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geqrt3(3) LAPACK geqrt3(3)

NAME

geqrt3 - geqrt3: QR factor, with T, recursive panel

SYNOPSIS

Functions


recursive subroutine cgeqrt3 (m, n, a, lda, t, ldt, info)
CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. recursive subroutine dgeqrt3 (m, n, a, lda, t, ldt, info)
DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. recursive subroutine sgeqrt3 (m, n, a, lda, t, ldt, info)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. recursive subroutine zgeqrt3 (m, n, a, lda, t, ldt, info)
ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Detailed Description

Function Documentation

recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:



 CGEQRT3 recursively computes a QR 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.

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.


  For details of the algorithm, see Elmroth and Gustavson (cited above).

recursive subroutine dgeqrt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:



 DGEQRT3 recursively computes a QR 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.

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.


  For details of the algorithm, see Elmroth and Gustavson (cited above).

recursive subroutine sgeqrt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:



 SGEQRT3 recursively computes a QR 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.

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.


  For details of the algorithm, see Elmroth and Gustavson (cited above).

recursive subroutine zgeqrt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:



 ZGEQRT3 recursively computes a QR 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.

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.


  For details of the algorithm, see Elmroth and Gustavson (cited above).

Author

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