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 is INTEGER


          The number of rows of the matrix A.  M >= N.



          N is INTEGER


          The number of columns of the matrix A.  N >= 0.



          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 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).

Definition at line 131 of file cgeqrt3.f.

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 is INTEGER


          The number of rows of the matrix A.  M >= N.



          N is INTEGER


          The number of columns of the matrix A.  N >= 0.



          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 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).

Definition at line 131 of file dgeqrt3.f.

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 is INTEGER


          The number of rows of the matrix A.  M >= N.



          N is INTEGER


          The number of columns of the matrix A.  N >= 0.



          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 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).

Definition at line 131 of file sgeqrt3.f.

recursive subroutine zgeqrt3 (integer m, integer n, complex16, dimension( lda, ) a, integer lda, complex16, 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 is INTEGER


          The number of rows of the matrix A.  M >= N.



          N is INTEGER


          The number of columns of the matrix A.  N >= 0.



          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 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).

Definition at line 131 of file zgeqrt3.f.

Author

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