Contents
cgghrd - reduce a pair of complex matrices (A,B) to general-
ized upper Hessenberg form using unitary transformations,
where A is a general matrix and B is upper triangular
SUBROUTINE CGGHRD(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ,
Z, LDZ, INFO)
CHARACTER * 1 COMPQ, COMPZ
COMPLEX A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)
INTEGER N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO
SUBROUTINE CGGHRD_64(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q,
LDQ, Z, LDZ, INFO)
CHARACTER * 1 COMPQ, COMPZ
COMPLEX A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)
INTEGER*8 N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO
F95 INTERFACE
SUBROUTINE GGHRD(COMPQ, COMPZ, [N], ILO, IHI, A, [LDA], B, [LDB], Q,
[LDQ], Z, [LDZ], [INFO])
CHARACTER(LEN=1) :: COMPQ, COMPZ
COMPLEX, DIMENSION(:,:) :: A, B, Q, Z
INTEGER :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO
SUBROUTINE GGHRD_64(COMPQ, COMPZ, [N], ILO, IHI, A, [LDA], B, [LDB],
Q, [LDQ], Z, [LDZ], [INFO])
CHARACTER(LEN=1) :: COMPQ, COMPZ
COMPLEX, DIMENSION(:,:) :: A, B, Q, Z
INTEGER(8) :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO
C INTERFACE
#include <sunperf.h>
void cgghrd(char compq, char compz, int n, int ilo, int ihi,
complex *a, int lda, complex *b, int ldb, complex
*q, int ldq, complex *z, int ldz, int *info);
void cgghrd_64(char compq, char compz, long n, long ilo,
long ihi, complex *a, long lda, complex *b, long
ldb, complex *q, long ldq, complex *z, long ldz,
long *info);
cgghrd reduces a pair of complex matrices (A,B) to general-
ized upper Hessenberg form using unitary transformations,
where A is a general matrix and B is upper triangular: Q' *
A * Z = H and Q' * B * Z = T, where H is upper Hessenberg, T
is upper triangular, and Q and Z are unitary, and ' means
conjugate transpose.
The unitary matrices Q and Z are determined as products of
Givens rotations. They may either be formed explicitly, or
they may be postmultiplied into input matrices Q1 and Z1, so
that
1 * A * Z1' = (Q1*Q) * H * (Z1*Z)'
COMPQ (input)
= 'N': do not compute Q;
= 'I': Q is initialized to the unit matrix, and
the unitary matrix Q is returned; = 'V': Q must
contain a unitary matrix Q1 on entry, and the pro-
duct Q1*Q is returned.
COMPZ (input)
= 'N': do not compute Q;
= 'I': Q is initialized to the unit matrix, and
the unitary matrix Q is returned; = 'V': Q must
contain a unitary matrix Q1 on entry, and the pro-
duct Q1*Q is returned.
N (input) The order of the matrices A and B. N >= 0.
ILO (input)
It is assumed that A is already upper triangular
in rows and columns 1:ILO-1 and IHI+1:N. ILO and
IHI are normally set by a previous call to CGGBAL;
otherwise they should be set to 1 and N respec-
tively. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and
IHI=0, if N=0.
IHI (input)
See description of ILO.
A (input/output)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first
subdiagonal of A are overwritten with the upper
Hessenberg matrix H, and the rest is set to zero.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
B (input/output)
On entry, the N-by-N upper triangular matrix B.
On exit, the upper triangular matrix T = Q' B Z.
The elements below the diagonal are set to zero.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,N).
Q (input/output)
If COMPQ='N': Q is not referenced.
If COMPQ='I': on entry, Q need not be set, and on
exit it contains the unitary matrix Q, where Q' is
the product of the Givens transformations which
are applied to A and B on the left. If COMPQ='V':
on entry, Q must contain a unitary matrix Q1, and
on exit this is overwritten by Q1*Q.
LDQ (input)
The leading dimension of the array Q. LDQ >= N if
COMPQ='V' or 'I'; LDQ >= 1 otherwise.
Z (input/output)
If COMPZ='N': Z is not referenced.
If COMPZ='I': on entry, Z need not be set, and on
exit it contains the unitary matrix Z, which is
the product of the Givens transformations which
are applied to A and B on the right. If
COMPZ='V': on entry, Z must contain a unitary
matrix Z1, and on exit this is overwritten by
Z1*Z.
LDZ (input)
The leading dimension of the array Z. LDZ >= N if
COMPZ='V' or 'I'; LDZ >= 1 otherwise.
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
This routine reduces A to Hessenberg and B to triangular
form by an unblocked reduction, as described in
_Matrix_Computations_, by Golub and van Loan (Johns Hopkins
Press).