geqrt(3)

NAME
geqrt - geqrt: QR factor, with T

SYNOPSIS

  Functions
subroutine cgeqrt (m, n, nb, a, lda, t, ldt, work, info)
CGEQRT
subroutine dgeqrt (m, n, nb, a, lda, t, ldt, work, info)
DGEQRT
subroutine sgeqrt (m, n, nb, a, lda, t, ldt, work, info)
SGEQRT
subroutine zgeqrt (m, n, nb, a, lda, t, ldt, work, info)
ZGEQRT

Detailed Description

Function Documentation

  subroutine cgeqrt (integer m, integer n, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer info)

CGEQRT

Purpose:

    !>
    !> CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
    !> using the compact WY representation of Q.
    !>

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.
    !>

    NB

    !>          NB is INTEGER
    !>          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.
    !>

    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 the columns of V.
    !>

    LDA

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

    T

    !>          T is COMPLEX array, dimension (LDT,MIN(M,N))
    !>          The upper triangular block reflectors stored in compact form
    !>          as a sequence of upper triangular blocks.  See below
    !>          for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= NB.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (NB*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.
    !>
    !>  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
    !>  block is of order NB except for the last block, which is of order
    !>  IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
    !>  for the last block) T's are stored in the NB-by-K matrix T as
    !>
    !>               T = (T1 T2 ... TB).
    !>

Definition at line 140 of file cgeqrt.f.

  subroutine dgeqrt (integer m, integer n, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info)

DGEQRT

Purpose:

    !>
    !> DGEQRT computes a blocked QR factorization of a real M-by-N matrix A
    !> using the compact WY representation of Q.
    !>

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.
    !>

    NB

    !>          NB is INTEGER
    !>          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.
    !>

    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 the columns of V.
    !>

    LDA

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

    T

    !>          T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
    !>          The upper triangular block reflectors stored in compact form
    !>          as a sequence of upper triangular blocks.  See below
    !>          for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= NB.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (NB*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.
    !>
    !>  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
    !>  block is of order NB except for the last block, which is of order
    !>  IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
    !>  for the last block) T's are stored in the NB-by-K matrix T as
    !>
    !>               T = (T1 T2 ... TB).
    !>

Definition at line 140 of file dgeqrt.f.

  subroutine sgeqrt (integer m, integer n, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)

SGEQRT

Purpose:

    !>
    !> SGEQRT computes a blocked QR factorization of a real M-by-N matrix A
    !> using the compact WY representation of Q.
    !>

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.
    !>

    NB

    !>          NB is INTEGER
    !>          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.
    !>

    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 the columns of V.
    !>

    LDA

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

    T

    !>          T is REAL array, dimension (LDT,MIN(M,N))
    !>          The upper triangular block reflectors stored in compact form
    !>          as a sequence of upper triangular blocks.  See below
    !>          for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= NB.
    !>

    WORK

    !>          WORK is REAL array, dimension (NB*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.
    !>
    !>  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
    !>  block is of order NB except for the last block, which is of order
    !>  IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
    !>  for the last block) T's are stored in the NB-by-K matrix T as
    !>
    !>               T = (T1 T2 ... TB).
    !>

Definition at line 140 of file sgeqrt.f.

  subroutine zgeqrt (integer m, integer n, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)

ZGEQRT

Purpose:

    !>
    !> ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
    !> using the compact WY representation of Q.
    !>

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.
    !>

    NB

    !>          NB is INTEGER
    !>          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.
    !>

    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 the columns of V.
    !>

    LDA

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

    T

    !>          T is COMPLEX*16 array, dimension (LDT,MIN(M,N))
    !>          The upper triangular block reflectors stored in compact form
    !>          as a sequence of upper triangular blocks.  See below
    !>          for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= NB.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (NB*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.
    !>
    !>  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
    !>  block is of order NB except for the last block, which is of order
    !>  IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
    !>  for the last block) T's are stored in the NB-by-K matrix T as
    !>
    !>               T = (T1 T2 ... TB).
    !>

Definition at line 140 of file zgeqrt.f.

Author

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