Man page - unm2r(3)

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Manual

unm2r

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cunm2r (character side, character trans, integer m, integer n,integer k, complex, dimension( lda, * ) a, integer lda, complex,dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc,complex, dimension( * ) work, integer info)
subroutine dorm2r (character side, character trans, integer m, integer n,integer k, double precision, dimension( lda, * ) a, integer lda, doubleprecision, dimension( * ) tau, double precision, dimension( ldc, * ) c,integer ldc, double precision, dimension( * ) work, integer info)
subroutine sorm2r (character side, character trans, integer m, integer n,integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * )work, integer info)
subroutine zunm2r (character side, character trans, integer m, integer n,integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc,complex*16, dimension( * ) work, integer info)
Author

NAME

unm2r - {un,or}m2r: multiply by Q from geqrf, level 2

SYNOPSIS

Functions

subroutine cunm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).
subroutine dorm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).
subroutine sorm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).
subroutine zunm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).

Detailed Description

Function Documentation

subroutine cunm2r (character side, character trans, integer m, integer n,integer k, complex, dimension( lda, * ) a, integer lda, complex,dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc,complex, dimension( * ) work, integer info)

CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).

Purpose:

CUNM2R overwrites the general complex m-by-n matrix C with

Q * C if SIDE = ’L’ and TRANS = ’N’, or

Q**H* C if SIDE = ’L’ and TRANS = ’C’, or

C * Q if SIDE = ’R’ and TRANS = ’N’, or

C * Q**H if SIDE = ’R’ and TRANS = ’C’,

where Q is a complex unitary matrix defined as the product of k
elementary reflectors

Q = H(1) H(2) . . . H(k)

as returned by CGEQRF. Q is of order m if SIDE = ’L’ and of order n
if SIDE = ’R’.

Parameters

SIDE

SIDE is CHARACTER*1
= ’L’: apply Q or Q**H from the Left
= ’R’: apply Q or Q**H from the Right

TRANS

TRANS is CHARACTER*1
= ’N’: apply Q (No transpose)
= ’C’: apply Q**H (Conjugate transpose)

M

M is INTEGER
The number of rows of the matrix C. M >= 0.

N

N is INTEGER
The number of columns of the matrix C. N >= 0.

K

K is INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = ’L’, M >= K >= 0;
if SIDE = ’R’, N >= K >= 0.

A

A is COMPLEX array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CGEQRF in the first k columns of its array argument A.
A is modified by the routine but restored on exit.

LDA

LDA is INTEGER
The leading dimension of the array A.
If SIDE = ’L’, LDA >= max(1,M);
if SIDE = ’R’, LDA >= max(1,N).

TAU

TAU is COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQRF.

C

C is COMPLEX array, dimension (LDC,N)
On entry, the m-by-n matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC

LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK

WORK is COMPLEX array, dimension
(N) if SIDE = ’L’,
(M) if SIDE = ’R’

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.

subroutine dorm2r (character side, character trans, integer m, integer n,integer k, double precision, dimension( lda, * ) a, integer lda, doubleprecision, dimension( * ) tau, double precision, dimension( ldc, * ) c,integer ldc, double precision, dimension( * ) work, integer info)

DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).

Purpose:

DORM2R overwrites the general real m by n matrix C with

Q * C if SIDE = ’L’ and TRANS = ’N’, or

Q**T* C if SIDE = ’L’ and TRANS = ’T’, or

C * Q if SIDE = ’R’ and TRANS = ’N’, or

C * Q**T if SIDE = ’R’ and TRANS = ’T’,

where Q is a real orthogonal matrix defined as the product of k
elementary reflectors

Q = H(1) H(2) . . . H(k)

as returned by DGEQRF. Q is of order m if SIDE = ’L’ and of order n
if SIDE = ’R’.

Parameters

SIDE

SIDE is CHARACTER*1
= ’L’: apply Q or Q**T from the Left
= ’R’: apply Q or Q**T from the Right

TRANS

TRANS is CHARACTER*1
= ’N’: apply Q (No transpose)
= ’T’: apply Q**T (Transpose)

M

M is INTEGER
The number of rows of the matrix C. M >= 0.

N

N is INTEGER
The number of columns of the matrix C. N >= 0.

