Man page - tpqrt(3)

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Manual

tpqrt

NAME
SYNOPSIS
Functions
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)
subroutine dtpqrt (integer m, integer n, integer l, integer nb, doubleprecision, 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)
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)
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)
Author

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
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 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)ā€™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) Tā€™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, doubleprecision, 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
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 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)ā€™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) Tā€™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
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 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)ā€™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) Tā€™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
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 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)ā€™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) Tā€™s are stored in the NB-by-N matrix T as

T = [T1 T2 ... TB].

Author

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