N) On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX array, dimension (M) The scalar factors of the elementary reflectors. 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 factorization is obtained by Householder's method. The kth transformation matrix, Z( k ), whose conjugate transpose is used to introduce zeros into the (m - k + 1)th row of A, is given in the form Z( k ) = ( I 0 ), ( 0 T( k ) ) where T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), ( 0 ) ( z( k ) ) tau is a scalar and z( k ) is an ( n - m ) element vector. tau and z( k ) are chosen to annihilate the elements of the kth row of X. The scalar tau is returned in the kth element of TAU and the vector u( k ) in the kth row of A, such that the elements of z( k ) are in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in the upper triangular part of A. Z is given by Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). Definition at line 139 of file ctzrqf.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 ctzrqf.f(3)
Check Out this Related Man Page
ctzrqf.f(3) LAPACK ctzrqf.f(3) NAME
ctzrqf.f - SYNOPSIS
Functions/Subroutines subroutine ctzrqf (M, N, A, LDA, TAU, INFO) CTZRQF Function/Subroutine Documentation subroutine ctzrqf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, integerINFO) CTZRQF Purpose: This routine is deprecated and has been replaced by routine CTZRZF. CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix. 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 >= M. A A is COMPLEX array, dimension (LDA,N) On entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX array, dimension (M) The scalar factors of the elementary reflectors. 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 factorization is obtained by Householder's method. The kth transformation matrix, Z( k ), whose conjugate transpose is used to introduce zeros into the (m - k + 1)th row of A, is given in the form Z( k ) = ( I 0 ), ( 0 T( k ) ) where T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), ( 0 ) ( z( k ) ) tau is a scalar and z( k ) is an ( n - m ) element vector. tau and z( k ) are chosen to annihilate the elements of the kth row of X. The scalar tau is returned in the kth element of TAU and the vector u( k ) in the kth row of A, such that the elements of z( k ) are in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in the upper triangular part of A. Z is given by Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). Definition at line 139 of file ctzrqf.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 ctzrqf.f(3)