table of contents
| lags2(3) | LAPACK | lags2(3) |
NAME¶
lags2 - lags2: 2x2 orthogonal factor, step in tgsja
SYNOPSIS¶
Functions¶
subroutine clags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu,
csv, snv, csq, snq)
CLAGS2 subroutine dlags2 (upper, a1, a2, a3, b1, b2, b3, csu,
snu, csv, snv, csq, snq)
DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies
them to matrices A and B such that the rows of the transformed A and B are
parallel. subroutine slags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu,
csv, snv, csq, snq)
SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies
them to matrices A and B such that the rows of the transformed A and B are
parallel. subroutine zlags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu,
csv, snv, csq, snq)
ZLAGS2
Detailed Description¶
Function Documentation¶
subroutine clags2 (logical upper, real a1, complex a2, real a3, real b1, complex b2, real b3, real csu, complex snu, real csv, complex snv, real csq, complex snq)¶
CLAGS2
Purpose:
CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
that if ( UPPER ) then
U**H *A*Q = U**H *( A1 A2 )*Q = ( x 0 )
( 0 A3 ) ( x x )
and
V**H*B*Q = V**H *( B1 B2 )*Q = ( x 0 )
( 0 B3 ) ( x x )
or if ( .NOT.UPPER ) then
U**H *A*Q = U**H *( A1 0 )*Q = ( x x )
( A2 A3 ) ( 0 x )
and
V**H *B*Q = V**H *( B1 0 )*Q = ( x x )
( B2 B3 ) ( 0 x )
where
U = ( CSU SNU ), V = ( CSV SNV ),
( -SNU**H CSU ) ( -SNV**H CSV )
Q = ( CSQ SNQ )
( -SNQ**H CSQ )
The rows of the transformed A and B are parallel. Moreover, if the
input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
of A is not zero. If the input matrices A and B are both not zero,
then the transformed (2,2) element of B is not zero, except when the
first rows of input A and B are parallel and the second rows are
zero.
Parameters
UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.
A1
A1 is REAL
A2
A2 is COMPLEX
A3
A3 is REAL
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.
B1
B1 is REAL
B2
B2 is COMPLEX
B3
B3 is REAL
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.
CSU
CSU is REAL
SNU
SNU is COMPLEX
The desired unitary matrix U.
CSV
CSV is REAL
SNV
SNV is COMPLEX
The desired unitary matrix V.
CSQ
CSQ is REAL
SNQ
SNQ is COMPLEX
The desired unitary matrix Q.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dlags2 (logical upper, double precision a1, double precision a2, double precision a3, double precision b1, double precision b2, double precision b3, double precision csu, double precision snu, double precision csv, double precision snv, double precision csq, double precision snq)¶
DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.
Purpose:
DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
that if ( UPPER ) then
U**T *A*Q = U**T *( A1 A2 )*Q = ( x 0 )
( 0 A3 ) ( x x )
and
V**T*B*Q = V**T *( B1 B2 )*Q = ( x 0 )
( 0 B3 ) ( x x )
or if ( .NOT.UPPER ) then
U**T *A*Q = U**T *( A1 0 )*Q = ( x x )
( A2 A3 ) ( 0 x )
and
V**T*B*Q = V**T*( B1 0 )*Q = ( x x )
( B2 B3 ) ( 0 x )
The rows of the transformed A and B are parallel, where
U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ )
( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ )
Z**T denotes the transpose of Z.
Parameters
UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.
A1
A1 is DOUBLE PRECISION
A2
A2 is DOUBLE PRECISION
A3
A3 is DOUBLE PRECISION
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.
B1
B1 is DOUBLE PRECISION
B2
B2 is DOUBLE PRECISION
B3
B3 is DOUBLE PRECISION
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.
CSU
CSU is DOUBLE PRECISION
SNU
SNU is DOUBLE PRECISION
The desired orthogonal matrix U.
CSV
CSV is DOUBLE PRECISION
SNV
SNV is DOUBLE PRECISION
The desired orthogonal matrix V.
CSQ
CSQ is DOUBLE PRECISION
SNQ
SNQ is DOUBLE PRECISION
The desired orthogonal matrix Q.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine slags2 (logical upper, real a1, real a2, real a3, real b1, real b2, real b3, real csu, real snu, real csv, real snv, real csq, real snq)¶
SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.
Purpose:
SLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
that if ( UPPER ) then
U**T *A*Q = U**T *( A1 A2 )*Q = ( x 0 )
( 0 A3 ) ( x x )
and
V**T*B*Q = V**T *( B1 B2 )*Q = ( x 0 )
( 0 B3 ) ( x x )
or if ( .NOT.UPPER ) then
U**T *A*Q = U**T *( A1 0 )*Q = ( x x )
( A2 A3 ) ( 0 x )
and
V**T*B*Q = V**T*( B1 0 )*Q = ( x x )
( B2 B3 ) ( 0 x )
The rows of the transformed A and B are parallel, where
U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ )
( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ )
Z**T denotes the transpose of Z.
Parameters
UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.
A1
A1 is REAL
A2
A2 is REAL
A3
A3 is REAL
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.
B1
B1 is REAL
B2
B2 is REAL
B3
B3 is REAL
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.
CSU
CSU is REAL
SNU
SNU is REAL
The desired orthogonal matrix U.
CSV
CSV is REAL
SNV
SNV is REAL
The desired orthogonal matrix V.
CSQ
CSQ is REAL
SNQ
SNQ is REAL
The desired orthogonal matrix Q.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zlags2 (logical upper, double precision a1, complex*16 a2, double precision a3, double precision b1, complex*16 b2, double precision b3, double precision csu, complex*16 snu, double precision csv, complex*16 snv, double precision csq, complex*16 snq)¶
ZLAGS2
Purpose:
ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
that if ( UPPER ) then
U**H *A*Q = U**H *( A1 A2 )*Q = ( x 0 )
( 0 A3 ) ( x x )
and
V**H*B*Q = V**H *( B1 B2 )*Q = ( x 0 )
( 0 B3 ) ( x x )
or if ( .NOT.UPPER ) then
U**H *A*Q = U**H *( A1 0 )*Q = ( x x )
( A2 A3 ) ( 0 x )
and
V**H *B*Q = V**H *( B1 0 )*Q = ( x x )
( B2 B3 ) ( 0 x )
where
U = ( CSU SNU ), V = ( CSV SNV ),
( -SNU**H CSU ) ( -SNV**H CSV )
Q = ( CSQ SNQ )
( -SNQ**H CSQ )
The rows of the transformed A and B are parallel. Moreover, if the
input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
of A is not zero. If the input matrices A and B are both not zero,
then the transformed (2,2) element of B is not zero, except when the
first rows of input A and B are parallel and the second rows are
zero.
Parameters
UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.
A1
A1 is DOUBLE PRECISION
A2
A2 is COMPLEX*16
A3
A3 is DOUBLE PRECISION
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.
B1
B1 is DOUBLE PRECISION
B2
B2 is COMPLEX*16
B3
B3 is DOUBLE PRECISION
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.
CSU
CSU is DOUBLE PRECISION
SNU
SNU is COMPLEX*16
The desired unitary matrix U.
CSV
CSV is DOUBLE PRECISION
SNV
SNV is COMPLEX*16
The desired unitary matrix V.
CSQ
CSQ is DOUBLE PRECISION
SNQ
SNQ is COMPLEX*16
The desired unitary matrix Q.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |