gemqr - Man Page

subroutine cgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
CGEMQR
subroutine dgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
DGEMQR
subroutine sgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
SGEMQR
subroutine zgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
ZGEMQR

CGEMQR

Purpose:

 CGEMQR overwrites the general real M-by-N matrix C with

                      SIDE = 'L'     SIDE = 'R'
      TRANS = 'N':      Q * C          C * Q
      TRANS = 'T':      Q**H * C       C * Q**H

 where Q is a complex unitary matrix defined as the product
 of blocked elementary reflectors computed by tall skinny
 QR factorization (CGEQR)

Parameters

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q or Q**H from the Left;
          = 'R': apply Q or Q**H from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Conjugate transpose, apply Q**H.

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 C. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

A

          A is COMPLEX array, dimension (LDA,K)
          Part of the data structure to represent Q as returned by CGEQR.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).

T

          T is COMPLEX array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by CGEQR.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is COMPLEX array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC

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

WORK

         (workspace) COMPLEX array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK
          is issued by XERBLA.

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

 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.
  This version of CGEMQR will use either CLAMTSQR or CGEMQRT to
  multiply matrix Q by another matrix.
  Further Details in CLAMTSQR or CGEMQRT.

Definition at line 172 of file cgemqr.f.

DGEMQR

Purpose:

 DGEMQR overwrites the general real M-by-N matrix C with

                      SIDE = 'L'     SIDE = 'R'
      TRANS = 'N':      Q * C          C * Q
      TRANS = 'T':      Q**T * C       C * Q**T

 where Q is a real orthogonal matrix defined as the product
 of blocked elementary reflectors computed by tall skinny
 QR factorization (DGEQR)

Parameters

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T.

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 C. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,K)
          Part of the data structure to represent Q as returned by DGEQR.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).

T

          T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by DGEQR.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC

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

WORK

         (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK
          is issued by XERBLA.

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

 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.
  This version of DGEMQR will use either DLAMTSQR or DGEMQRT to
  multiply matrix Q by another matrix.
  Further Details in DLATMSQR or DGEMQRT.

Definition at line 172 of file dgemqr.f.

SGEMQR

Purpose:

 SGEMQR overwrites the general real M-by-N matrix C with

                      SIDE = 'L'     SIDE = 'R'
     TRANS = 'N':      Q * C          C * Q
     TRANS = 'T':      Q**T * C       C * Q**T

 where Q is a real orthogonal matrix defined as the product
 of blocked elementary reflectors computed by tall skinny
 QR factorization (SGEQR)

Parameters

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T.

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 C. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

A

          A is REAL array, dimension (LDA,K)
          Part of the data structure to represent Q as returned by SGEQR.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).

T

          T is REAL array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by SGEQR.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is REAL array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC

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

WORK

         (workspace) REAL array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK
          is issued by XERBLA.

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

 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.
  This version of SGEMQR will use either SLAMTSQR or SGEMQRT to
  multiply matrix Q by another matrix.
  Further Details in SLAMTSQR or SGEMQRT.

Definition at line 172 of file sgemqr.f.

ZGEMQR

Purpose:

 ZGEMQR overwrites the general real M-by-N matrix C with

                      SIDE = 'L'     SIDE = 'R'
      TRANS = 'N':      Q * C          C * Q
      TRANS = 'T':      Q**H * C       C * Q**H

 where Q is a complex unitary matrix defined as the product
 of blocked elementary reflectors computed by tall skinny
 QR factorization (ZGEQR)

Parameters

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q or Q**H from the Left;
          = 'R': apply Q or Q**H from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Conjugate transpose, apply Q**H.

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 C. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,K)
          Part of the data structure to represent Q as returned by ZGEQR.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).

T

          T is COMPLEX*16 array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by ZGEQR.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is COMPLEX*16 array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC

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

WORK

         (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK
          is issued by XERBLA.

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

 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.
  This version of ZGEMQR will use either ZLAMTSQR or ZGEMQRT to
  multiply matrix Q by another matrix.
  Further Details in ZLAMTSQR or ZGEMQRT.

Definition at line 172 of file zgemqr.f.