Man page - tpqrt2(3)

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Manual

tpqrt2

NAME
SYNOPSIS
Functions
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)
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)
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)
subroutine ztpqrt2 (integer m, integer n, integer l, complex*16, dimension(lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integerldb, complex*16, dimension( ldt, * ) t, integer ldt, integer info)
Author

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 ā€™triangular-pentagonalā€™ 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 ā€™triangular-pentagonalā€™ 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 ā€™triangular-pentagonalā€™ 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 ā€™triangular-pentagonalā€™ 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 ā€™triangular-pentagonalā€™ 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 ā€™triangular-pentagonalā€™
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)ā€™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 ā€™triangular-pentagonalā€™ 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 ā€™triangular-pentagonalā€™
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)ā€™s.
The (M+N)-by-(M+N) block reflector H is then given by

H = I - W * T * W**T

where WĖ†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 ā€™triangular-pentagonalā€™ 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 ā€™triangular-pentagonalā€™
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)ā€™s.
The (M+N)-by-(M+N) block reflector H is then given by

H = I - W * T * WĖ†H

where WĖ†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, integerldb, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZTPQRT2 computes a QR factorization of a real or complex ā€™triangular-pentagonalā€™ 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 ā€™triangular-pentagonalā€™
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)ā€™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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