geqr - Man Page

geqr: QR factor, flexible

Synopsis

Functions

subroutine cgeqr (m, n, a, lda, t, tsize, work, lwork, info)
CGEQR
subroutine dgeqr (m, n, a, lda, t, tsize, work, lwork, info)
DGEQR
subroutine sgeqr (m, n, a, lda, t, tsize, work, lwork, info)
SGEQR
subroutine zgeqr (m, n, a, lda, t, tsize, work, lwork, info)
ZGEQR

Detailed Description

Function Documentation

subroutine cgeqr (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) t, integer tsize, complex, dimension( * ) work, integer lwork, integer info)

CGEQR

Purpose:

 CGEQR computes a QR factorization of a complex M-by-N matrix A:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a M-by-M orthogonal matrix;
    R is an upper-triangular N-by-N matrix;
    0 is a (M-N)-by-N zero matrix, if M > N.
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.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R
          (R is upper triangular if M >= N);
          the elements below the diagonal are used to store part of the 
          data structure to represent Q.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

T

          T is COMPLEX array, dimension (MAX(5,TSIZE))
          On exit, if INFO = 0, T(1) returns optimal (or either minimal 
          or optimal, if query is assumed) TSIZE. See TSIZE for details.
          Remaining T contains part of the data structure used to represent Q.
          If one wants to apply or construct Q, then one needs to keep T 
          (in addition to A) and pass it to further subroutines.

TSIZE

          TSIZE is INTEGER
          If TSIZE >= 5, the dimension of the array T.
          If TSIZE = -1 or -2, then a workspace query is assumed. The routine
          only calculates the sizes of the T and WORK arrays, returns these
          values as the first entries of the T and WORK arrays, and no error
          message related to T or WORK is issued by XERBLA.
          If TSIZE = -1, the routine calculates optimal size of T for the 
          optimum performance and returns this value in T(1).
          If TSIZE = -2, the routine calculates minimal size of T and 
          returns this value in T(1).

WORK

          (workspace) COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
          or optimal, if query was assumed) LWORK.
          See LWORK for details.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1 or -2, then a workspace query is assumed. The routine
          only calculates the sizes of the T and WORK arrays, returns these
          values as the first entries of the T and WORK arrays, and no error
          message related to T or WORK is issued by XERBLA.
          If LWORK = -1, the routine calculates optimal size of WORK for the
          optimal performance and returns this value in WORK(1).
          If LWORK = -2, the routine calculates minimal size of WORK and 
          returns this value in WORK(1).

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 goal of the interface is to give maximum freedom to the developers for
 creating any QR factorization algorithm they wish. The triangular 
 (trapezoidal) R has to be stored in the upper part of A. The lower part of A
 and the array T can be used to store any relevant information for applying or
 constructing the Q factor. The WORK array can safely be discarded after exit.

 Caution: One should not expect the sizes of T and WORK to be the same from one 
 LAPACK implementation to the other, or even from one execution to the other.
 A workspace query (for T and WORK) is needed at each execution. However, 
 for a given execution, the size of T and WORK are fixed and will not change 
 from one query to the next.

Further Details particular to this LAPACK implementation:

 These details are particular for this LAPACK implementation. Users should not 
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           CLATSQR or CGEQRT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, CGEQR will use either
  CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute
  the QR factorization.

Definition at line 174 of file cgeqr.f.

subroutine dgeqr (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) t, integer tsize, double precision, dimension( * ) work, integer lwork, integer info)

DGEQR

Purpose:

 DGEQR computes a QR factorization of a real M-by-N matrix A:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a M-by-M orthogonal matrix;
    R is an upper-triangular N-by-N matrix;
    0 is a (M-N)-by-N zero matrix, if M > N.
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.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R
          (R is upper triangular if M >= N);
          the elements below the diagonal are used to store part of the 
          data structure to represent Q.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

T

          T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE))
          On exit, if INFO = 0, T(1) returns optimal (or either minimal 
          or optimal, if query is assumed) TSIZE. See TSIZE for details.
          Remaining T contains part of the data structure used to represent Q.
          If one wants to apply or construct Q, then one needs to keep T 
          (in addition to A) and pass it to further subroutines.

