Man page - unm2l(3)

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Manual

unm2l

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cunm2l (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 dorm2l (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 sorm2l (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 zunm2l (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

unm2l - {un,or}m2l: step in unmql

SYNOPSIS

Functions

subroutine cunm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
CUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm).
subroutine dorm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).
subroutine sorm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).
subroutine zunm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm).

Detailed Description

Function Documentation

subroutine cunm2l (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)

CUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm).

Purpose:

CUNM2L 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(k) . . . H(2) H(1)

as returned by CGEQLF. 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
CGEQLF in the last 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 CGEQLF.

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 dorm2l (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)

DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose:

DORM2L 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(k) . . . H(2) H(1)

as returned by DGEQLF. 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
DGEQLF in the last 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 DGEQLF.

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 sorm2l (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)

SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose:

SORM2L 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(k) . . . H(2) H(1)

as returned by SGEQLF. 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
SGEQLF in the last 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 SGEQLF.

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 zunm2l (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)

ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm).

Purpose:

ZUNM2L 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(k) . . . H(2) H(1)

as returned by ZGEQLF. 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
ZGEQLF in the last 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 ZGEQLF.

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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