gelqt - Man Page

subroutine cgelqt (m, n, mb, a, lda, t, ldt, work, info)
CGELQT
subroutine dgelqt (m, n, mb, a, lda, t, ldt, work, info)
DGELQT
subroutine sgelqt (m, n, mb, a, lda, t, ldt, work, info)
SGELQT
subroutine zgelqt (m, n, mb, a, lda, t, ldt, work, info)
ZGELQT

CGELQT

Purpose:

 CGELQT computes a blocked LQ 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.

MB

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

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
          lower triangular if M <= N); the elements above the diagonal
          are the rows 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 >= MB.

WORK

          WORK is COMPLEX array, dimension (MB*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 row
  above the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (         1 v3 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/MB), where each
  block is of order MB except for the last block, which is of order
  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
  for the last block) T's are stored in the MB-by-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 123 of file cgelqt.f.

DGELQT  

Purpose:

 DGELQT computes a blocked LQ 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.

MB

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

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
          lower triangular if M <= N); the elements above the diagonal
          are the rows 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 >= MB.

WORK

          WORK is DOUBLE PRECISION array, dimension (MB*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 row
  above the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (         1 v3 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/MB), where each
  block is of order MB except for the last block, which is of order
  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
  for the last block) T's are stored in the MB-by-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 138 of file dgelqt.f.

SGELQT

Purpose:

 DGELQT computes a blocked LQ 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.

MB

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

A

          A is REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
          lower triangular if M <= N); the elements above the diagonal
          are the rows 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 >= MB.

WORK

          WORK is REAL array, dimension (MB*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 row
  above the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (         1 v3 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/MB), where each
  block is of order MB except for the last block, which is of order
  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
  for the last block) T's are stored in the MB-by-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 123 of file sgelqt.f.

ZGELQT  

Purpose:

 ZGELQT computes a blocked LQ 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.

MB

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

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
          lower triangular if M <= N); the elements above the diagonal
          are the rows 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 >= MB.

WORK

          WORK is COMPLEX*16 array, dimension (MB*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 row
  above the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (         1 v3 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/MB), where each
  block is of order MB except for the last block, which is of order
  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
  for the last block) T's are stored in the MB-by-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 138 of file zgelqt.f.