K

K is INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = ’L’, M >= K >= 0;
if SIDE = ’R’, N >= K >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGEQRF in the first k columns of its array argument A.

LDA

LDA is INTEGER
The leading dimension of the array A.
If SIDE = ’L’, LDA >= max(1,M);
if SIDE = ’R’, LDA >= max(1,N).

TAU

TAU is DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.

C

C is DOUBLE PRECISION array, dimension (LDC,N)
On entry, the m by n matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC

LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK

WORK is DOUBLE PRECISION array, dimension
(N) if SIDE = ’L’,
(M) if SIDE = ’R’

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.

subroutine sorm2r (character side, character trans, integer m, integer n,integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * )work, integer info)

SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).

Purpose:

SORM2R overwrites the general real m by n matrix C with

Q * C if SIDE = ’L’ and TRANS = ’N’, or

Q**T* C if SIDE = ’L’ and TRANS = ’T’, or

C * Q if SIDE = ’R’ and TRANS = ’N’, or

C * Q**T if SIDE = ’R’ and TRANS = ’T’,

where Q is a real orthogonal matrix defined as the product of k
elementary reflectors

Q = H(1) H(2) . . . H(k)

as returned by SGEQRF. Q is of order m if SIDE = ’L’ and of order n
if SIDE = ’R’.

Parameters

SIDE

SIDE is CHARACTER*1
= ’L’: apply Q or Q**T from the Left
= ’R’: apply Q or Q**T from the Right

TRANS

TRANS is CHARACTER*1
= ’N’: apply Q (No transpose)
= ’T’: apply Q**T (Transpose)

M

M is INTEGER
The number of rows of the matrix C. M >= 0.

N

N is INTEGER
The number of columns of the matrix C. N >= 0.

K

K is INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = ’L’, M >= K >= 0;
if SIDE = ’R’, N >= K >= 0.

A

A is REAL array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
SGEQRF in the first k columns of its array argument A.
A is modified by the routine but restored on exit.

LDA

LDA is INTEGER
The leading dimension of the array A.
If SIDE = ’L’, LDA >= max(1,M);
if SIDE = ’R’, LDA >= max(1,N).

TAU

TAU is REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQRF.

C

C is REAL array, dimension (LDC,N)
On entry, the m by n matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC

LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK

WORK is REAL array, dimension
(N) if SIDE = ’L’,
(M) if SIDE = ’R’

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.

subroutine zunm2r (character side, character trans, integer m, integer n,integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc,complex*16, dimension( * ) work, integer info)

ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).

Purpose:

ZUNM2R overwrites the general complex m-by-n matrix C with

Q * C if SIDE = ’L’ and TRANS = ’N’, or

Q**H* C if SIDE = ’L’ and TRANS = ’C’, or

C * Q if SIDE = ’R’ and TRANS = ’N’, or

C * Q**H if SIDE = ’R’ and TRANS = ’C’,

where Q is a complex unitary matrix defined as the product of k
elementary reflectors

Q = H(1) H(2) . . . H(k)

as returned by ZGEQRF. Q is of order m if SIDE = ’L’ and of order n
if SIDE = ’R’.

Parameters

SIDE

SIDE is CHARACTER*1
= ’L’: apply Q or Q**H from the Left
= ’R’: apply Q or Q**H from the Right

TRANS

TRANS is CHARACTER*1
= ’N’: apply Q (No transpose)
= ’C’: apply Q**H (Conjugate transpose)

M

M is INTEGER
The number of rows of the matrix C. M >= 0.

N

N is INTEGER
The number of columns of the matrix C. N >= 0.

K

K is INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = ’L’, M >= K >= 0;
if SIDE = ’R’, N >= K >= 0.

A

A is COMPLEX*16 array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGEQRF in the first k columns of its array argument A.
A is modified by the routine but restored on exit.

LDA

LDA is INTEGER
The leading dimension of the array A.
If SIDE = ’L’, LDA >= max(1,M);
if SIDE = ’R’, LDA >= max(1,N).

TAU

TAU is COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.

C

C is COMPLEX*16 array, dimension (LDC,N)
On entry, the m-by-n matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC

LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK

WORK is COMPLEX*16 array, dimension
(N) if SIDE = ’L’,
(M) if SIDE = ’R’

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.

Author

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