tplqt - Man Page

subroutine ctplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
CTPLQT
subroutine dtplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
DTPLQT
subroutine stplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
STPLQT
subroutine ztplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
ZTPLQT

CTPLQT

Purpose:

 CTPLQT computes a blocked LQ factorization of a complex
 'triangular-pentagonal' matrix C, which is composed of a
 triangular block A and pentagonal block B, using the compact
 WY representation for Q.

Parameters

M

          M is INTEGER
          The number of rows of the matrix B, and the order of the
          triangular matrix A.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix B.
          N >= 0.

L

          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

MB

          MB is INTEGER
          The block size to be used in the blocked QR.  M >= MB >= 1.

A

          A is COMPLEX array, dimension (LDA,M)
          On entry, the lower triangular M-by-M matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the lower triangular matrix L.

LDA

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

B

          B is COMPLEX array, dimension (LDB,N)
          On entry, the pentagonal M-by-N matrix B.  The first N-L columns
          are rectangular, and the last L columns are lower trapezoidal.
          On exit, B contains the pentagonal matrix V.  See Further Details.

LDB

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

T

          T is COMPLEX array, dimension (LDT,N)
          The lower triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See Further Details.

LDT

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

WORK

          WORK is COMPLEX array, dimension (MB*M)

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 input matrix C is a M-by-(M+N) matrix

               C = [ A ] [ B ]


  where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
  matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
  upper trapezoidal matrix B2:
          [ B ] = [ B1 ] [ B2 ]
                   [ B1 ]  <- M-by-(N-L) rectangular
                   [ B2 ]  <-     M-by-L lower trapezoidal.

  The lower trapezoidal matrix B2 consists of the first L columns of a
  M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
  B is rectangular M-by-N; if M=L=N, B is lower triangular.

  The matrix W stores the elementary reflectors H(i) in the i-th row
  above the diagonal (of A) in the M-by-(M+N) input matrix C
            [ C ] = [ A ] [ B ]
                   [ A ]  <- lower triangular M-by-M
                   [ B ]  <- M-by-N pentagonal

  so that W can be represented as
            [ W ] = [ I ] [ V ]
                   [ I ]  <- identity, M-by-M
                   [ V ]  <- M-by-N, same form as B.

  Thus, all of information needed for W is contained on exit in B, which
  we call V above.  Note that V has the same form as B; that is,
            [ V ] = [ V1 ] [ V2 ]
                   [ V1 ] <- M-by-(N-L) rectangular
                   [ V2 ] <-     M-by-L lower trapezoidal.

  The rows of V represent the vectors which define the H(i)'s.

  The number of blocks is B = ceiling(M/MB), where each
  block is of order MB except for the last block, which is of order
  IB = M - (M-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-N matrix T as

               T = [T1 T2 ... TB].

Definition at line 172 of file ctplqt.f.

DTPLQT  

Purpose:

 DTPLQT computes a blocked LQ factorization of a real
 'triangular-pentagonal' matrix C, which is composed of a
 triangular block A and pentagonal block B, using the compact
 WY representation for Q.

Parameters

M

          M is INTEGER
          The number of rows of the matrix B, and the order of the
          triangular matrix A.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix B.
          N >= 0.

L

          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

MB

          MB is INTEGER
          The block size to be used in the blocked QR.  M >= MB >= 1.

A

          A is DOUBLE PRECISION array, dimension (LDA,M)
          On entry, the lower triangular M-by-M matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the lower triangular matrix L.

LDA

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

B

          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the pentagonal M-by-N matrix B.  The first N-L columns
          are rectangular, and the last L columns are lower trapezoidal.
          On exit, B contains the pentagonal matrix V.  See Further Details.

LDB

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

T

          T is DOUBLE PRECISION array, dimension (LDT,N)
          The lower triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See Further Details.

LDT

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

WORK

          WORK is DOUBLE PRECISION array, dimension (MB*M)

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 input matrix C is a M-by-(M+N) matrix

               C = [ A ] [ B ]


  where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
  matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
  upper trapezoidal matrix B2:
          [ B ] = [ B1 ] [ B2 ]
                   [ B1 ]  <- M-by-(N-L) rectangular
                   [ B2 ]  <-     M-by-L lower trapezoidal.

  The lower trapezoidal matrix B2 consists of the first L columns of a
  M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
  B is rectangular M-by-N; if M=L=N, B is lower triangular.

  The matrix W stores the elementary reflectors H(i) in the i-th row
  above the diagonal (of A) in the M-by-(M+N) input matrix C
            [ C ] = [ A ] [ B ]
                   [ A ]  <- lower triangular M-by-M
                   [ B ]  <- M-by-N pentagonal

  so that W can be represented as
            [ W ] = [ I ] [ V ]
                   [ I ]  <- identity, M-by-M
                   [ V ]  <- M-by-N, same form as B.

  Thus, all of information needed for W is contained on exit in B, which
  we call V above.  Note that V has the same form as B; that is,
            [ V ] = [ V1 ] [ V2 ]
                   [ V1 ] <- M-by-(N-L) rectangular
                   [ V2 ] <-     M-by-L lower trapezoidal.

  The rows of V represent the vectors which define the H(i)'s.

  The number of blocks is B = ceiling(M/MB), where each
  block is of order MB except for the last block, which is of order
  IB = M - (M-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-N matrix T as

               T = [T1 T2 ... TB].

