tpqrt(3)

NAME
tpqrt - tpqrt: QR factor

SYNOPSIS

  Functions

subroutine ctpqrt (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
CTPQRT
subroutine dtpqrt (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
DTPQRT
subroutine stpqrt (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
STPQRT
subroutine ztpqrt (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
ZTPQRT

Detailed Description

Function Documentation

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

CTPQRT

Purpose:

    !>
    !> CTPQRT computes a blocked QR 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.
    !>          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 upper trapezoidal part of B.
    !>          MIN(M,N) >= L >= 0.  See Further Details.
    !>

    NB

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the upper triangular N-by-N matrix A.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the upper triangular matrix R.
    !>

    LDA

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

    B

    !>          B is COMPLEX array, dimension (LDB,N)
    !>          On entry, the pentagonal M-by-N matrix B.  The first M-L rows
    !>          are rectangular, and the last L rows are upper 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 upper 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 >= NB.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (NB*N)
    !>

    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 (N+M)-by-N matrix
    !>
    !>               C = [ A ]
    !>                   [ B ]
    !>
    !>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
    !>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
    !>  upper trapezoidal matrix B2:
    !>
    !>               B = [ B1 ]  <- (M-L)-by-N rectangular
    !>                   [ B2 ]  <-     L-by-N upper trapezoidal.
    !>
    !>  The upper trapezoidal matrix B2 consists of the first L rows of a
    !>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
    !>  B is rectangular M-by-N; if M=L=N, B is upper triangular.
    !>
    !>  The matrix W stores the elementary reflectors H(i) in the i-th column
    !>  below the diagonal (of A) in the (N+M)-by-N input matrix C
    !>
    !>               C = [ A ]  <- upper triangular N-by-N
    !>                   [ B ]  <- M-by-N pentagonal
    !>
    !>  so that W can be represented as
    !>
    !>               W = [ I ]  <- identity, N-by-N
    !>                   [ 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 ] <- (M-L)-by-N rectangular
    !>                   [ V2 ] <-     L-by-N upper trapezoidal.
    !>
    !>  The columns of V represent the vectors which define the H(i)'s.
    !>
    !>  The number of blocks is B = ceiling(N/NB), where each
    !>  block is of order NB except for the last block, which is of order
    !>  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
    !>  for the last block) T's are stored in the NB-by-N matrix T as
    !>
    !>               T = [T1 T2 ... TB].
    !>

  subroutine dtpqrt (integer m, integer n, integer l, integer nb, 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)

DTPQRT

Purpose:

    !>
    !> DTPQRT computes a blocked QR 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.
    !>          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 upper trapezoidal part of B.
    !>          MIN(M,N) >= L >= 0.  See Further Details.
    !>

    NB

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

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the upper triangular N-by-N matrix A.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the upper triangular matrix R.
    !>

    LDA

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

    B

    !>          B is DOUBLE PRECISION array, dimension (LDB,N)
    !>          On entry, the pentagonal M-by-N matrix B.  The first M-L rows
    !>          are rectangular, and the last L rows are upper 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 upper 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 >= NB.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (NB*N)
    !>

    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 (N+M)-by-N matrix
    !>
    !>               C = [ A ]
    !>                   [ B ]
    !>
    !>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
    !>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
    !>  upper trapezoidal matrix B2:
    !>
    !>               B = [ B1 ]  <- (M-L)-by-N rectangular
    !>                   [ B2 ]  <-     L-by-N upper trapezoidal.
    !>
    !>  The upper trapezoidal matrix B2 consists of the first L rows of a
    !>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
    !>  B is rectangular M-by-N; if M=L=N, B is upper triangular.
    !>
    !>  The matrix W stores the elementary reflectors H(i) in the i-th column
    !>  below the diagonal (of A) in the (N+M)-by-N input matrix C
    !>
    !>               C = [ A ]  <- upper triangular N-by-N
    !>                   [ B ]  <- M-by-N pentagonal
    !>
    !>  so that W can be represented as
    !>
    !>               W = [ I ]  <- identity, N-by-N
    !>                   [ 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 ] <- (M-L)-by-N rectangular
    !>                   [ V2 ] <-     L-by-N upper trapezoidal.
    !>
    !>  The columns of V represent the vectors which define the H(i)'s.
    !>
    !>  The number of blocks is B = ceiling(N/NB), where each
    !>  block is of order NB except for the last block, which is of order
    !>  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
    !>  for the last block) T's are stored in the NB-by-N matrix T as
    !>
    !>               T = [T1 T2 ... TB].
    !>

