lamtsqr - Man Page

subroutine clamtsqr (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
CLAMTSQR
subroutine dlamtsqr (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
DLAMTSQR
subroutine slamtsqr (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
SLAMTSQR
subroutine zlamtsqr (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
ZLAMTSQR

CLAMTSQR

Purpose:

      CLAMTSQR overwrites the general complex M-by-N matrix C with


                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'C':      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 (CLATSQR)

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. M >= K >= 0;

MB

          MB is INTEGER
          The block size to be used in the blocked QR.
          MB > N. (must be the same as CLATSQR)

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          N >= NB >= 1.

A

          A is COMPLEX array, dimension (LDA,K)
          The i-th column must contain the vector which defines the
          blockedelementary reflector H(i), for i = 1,2,...,k, as
          returned by CLATSQR in the first k columns of
          its array argument A.

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
          ( N * Number of blocks(CEIL(M-K/MB-K)),
          The blocked 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.

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 SIDE = 'L', LWORK >= max(1,N)*NB;
          if SIDE = 'R', LWORK >= max(1,MB)*NB.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK 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:

 Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
 representing Q as a product of other unitary matrices
   Q = Q(1) * Q(2) * . . . * Q(k)
 where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
   Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
   Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
   . . .

 Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
 stored under the diagonal of rows 1:MB of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,1:N).
 For more information see Further Details in GEQRT.

 Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
 stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
 The last Q(k) may use fewer rows.
 For more information see Further Details in TPQRT.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2.2 of [1].

 [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
     SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 197 of file clamtsqr.f.

DLAMTSQR

Purpose:

      DLAMTSQR 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 (DLATSQR)

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. M >= K >= 0;

MB

          MB is INTEGER
          The block size to be used in the blocked QR.
          MB > N. (must be the same as DLATSQR)

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          N >= NB >= 1.

A

          A is DOUBLE PRECISION array, dimension (LDA,K)
          The i-th column must contain the vector which defines the
          blockedelementary reflector H(i), for i = 1,2,...,k, as
          returned by DLATSQR in the first k columns of
          its array argument A.

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
          ( N * Number of blocks(CEIL(M-K/MB-K)),
          The blocked 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.

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 SIDE = 'L', LWORK >= max(1,N)*NB;
          if SIDE = 'R', LWORK >= max(1,MB)*NB.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK 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:

 Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations,
 representing Q as a product of other orthogonal matrices
   Q = Q(1) * Q(2) * . . . * Q(k)
 where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
   Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
   Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
   . . .

 Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
 stored under the diagonal of rows 1:MB of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,1:N).
 For more information see Further Details in GEQRT.

 Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
 stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
 The last Q(k) may use fewer rows.
 For more information see Further Details in TPQRT.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2.2 of [1].

 [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
     SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 197 of file dlamtsqr.f.

SLAMTSQR

Purpose:

      SLAMTSQR 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 (SLATSQR)

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. M >= K >= 0;

MB

          MB is INTEGER
          The block size to be used in the blocked QR.
          MB > N. (must be the same as SLATSQR)

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          N >= NB >= 1.

A

          A is REAL array, dimension (LDA,K)
          The i-th column must contain the vector which defines the
          blockedelementary reflector H(i), for i = 1,2,...,k, as
          returned by SLATSQR in the first k columns of
          its array argument A.

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
          ( N * Number of blocks(CEIL(M-K/MB-K)),
          The blocked 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.

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 SIDE = 'L', LWORK >= max(1,N)*NB;
          if SIDE = 'R', LWORK >= max(1,MB)*NB.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK 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:

 Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations,
 representing Q as a product of other orthogonal matrices
   Q = Q(1) * Q(2) * . . . * Q(k)
 where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
   Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
   Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
   . . .

 Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
 stored under the diagonal of rows 1:MB of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,1:N).
 For more information see Further Details in GEQRT.

 Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
 stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
 The last Q(k) may use fewer rows.
 For more information see Further Details in TPQRT.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2.2 of [1].

 [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
     SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 197 of file slamtsqr.f.

ZLAMTSQR

Purpose:

      ZLAMTSQR overwrites the general complex M-by-N matrix C with


                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'C':      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 (ZLATSQR)

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. M >= K >= 0;

MB

          MB is INTEGER
          The block size to be used in the blocked QR.
          MB > N. (must be the same as ZLATSQR)

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          N >= NB >= 1.

A

          A is COMPLEX*16 array, dimension (LDA,K)
          The i-th column must contain the vector which defines the
          blockedelementary reflector H(i), for i = 1,2,...,k, as
          returned by ZLATSQR in the first k columns of
          its array argument A.

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
          ( N * Number of blocks(CEIL(M-K/MB-K)),
          The blocked 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.

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 SIDE = 'L', LWORK >= max(1,N)*NB;
          if SIDE = 'R', LWORK >= max(1,MB)*NB.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK 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:

 Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
 representing Q as a product of other unitary matrices
   Q = Q(1) * Q(2) * . . . * Q(k)
 where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
   Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
   Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
   . . .

 Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
 stored under the diagonal of rows 1:MB of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,1:N).
 For more information see Further Details in GEQRT.

 Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
 stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
 The last Q(k) may use fewer rows.
 For more information see Further Details in TPQRT.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2.2 of [1].

 [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
     SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 197 of file zlamtsqr.f.