Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       latrz - latrz: RZ factor step

SYNOPSIS

   Functions
       subroutine clatrz (m, n, l, a, lda, tau, work)
           CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.
       subroutine dlatrz (m, n, l, a, lda, tau, work)
           DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.
       subroutine slatrz (m, n, l, a, lda, tau, work)
           SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.
       subroutine zlatrz (m, n, l, a, lda, tau, work)
           ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

Detailed Description

Function Documentation

   subroutine clatrz (integer m, integer n, integer l, complex, dimension( lda, * ) a, integer
       lda, complex, dimension( * ) tau, complex, dimension( * ) work)
       CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

       Purpose:

            CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
            [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z by means
            of unitary transformations, where  Z is an (M+L)-by-(M+L) unitary
            matrix and, R and A1 are M-by-M upper triangular matrices.

       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 >= 0.

           L

                     L is INTEGER
                     The number of columns of the matrix A containing the
                     meaningful part of the Householder vectors. N-M >= L >= 0.

           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 N-L+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.

           WORK

                     WORK is COMPLEX array, dimension (M)

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       Further Details:

             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

                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 l element vector. tau and z( k )
             are chosen to annihilate the elements of the kth row of A2.

             The scalar tau is returned in the kth element of TAU and the vector
             u( k ) in the kth row of A2, such that the elements of z( k ) are
             in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
             the upper triangular part of A1.

             Z is given by

                Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

   subroutine dlatrz (integer m, integer n, integer l, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work)
       DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

       Purpose:

            DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
            [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z, by means
            of orthogonal transformations.  Z is an (M+L)-by-(M+L) orthogonal
            matrix and, R and A1 are M-by-M upper triangular matrices.

       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 >= 0.

           L

                     L is INTEGER
                     The number of columns of the matrix A containing the
                     meaningful part of the Householder vectors. N-M >= L >= 0.

           A

                     A is DOUBLE PRECISION 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 N-L+1 to
                     N of the first M rows of A, with the array TAU, represent the
                     orthogonal 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 DOUBLE PRECISION array, dimension (M)
                     The scalar factors of the elementary reflectors.

           WORK

                     WORK is DOUBLE PRECISION array, dimension (M)

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       Further Details:

             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

                Z( k ) = ( I     0   ),
                         ( 0  T( k ) )

             where

                T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
                                                            (   0    )
                                                            ( z( k ) )

             tau is a scalar and z( k ) is an l element vector. tau and z( k )
             are chosen to annihilate the elements of the kth row of A2.

             The scalar tau is returned in the kth element of TAU and the vector
             u( k ) in the kth row of A2, such that the elements of z( k ) are
             in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
             the upper triangular part of A1.

             Z is given by

                Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

   subroutine slatrz (integer m, integer n, integer l, real, dimension( lda, * ) a, integer lda,
       real, dimension( * ) tau, real, dimension( * ) work)
       SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

       Purpose:

            SLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
            [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z, by means
            of orthogonal transformations.  Z is an (M+L)-by-(M+L) orthogonal
            matrix and, R and A1 are M-by-M upper triangular matrices.

       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 >= 0.

           L

                     L is INTEGER
                     The number of columns of the matrix A containing the
                     meaningful part of the Householder vectors. N-M >= L >= 0.

           A

                     A is REAL 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 N-L+1 to
                     N of the first M rows of A, with the array TAU, represent the
                     orthogonal 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 REAL array, dimension (M)
                     The scalar factors of the elementary reflectors.

           WORK

                     WORK is REAL array, dimension (M)

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       Further Details:

             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

                Z( k ) = ( I     0   ),
                         ( 0  T( k ) )

             where

                T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
                                                            (   0    )
                                                            ( z( k ) )

             tau is a scalar and z( k ) is an l element vector. tau and z( k )
             are chosen to annihilate the elements of the kth row of A2.

             The scalar tau is returned in the kth element of TAU and the vector
             u( k ) in the kth row of A2, such that the elements of z( k ) are
             in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
             the upper triangular part of A1.

             Z is given by

                Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

   subroutine zlatrz (integer m, integer n, integer l, complex*16, dimension( lda, * ) a, integer
       lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work)
       ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

       Purpose:

            ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
            [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z by means
            of unitary transformations, where  Z is an (M+L)-by-(M+L) unitary
            matrix and, R and A1 are M-by-M upper triangular matrices.

       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 >= 0.

           L

                     L is INTEGER
                     The number of columns of the matrix A containing the
                     meaningful part of the Householder vectors. N-M >= L >= 0.

           A

                     A is COMPLEX*16 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 N-L+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*16 array, dimension (M)
                     The scalar factors of the elementary reflectors.

           WORK

                     WORK is COMPLEX*16 array, dimension (M)

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       Further Details:

             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

                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 l element vector. tau and z( k )
             are chosen to annihilate the elements of the kth row of A2.

             The scalar tau is returned in the kth element of TAU and the vector
             u( k ) in the kth row of A2, such that the elements of z( k ) are
             in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
             the upper triangular part of A1.

             Z is given by

                Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

Author

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