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

STPQRT

Purpose:

    !>
    !> STPQRT computes a blocked QR 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.
    !>          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 upper trapezoidal part of B.
    !>          MIN(M,N) >= L >= 0.  See Further Details.
    !>

    NB

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

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the upper triangular N-by-N matrix A.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the upper triangular matrix R.
    !>

    LDA

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

    B

    !>          B is REAL array, dimension (LDB,N)
    !>          On entry, the pentagonal M-by-N matrix B.  The first M-L rows
    !>          are rectangular, and the last L rows are upper 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 upper 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 >= NB.
    !>

    WORK

    !>          WORK is REAL array, dimension (NB*N)
    !>

    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 (N+M)-by-N matrix
    !>
    !>               C = [ A ]
    !>                   [ B ]
    !>
    !>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
    !>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
    !>  upper trapezoidal matrix B2:
    !>
    !>               B = [ B1 ]  <- (M-L)-by-N rectangular
    !>                   [ B2 ]  <-     L-by-N upper trapezoidal.
    !>
    !>  The upper trapezoidal matrix B2 consists of the first L rows of a
    !>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
    !>  B is rectangular M-by-N; if M=L=N, B is upper triangular.
    !>
    !>  The matrix W stores the elementary reflectors H(i) in the i-th column
    !>  below the diagonal (of A) in the (N+M)-by-N input matrix C
    !>
    !>               C = [ A ]  <- upper triangular N-by-N
    !>                   [ B ]  <- M-by-N pentagonal
    !>
    !>  so that W can be represented as
    !>
    !>               W = [ I ]  <- identity, N-by-N
    !>                   [ 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 ] <- (M-L)-by-N rectangular
    !>                   [ V2 ] <-     L-by-N upper trapezoidal.
    !>
    !>  The columns of V represent the vectors which define the H(i)'s.
    !>
    !>  The number of blocks is B = ceiling(N/NB), where each
    !>  block is of order NB except for the last block, which is of order
    !>  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
    !>  for the last block) T's are stored in the NB-by-N matrix T as
    !>
    !>               T = [T1 T2 ... TB].
    !>

  subroutine ztpqrt (integer m, integer n, integer l, integer nb, 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)

ZTPQRT

Purpose:

    !>
    !> ZTPQRT computes a blocked QR 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.
    !>          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 upper trapezoidal part of B.
    !>          MIN(M,N) >= L >= 0.  See Further Details.
    !>

    NB

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the upper triangular N-by-N matrix A.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the upper triangular matrix R.
    !>

    LDA

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

    B

    !>          B is COMPLEX*16 array, dimension (LDB,N)
    !>          On entry, the pentagonal M-by-N matrix B.  The first M-L rows
    !>          are rectangular, and the last L rows are upper 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 upper 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 >= NB.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (NB*N)
    !>

    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 (N+M)-by-N matrix
    !>
    !>               C = [ A ]
    !>                   [ B ]
    !>
    !>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
    !>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
    !>  upper trapezoidal matrix B2:
    !>
    !>               B = [ B1 ]  <- (M-L)-by-N rectangular
    !>                   [ B2 ]  <-     L-by-N upper trapezoidal.
    !>
    !>  The upper trapezoidal matrix B2 consists of the first L rows of a
    !>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
    !>  B is rectangular M-by-N; if M=L=N, B is upper triangular.
    !>
    !>  The matrix W stores the elementary reflectors H(i) in the i-th column
    !>  below the diagonal (of A) in the (N+M)-by-N input matrix C
    !>
    !>               C = [ A ]  <- upper triangular N-by-N
    !>                   [ B ]  <- M-by-N pentagonal
    !>
    !>  so that W can be represented as
    !>
    !>               W = [ I ]  <- identity, N-by-N
    !>                   [ 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 ] <- (M-L)-by-N rectangular
    !>                   [ V2 ] <-     L-by-N upper trapezoidal.
    !>
    !>  The columns of V represent the vectors which define the H(i)'s.
    !>
    !>  The number of blocks is B = ceiling(N/NB), where each
    !>  block is of order NB except for the last block, which is of order
    !>  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
    !>  for the last block) T's are stored in the NB-by-N matrix T as
    !>
    !>               T = [T1 T2 ... TB].
    !>

Author

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