tpqrt2(3)

NAME
tpqrt2 - tpqrt2: QR factor, level 2

SYNOPSIS

  Functions

subroutine ctpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
CTPQRT2 computes a QR factorization of a real or complex triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.
subroutine dtpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
DTPQRT2 computes a QR factorization of a real or complex triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.
subroutine stpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
STPQRT2 computes a QR factorization of a real or complex triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.
subroutine ztpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
ZTPQRT2 computes a QR factorization of a real or complex triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.

Detailed Description

Function Documentation

  subroutine ctpqrt2 (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)

CTPQRT2 computes a QR 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:

    !>
    !> CTPQRT2 computes a 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 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 upper trapezoidal part of B.
    !>          MIN(M,N) >= L >= 0.  See Further Details.
    !>

    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 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,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 (M+N)-by-(M+N) block reflector H is then given by
    !>
    !>               H = I - W * T * W**H
    !>
    !>  where W**H is the conjugate transpose of W and T is the upper triangular
    !>  factor of the block reflector.
    !>

  subroutine dtpqrt2 (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)

DTPQRT2 computes a QR 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:

    !>
    !> DTPQRT2 computes a 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 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 upper trapezoidal part of B.
    !>          MIN(M,N) >= L >= 0.  See Further Details.
    !>

    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 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,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 (M+N)-by-(M+N) block reflector H is then given by
    !>
    !>               H = I - W * T * W**T
    !>
    !>  where W^H is the conjugate transpose of W and T is the upper triangular
    !>  factor of the block reflector.
    !>

  subroutine stpqrt2 (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)

STPQRT2 computes a QR 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:

    !>
    !> STPQRT2 computes a 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 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 upper trapezoidal part of B.
    !>          MIN(M,N) >= L >= 0.  See Further Details.
    !>

    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 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,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 (M+N)-by-(M+N) block reflector H is then given by
    !>
    !>               H = I - W * T * W^H
    !>
    !>  where W^H is the conjugate transpose of W and T is the upper triangular
    !>  factor of the block reflector.
    !>

  subroutine ztpqrt2 (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)

ZTPQRT2 computes a QR 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:

    !>
    !> ZTPQRT2 computes a 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 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 upper trapezoidal part of B.
    !>          MIN(M,N) >= L >= 0.  See Further Details.
    !>

    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 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,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 (M+N)-by-(M+N) block reflector H is then given by
    !>
    !>               H = I - W * T * W**H
    !>
    !>  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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