Definition at line 187 of file dtplqt.f.

STPLQT  

Purpose:

 STPLQT computes a blocked LQ factorization of a real
 'triangular-pentagonal' matrix C, which is composed of a
 triangular block A and pentagonal block B, using the compact
 WY representation for Q.

Parameters

M

          M is INTEGER
          The number of rows of the matrix B, and the order of the
          triangular matrix A.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix B.
          N >= 0.

L

          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

MB

          MB is INTEGER
          The block size to be used in the blocked QR.  M >= MB >= 1.

A

          A is REAL array, dimension (LDA,M)
          On entry, the lower triangular M-by-M matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the lower triangular matrix L.

LDA

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

B

          B is REAL array, dimension (LDB,N)
          On entry, the pentagonal M-by-N matrix B.  The first N-L columns
          are rectangular, and the last L columns are lower trapezoidal.
          On exit, B contains the pentagonal matrix V.  See Further Details.

LDB

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

T

          T is REAL array, dimension (LDT,N)
          The lower triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See Further Details.

LDT

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

WORK

          WORK is REAL array, dimension (MB*M)

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 input matrix C is a M-by-(M+N) matrix

               C = [ A ] [ B ]


  where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
  matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
  upper trapezoidal matrix B2:
          [ B ] = [ B1 ] [ B2 ]
                   [ B1 ]  <- M-by-(N-L) rectangular
                   [ B2 ]  <-     M-by-L lower trapezoidal.

  The lower trapezoidal matrix B2 consists of the first L columns of a
  M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
  B is rectangular M-by-N; if M=L=N, B is lower triangular.

  The matrix W stores the elementary reflectors H(i) in the i-th row
  above the diagonal (of A) in the M-by-(M+N) input matrix C
            [ C ] = [ A ] [ B ]
                   [ A ]  <- lower triangular M-by-M
                   [ B ]  <- M-by-N pentagonal

  so that W can be represented as
            [ W ] = [ I ] [ V ]
                   [ I ]  <- identity, M-by-M
                   [ V ]  <- M-by-N, same form as B.

  Thus, all of information needed for W is contained on exit in B, which
  we call V above.  Note that V has the same form as B; that is,
            [ V ] = [ V1 ] [ V2 ]
                   [ V1 ] <- M-by-(N-L) rectangular
                   [ V2 ] <-     M-by-L lower trapezoidal.

  The rows of V represent the vectors which define the H(i)'s.

  The number of blocks is B = ceiling(M/MB), where each
  block is of order MB except for the last block, which is of order
  IB = M - (M-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-N matrix T as

               T = [T1 T2 ... TB].

Definition at line 187 of file stplqt.f.

ZTPLQT  

Purpose:

 ZTPLQT computes a blocked LQ factorization of a complex
 'triangular-pentagonal' matrix C, which is composed of a
 triangular block A and pentagonal block B, using the compact
 WY representation for Q.

Parameters

M

          M is INTEGER
          The number of rows of the matrix B, and the order of the
          triangular matrix A.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix B.
          N >= 0.

L

          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

MB

          MB is INTEGER
          The block size to be used in the blocked QR.  M >= MB >= 1.

A

          A is COMPLEX*16 array, dimension (LDA,M)
          On entry, the lower triangular M-by-M matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the lower triangular matrix L.

LDA

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

B

          B is COMPLEX*16 array, dimension (LDB,N)
          On entry, the pentagonal M-by-N matrix B.  The first N-L columns
          are rectangular, and the last L columns are lower trapezoidal.
          On exit, B contains the pentagonal matrix V.  See Further Details.

LDB

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

T

          T is COMPLEX*16 array, dimension (LDT,N)
          The lower triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See Further Details.

LDT

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

WORK

          WORK is COMPLEX*16 array, dimension (MB*M)

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 input matrix C is a M-by-(M+N) matrix

               C = [ A ] [ B ]


  where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
  matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
  upper trapezoidal matrix B2:
          [ B ] = [ B1 ] [ B2 ]
                   [ B1 ]  <- M-by-(N-L) rectangular
                   [ B2 ]  <-     M-by-L lower trapezoidal.

  The lower trapezoidal matrix B2 consists of the first L columns of a
  M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
  B is rectangular M-by-N; if M=L=N, B is lower triangular.

  The matrix W stores the elementary reflectors H(i) in the i-th row
  above the diagonal (of A) in the M-by-(M+N) input matrix C
            [ C ] = [ A ] [ B ]
                   [ A ]  <- lower triangular M-by-M
                   [ B ]  <- M-by-N pentagonal

  so that W can be represented as
            [ W ] = [ I ] [ V ]
                   [ I ]  <- identity, M-by-M
                   [ V ]  <- M-by-N, same form as B.

  Thus, all of information needed for W is contained on exit in B, which
  we call V above.  Note that V has the same form as B; that is,
            [ V ] = [ V1 ] [ V2 ]
                   [ V1 ] <- M-by-(N-L) rectangular
                   [ V2 ] <-     M-by-L lower trapezoidal.

  The rows of V represent the vectors which define the H(i)'s.

  The number of blocks is B = ceiling(M/MB), where each
  block is of order MB except for the last block, which is of order
  IB = M - (M-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-N matrix T as

               T = [T1 T2 ... TB].

Definition at line 187 of file ztplqt.f.