Man page - unm22(3)

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Manual

unm22

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cunm22 (character side, character trans, integer m, integer n,integer n1, integer n2, complex, dimension( ldq, * ) q, integer ldq,complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * )work, integer lwork, integer info)
subroutine dorm22 (character side, character trans, integer m, integer n,integer n1, integer n2, double precision, dimension( ldq, * ) q,integer ldq, double precision, dimension( ldc, * ) c, integer ldc,double precision, dimension( * ) work, integer lwork, integer info)
subroutine sorm22 (character side, character trans, integer m, integer n,integer n1, integer n2, real, dimension( ldq, * ) q, integer ldq, real,dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integerlwork, integer info)
subroutine zunm22 (character side, character trans, integer m, integer n,integer n1, integer n2, complex*16, dimension( ldq, * ) q, integer ldq,complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension(* ) work, integer lwork, integer info)
Author

NAME

unm22 - {un,or}m22: multiply by banded Q, step in gghd3

SYNOPSIS

Functions

subroutine cunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
CUNM22 multiplies a general matrix by a banded unitary matrix.
subroutine dorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
DORM22 multiplies a general matrix by a banded orthogonal matrix.
subroutine sorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
SORM22 multiplies a general matrix by a banded orthogonal matrix.
subroutine zunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
ZUNM22 multiplies a general matrix by a banded unitary matrix.

Detailed Description

Function Documentation

subroutine cunm22 (character side, character trans, integer m, integer n,integer n1, integer n2, complex, dimension( ldq, * ) q, integer ldq,complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * )work, integer lwork, integer info)

CUNM22 multiplies a general matrix by a banded unitary matrix.

Purpose

CUNM22 overwrites the general complex M-by-N matrix C with

SIDE = ’L’ SIDE = ’R’
TRANS = ’N’: Q * C C * Q
TRANS = ’C’: Q**H * C C * Q**H

where Q is a complex unitary matrix of order NQ, with NQ = M if
SIDE = ’L’ and NQ = N if SIDE = ’R’.
The unitary matrix Q processes a 2-by-2 block structure

[ Q11 Q12 ]
Q = [ ]
[ Q21 Q22 ],

where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
N2-by-N2 upper triangular matrix.

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.

N1
N2

N1 is INTEGER
N2 is INTEGER
The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
The following requirement must be satisfied:
N1 + N2 = M if SIDE = ’L’ and N1 + N2 = N if SIDE = ’R’.

Q

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

LDQ

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

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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ’L’, LWORK >= max(1,N);
if SIDE = ’R’, LWORK >= max(1,M).
For optimum performance LWORK >= M*N.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

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 dorm22 (character side, character trans, integer m, integer n,integer n1, integer n2, double precision, dimension( ldq, * ) q,integer ldq, double precision, dimension( ldc, * ) c, integer ldc,double precision, dimension( * ) work, integer lwork, integer info)

DORM22 multiplies a general matrix by a banded orthogonal matrix.

Purpose

DORM22 overwrites the general real M-by-N matrix C with

SIDE = ’L’ SIDE = ’R’
TRANS = ’N’: Q * C C * Q
TRANS = ’T’: Q**T * C C * Q**T

where Q is a real orthogonal matrix of order NQ, with NQ = M if
SIDE = ’L’ and NQ = N if SIDE = ’R’.
The orthogonal matrix Q processes a 2-by-2 block structure

[ Q11 Q12 ]
Q = [ ]
[ Q21 Q22 ],

where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
N2-by-N2 upper triangular matrix.

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);
= ’C’: apply Q**T (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.

N1
N2

N1 is INTEGER
N2 is INTEGER
The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
The following requirement must be satisfied:
N1 + N2 = M if SIDE = ’L’ and N1 + N2 = N if SIDE = ’R’.

Q

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

LDQ

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

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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ’L’, LWORK >= max(1,N);
if SIDE = ’R’, LWORK >= max(1,M).
For optimum performance LWORK >= M*N.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

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 sorm22 (character side, character trans, integer m, integer n,integer n1, integer n2, real, dimension( ldq, * ) q, integer ldq, real,dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integerlwork, integer info)

SORM22 multiplies a general matrix by a banded orthogonal matrix.

Purpose

SORM22 overwrites the general real M-by-N matrix C with

SIDE = ’L’ SIDE = ’R’
TRANS = ’N’: Q * C C * Q
TRANS = ’T’: Q**T * C C * Q**T

where Q is a real orthogonal matrix of order NQ, with NQ = M if
SIDE = ’L’ and NQ = N if SIDE = ’R’.
The orthogonal matrix Q processes a 2-by-2 block structure

[ Q11 Q12 ]
Q = [ ]
[ Q21 Q22 ],

where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
N2-by-N2 upper triangular matrix.

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);
= ’C’: apply Q**T (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.

N1
N2

N1 is INTEGER
N2 is INTEGER
The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
The following requirement must be satisfied:
N1 + N2 = M if SIDE = ’L’ and N1 + N2 = N if SIDE = ’R’.

Q

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

LDQ

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

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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ’L’, LWORK >= max(1,N);
if SIDE = ’R’, LWORK >= max(1,M).
For optimum performance LWORK >= M*N.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

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 zunm22 (character side, character trans, integer m, integer n,integer n1, integer n2, complex*16, dimension( ldq, * ) q, integer ldq,complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension(* ) work, integer lwork, integer info)

ZUNM22 multiplies a general matrix by a banded unitary matrix.

Purpose

ZUNM22 overwrites the general complex M-by-N matrix C with

SIDE = ’L’ SIDE = ’R’
TRANS = ’N’: Q * C C * Q
TRANS = ’C’: Q**H * C C * Q**H

where Q is a complex unitary matrix of order NQ, with NQ = M if
SIDE = ’L’ and NQ = N if SIDE = ’R’.
The unitary matrix Q processes a 2-by-2 block structure

[ Q11 Q12 ]
Q = [ ]
[ Q21 Q22 ],

where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
N2-by-N2 upper triangular matrix.

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.

N1
N2

N1 is INTEGER
N2 is INTEGER
The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
The following requirement must be satisfied:
N1 + N2 = M if SIDE = ’L’ and N1 + N2 = N if SIDE = ’R’.

Q

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

LDQ

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

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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ’L’, LWORK >= max(1,N);
if SIDE = ’R’, LWORK >= max(1,M).
For optimum performance LWORK >= M*N.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

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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