TSIZE

          TSIZE is INTEGER
          If TSIZE >= 5, the dimension of the array T.
          If TSIZE = -1 or -2, then a workspace query is assumed. The routine
          only calculates the sizes of the T and WORK arrays, returns these
          values as the first entries of the T and WORK arrays, and no error
          message related to T or WORK is issued by XERBLA.
          If TSIZE = -1, the routine calculates optimal size of T for the 
          optimum performance and returns this value in T(1).
          If TSIZE = -2, the routine calculates minimal size of T and 
          returns this value in T(1).

WORK

          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
          or optimal, if query was assumed) LWORK.
          See LWORK for details.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1 or -2, then a workspace query is assumed. The routine
          only calculates the sizes of the T and WORK arrays, returns these
          values as the first entries of the T and WORK arrays, and no error
          message related to T or WORK is issued by XERBLA.
          If LWORK = -1, the routine calculates optimal size of WORK for the
          optimal performance and returns this value in WORK(1).
          If LWORK = -2, the routine calculates minimal size of WORK and 
          returns this value in WORK(1).

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 goal of the interface is to give maximum freedom to the developers for
 creating any QR factorization algorithm they wish. The triangular 
 (trapezoidal) R has to be stored in the upper part of A. The lower part of A
 and the array T can be used to store any relevant information for applying or
 constructing the Q factor. The WORK array can safely be discarded after exit.

 Caution: One should not expect the sizes of T and WORK to be the same from one 
 LAPACK implementation to the other, or even from one execution to the other.
 A workspace query (for T and WORK) is needed at each execution. However, 
 for a given execution, the size of T and WORK are fixed and will not change 
 from one query to the next.

Further Details particular to this LAPACK implementation:

 These details are particular for this LAPACK implementation. Users should not 
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           DLATSQR or DGEQRT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, DGEQR will use either
  DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
  the QR factorization.

Definition at line 174 of file dgeqr.f.

subroutine sgeqr (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) t, integer tsize, real, dimension( * ) work, integer lwork, integer info)

SGEQR

Purpose:

 SGEQR computes a QR factorization of a real M-by-N matrix A:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a M-by-M orthogonal matrix;
    R is an upper-triangular N-by-N matrix;
    0 is a (M-N)-by-N zero matrix, if M > N.
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.

A

          A is REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R
          (R is upper triangular if M >= N);
          the elements below the diagonal are used to store part of the 
          data structure to represent Q.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

T

          T is REAL array, dimension (MAX(5,TSIZE))
          On exit, if INFO = 0, T(1) returns optimal (or either minimal 
          or optimal, if query is assumed) TSIZE. See TSIZE for details.
          Remaining T contains part of the data structure used to represent Q.
          If one wants to apply or construct Q, then one needs to keep T 
          (in addition to A) and pass it to further subroutines.

TSIZE

          TSIZE is INTEGER
          If TSIZE >= 5, the dimension of the array T.
          If TSIZE = -1 or -2, then a workspace query is assumed. The routine
          only calculates the sizes of the T and WORK arrays, returns these
          values as the first entries of the T and WORK arrays, and no error
          message related to T or WORK is issued by XERBLA.
          If TSIZE = -1, the routine calculates optimal size of T for the 
          optimum performance and returns this value in T(1).
          If TSIZE = -2, the routine calculates minimal size of T and 
          returns this value in T(1).

WORK

          (workspace) REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
          or optimal, if query was assumed) LWORK.
          See LWORK for details.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1 or -2, then a workspace query is assumed. The routine
          only calculates the sizes of the T and WORK arrays, returns these
          values as the first entries of the T and WORK arrays, and no error
          message related to T or WORK is issued by XERBLA.
          If LWORK = -1, the routine calculates optimal size of WORK for the
          optimal performance and returns this value in WORK(1).
          If LWORK = -2, the routine calculates minimal size of WORK and 
          returns this value in WORK(1).

