From 2a41d09a428b2b1c77650a636ca7dffae6127b43 Mon Sep 17 00:00:00 2001 From: james Date: Thu, 8 Dec 2011 23:55:05 +0000 Subject: corrected documentation --- SRC/ctzrzf.f | 27 +++++++++------------------ SRC/dtzrzf.f | 27 +++++++++------------------ SRC/stzrzf.f | 27 +++++++++------------------ SRC/ztzrzf.f | 27 +++++++++------------------ 4 files changed, 36 insertions(+), 72 deletions(-) diff --git a/SRC/ctzrzf.f b/SRC/ctzrzf.f index 784de3ad..2cc21b5b 100644 --- a/SRC/ctzrzf.f +++ b/SRC/ctzrzf.f @@ -130,31 +130,22 @@ *> *> \verbatim *> -*> The factorization is obtained by Householder's method. The kth -*> transformation matrix, Z( k ), which is used to introduce zeros into -*> the ( m - k + 1 )th row of A, is given in the form +*> The N-by-N matrix Z can be computed by *> -*> Z( k ) = ( I 0 ), -*> ( 0 T( k ) ) +*> Z = Z(1)*Z(2)* ... *Z(M) *> -*> where +*> where each N-by-N Z(k) is given by *> -*> T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), -*> ( 0 ) -*> ( z( k ) ) +*> Z(k) = I - tau(k)*v(k)*v(k)**H *> -*> 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. +*> with v(k) is the kth row vector of the M-by-N matrix *> -*> 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. +*> V = ( I A(:,M+1:N) ) *> -*> Z is given by +*> I is the M-by-M identity matrix, A(:,M+1:N) +*> is the output stored in A on exit from DTZRZF, +*> and tau(k) is the kth element of the array TAU. *> -*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). *> \endverbatim *> * ===================================================================== diff --git a/SRC/dtzrzf.f b/SRC/dtzrzf.f index 7177de09..520a60bd 100644 --- a/SRC/dtzrzf.f +++ b/SRC/dtzrzf.f @@ -130,31 +130,22 @@ *> *> \verbatim *> -*> The factorization is obtained by Householder's method. The kth -*> transformation matrix, Z( k ), which is used to introduce zeros into -*> the ( m - k + 1 )th row of A, is given in the form +*> The N-by-N matrix Z can be computed by *> -*> Z( k ) = ( I 0 ), -*> ( 0 T( k ) ) +*> Z = Z(1)*Z(2)* ... *Z(M) *> -*> where +*> where each N-by-N Z(k) is given by *> -*> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ), -*> ( 0 ) -*> ( z( k ) ) +*> Z(k) = I - tau(k)*v(k)*v(k)**T *> -*> 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. +*> with v(k) is the kth row vector of the M-by-N matrix *> -*> 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. +*> V = ( I A(:,M+1:N) ) *> -*> Z is given by +*> I is the M-by-M identity matrix, A(:,M+1:N) +*> is the output stored in A on exit from DTZRZF, +*> and tau(k) is the kth element of the array TAU. *> -*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). *> \endverbatim *> * ===================================================================== diff --git a/SRC/stzrzf.f b/SRC/stzrzf.f index 1baaa3ed..4e2545f7 100644 --- a/SRC/stzrzf.f +++ b/SRC/stzrzf.f @@ -130,31 +130,22 @@ *> *> \verbatim *> -*> The factorization is obtained by Householder's method. The kth -*> transformation matrix, Z( k ), which is used to introduce zeros into -*> the ( m - k + 1 )th row of A, is given in the form +*> The N-by-N matrix Z can be computed by *> -*> Z( k ) = ( I 0 ), -*> ( 0 T( k ) ) +*> Z = Z(1)*Z(2)* ... *Z(M) *> -*> where +*> where each N-by-N Z(k) is given by *> -*> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ), -*> ( 0 ) -*> ( z( k ) ) +*> Z(k) = I - tau(k)*v(k)*v(k)**T *> -*> 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. +*> with v(k) is the kth row vector of the M-by-N matrix *> -*> 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. +*> V = ( I A(:,M+1:N) ) *> -*> Z is given by +*> I is the M-by-M identity matrix, A(:,M+1:N) +*> is the output stored in A on exit from DTZRZF, +*> and tau(k) is the kth element of the array TAU. *> -*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). *> \endverbatim *> * ===================================================================== diff --git a/SRC/ztzrzf.f b/SRC/ztzrzf.f index 5c1e6f41..0870a25f 100644 --- a/SRC/ztzrzf.f +++ b/SRC/ztzrzf.f @@ -130,31 +130,22 @@ *> *> \verbatim *> -*> The factorization is obtained by Householder's method. The kth -*> transformation matrix, Z( k ), which is used to introduce zeros into -*> the ( m - k + 1 )th row of A, is given in the form +*> The N-by-N matrix Z can be computed by *> -*> Z( k ) = ( I 0 ), -*> ( 0 T( k ) ) +*> Z = Z(1)*Z(2)* ... *Z(M) *> -*> where +*> where each N-by-N Z(k) is given by *> -*> T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), -*> ( 0 ) -*> ( z( k ) ) +*> Z(k) = I - tau(k)*v(k)*v(k)**H *> -*> 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. +*> with v(k) is the kth row vector of the M-by-N matrix *> -*> 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. +*> V = ( I A(:,M+1:N) ) *> -*> Z is given by +*> I is the M-by-M identity matrix, A(:,M+1:N) +*> is the output stored in A on exit from DTZRZF, +*> and tau(k) is the kth element of the array TAU. *> -*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). *> \endverbatim *> * ===================================================================== -- cgit v1.2.3