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tpqrt2(3) Library Functions Manual 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, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. 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, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. 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, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. 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, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

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.
!>

Definition at line 172 of file ctpqrt2.f.

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.
!>

Definition at line 172 of file dtpqrt2.f.

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.
!>

Definition at line 172 of file stpqrt2.f.

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.
!>

Definition at line 172 of file ztpqrt2.f.

Author

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