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 goal of the interface is to give maximum freedom to the developers for
 creating any QR factorization algorithm they wish. The triangular 
 (trapezoidal) R has to be stored in the upper part of A. The lower part of A
 and the array T can be used to store any relevant information for applying or
 constructing the Q factor. The WORK array can safely be discarded after exit.

 Caution: One should not expect the sizes of T and WORK to be the same from one 
 LAPACK implementation to the other, or even from one execution to the other.
 A workspace query (for T and WORK) is needed at each execution. However, 
 for a given execution, the size of T and WORK are fixed and will not change 
 from one query to the next.

Further Details particular to this LAPACK implementation:

 These details are particular for this LAPACK implementation. Users should not 
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           SLATSQR or SGEQRT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, SGEQR will use either
  SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute
  the QR factorization.

Definition at line 174 of file sgeqr.f.

subroutine zgeqr (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) t, integer tsize, complex*16, dimension( * ) work, integer lwork, integer info)

ZGEQR

Purpose:

 ZGEQR computes a QR factorization of a complex M-by-N matrix A:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a M-by-M orthogonal matrix;
    R is an upper-triangular N-by-N matrix;
    0 is a (M-N)-by-N zero matrix, if M > N.
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.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R
          (R is upper triangular if M >= N);
          the elements below the diagonal are used to store part of the 
          data structure to represent Q.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

T

          T is COMPLEX*16 array, dimension (MAX(5,TSIZE))
          On exit, if INFO = 0, T(1) returns optimal (or either minimal 
          or optimal, if query is assumed) TSIZE. See TSIZE for details.
          Remaining T contains part of the data structure used to represent Q.
          If one wants to apply or construct Q, then one needs to keep T 
          (in addition to A) and pass it to further subroutines.

TSIZE

          TSIZE is INTEGER
          If TSIZE >= 5, the dimension of the array T.
          If TSIZE = -1 or -2, then a workspace query is assumed. The routine
          only calculates the sizes of the T and WORK arrays, returns these
          values as the first entries of the T and WORK arrays, and no error
          message related to T or WORK is issued by XERBLA.
          If TSIZE = -1, the routine calculates optimal size of T for the 
          optimum performance and returns this value in T(1).
          If TSIZE = -2, the routine calculates minimal size of T and 
          returns this value in T(1).

WORK

          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
          or optimal, if query was assumed) LWORK.
          See LWORK for details.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1 or -2, then a workspace query is assumed. The routine
          only calculates the sizes of the T and WORK arrays, returns these
          values as the first entries of the T and WORK arrays, and no error
          message related to T or WORK is issued by XERBLA.
          If LWORK = -1, the routine calculates optimal size of WORK for the
          optimal performance and returns this value in WORK(1).
          If LWORK = -2, the routine calculates minimal size of WORK and 
          returns this value in WORK(1).

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 goal of the interface is to give maximum freedom to the developers for
 creating any QR factorization algorithm they wish. The triangular 
 (trapezoidal) R has to be stored in the upper part of A. The lower part of A
 and the array T can be used to store any relevant information for applying or
 constructing the Q factor. The WORK array can safely be discarded after exit.

 Caution: One should not expect the sizes of T and WORK to be the same from one 
 LAPACK implementation to the other, or even from one execution to the other.
 A workspace query (for T and WORK) is needed at each execution. However, 
 for a given execution, the size of T and WORK are fixed and will not change 
 from one query to the next.

Further Details particular to this LAPACK implementation:

 These details are particular for this LAPACK implementation. Users should not 
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           ZLATSQR or ZGEQRT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, ZGEQR will use either
  ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute
  the QR factorization.

Definition at line 174 of file zgeqr.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK