tplqt(3)

NAME
tplqt - tplqt: QR factor

SYNOPSIS

  Functions

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

Detailed Description

Function Documentation

  subroutine ctplqt (integer m, integer n, integer l, integer mb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer info)

CTPLQT

Purpose:

    !>
    !> CTPLQT computes a blocked LQ factorization of a complex
    !>  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].
    !>

  subroutine dtplqt (integer m, integer n, integer l, integer mb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info)

DTPLQT

Purpose:

    !>
    !> DTPLQT computes a blocked LQ factorization of a real
    !>  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].
    !>

  subroutine stplqt (integer m, integer n, integer l, integer mb, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)

STPLQT

Purpose:

    !>
    !> STPLQT computes a blocked LQ factorization of a real
    !>  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].
    !>

  subroutine ztplqt (integer m, integer n, integer l, integer mb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)

ZTPLQT

Purpose:

    !>
    !> ZTPLQT computes a blocked LQ factorization of a complex
    !>  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].
    !>

Author

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