tplqt2(3)

NAME
tplqt2 - tplqt2: QR factor, level 2

SYNOPSIS

  Functions

subroutine ctplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
CTPLQT2
subroutine dtplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
DTPLQT2 computes a LQ factorization of a real or complex triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.
subroutine stplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
STPLQT2 computes a LQ factorization of a real or complex triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.
subroutine ztplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
ZTPLQT2 computes a LQ factorization of a real or complex triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.

Detailed Description

Function Documentation

  subroutine ctplqt2 (integer m, integer n, integer l, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldt, * ) t, integer ldt, integer info)

CTPLQT2

Purpose:

    !>
    !> CTPLQT2 computes a LQ a 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 total number of rows of the matrix B.
    !>          M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix B, and the order of
    !>          the triangular matrix A.
    !>          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.
    !>

    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,M)
    !>          The N-by-N upper triangular factor T of the block reflector.
    !>          See Further Details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= max(1,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 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
    !>  N-by-N 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,
    !>
    !>               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by
    !>
    !>               H = I - W**T * T * W
    !>
    !>  where W^H is the conjugate transpose of W and T is the upper triangular
    !>  factor of the block reflector.
    !>

  subroutine dtplqt2 (integer m, integer n, integer l, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DTPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Purpose:

    !>
    !> DTPLQT2 computes a LQ a 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 total number of rows of the matrix B.
    !>          M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix B, and the order of
    !>          the triangular matrix A.
    !>          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.
    !>

    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,M)
    !>          The N-by-N upper triangular factor T of the block reflector.
    !>          See Further Details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= max(1,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 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
    !>  N-by-N 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,
    !>
    !>               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by
    !>
    !>               H = I - W**T * T * W
    !>
    !>  where W^H is the conjugate transpose of W and T is the upper triangular
    !>  factor of the block reflector.
    !>

  subroutine stplqt2 (integer m, integer n, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldt, * ) t, integer ldt, integer info)

STPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Purpose:

    !>
    !> STPLQT2 computes a LQ a 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 total number of rows of the matrix B.
    !>          M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix B, and the order of
    !>          the triangular matrix A.
    !>          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.
    !>

    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,M)
    !>          The N-by-N upper triangular factor T of the block reflector.
    !>          See Further Details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= max(1,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 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
    !>  N-by-N 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,
    !>
    !>               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by
    !>
    !>               H = I - W**T * T * W
    !>
    !>  where W^H is the conjugate transpose of W and T is the upper triangular
    !>  factor of the block reflector.
    !>

  subroutine ztplqt2 (integer m, integer n, integer l, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZTPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Purpose:

    !>
    !> ZTPLQT2 computes a LQ a 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 total number of rows of the matrix B.
    !>          M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix B, and the order of
    !>          the triangular matrix A.
    !>          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.
    !>

    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,M)
    !>          The N-by-N upper triangular factor T of the block reflector.
    !>          See Further Details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= max(1,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 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
    !>  N-by-N 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,
    !>
    !>               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by
    !>
    !>               H = I - W**T * T * W
    !>
    !>  where W^H is the conjugate transpose of W and T is the upper triangular
    !>  factor of the block reflector.
    !>

Author

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