sgghrd - senberg form using orthogonal transformations, where A is a general matrix and B is upper triangular
SUBROUTINE SGGHRD(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) CHARACTER*1 COMPQ, COMPZ INTEGER N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO REAL A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*) SUBROUTINE SGGHRD_64(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) CHARACTER*1 COMPQ, COMPZ INTEGER*8 N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO REAL A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*) F95 INTERFACE SUBROUTINE GGHRD(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) CHARACTER(LEN=1) :: COMPQ, COMPZ INTEGER :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO REAL, DIMENSION(:,:) :: A, B, Q, Z SUBROUTINE GGHRD_64(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) CHARACTER(LEN=1) :: COMPQ, COMPZ INTEGER(8) :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO REAL, DIMENSION(:,:) :: A, B, Q, Z C INTERFACE #include <sunperf.h> void sgghrd(char compq, char compz, int n, int ilo, int ihi, float *a, int lda, float *b, int ldb, float *q, int ldq, float *z, int ldz, int *info); void sgghrd_64(char compq, char compz, long n, long ilo, long ihi, float *a, long lda, float *b, long ldb, float *q, long ldq, float *z, long ldz, long *info);
Oracle Solaris Studio Performance Library sgghrd(3P) NAME sgghrd - reduce a pair of real matrices (A,B) to generalized upper Hes- senberg form using orthogonal transformations, where A is a general matrix and B is upper triangular SYNOPSIS SUBROUTINE SGGHRD(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) CHARACTER*1 COMPQ, COMPZ INTEGER N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO REAL A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*) SUBROUTINE SGGHRD_64(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) CHARACTER*1 COMPQ, COMPZ INTEGER*8 N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO REAL A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*) F95 INTERFACE SUBROUTINE GGHRD(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) CHARACTER(LEN=1) :: COMPQ, COMPZ INTEGER :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO REAL, DIMENSION(:,:) :: A, B, Q, Z SUBROUTINE GGHRD_64(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO) CHARACTER(LEN=1) :: COMPQ, COMPZ INTEGER(8) :: N, ILO, IHI, LDA, LDB, LDQ, LDZ, INFO REAL, DIMENSION(:,:) :: A, B, Q, Z C INTERFACE #include <sunperf.h> void sgghrd(char compq, char compz, int n, int ilo, int ihi, float *a, int lda, float *b, int ldb, float *q, int ldq, float *z, int ldz, int *info); void sgghrd_64(char compq, char compz, long n, long ilo, long ihi, float *a, long lda, float *b, long ldb, float *q, long ldq, float *z, long ldz, long *info); PURPOSE sgghrd reduces a pair of real matrices (A,B) to generalized upper Hes- senberg form using orthogonal 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 orthogonal, and ' means transpose. The orthogonal matrices Q and Z are determined as products of Givens rotations. They may either be formed explicitly, or they may be post- multiplied into input matrices Q1 and Z1, so that 1 * A * Z1' = (Q1*Q) * H * (Z1*Z)' ARGUMENTS COMPQ (input) = 'N': do not compute Q; = 'I': Q is initialized to the unit matrix, and the orthogo- nal matrix Q is returned; = 'V': Q must contain an orthogonal matrix Q1 on entry, and the product Q1*Q is returned. COMPZ (input) = 'N': do not compute Z; = 'I': Z is initialized to the unit matrix, and the orthogo- nal matrix Z is returned; = 'V': Z must contain an orthogonal matrix Z1 on entry, and the product Z1*Z 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 SGGBAL; otherwise they should be set to 1 and N respectively. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. IHI (input) See the 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 over- written 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 orthogonal 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 an orthog- onal 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 orthogonal 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 an orthogonal 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 illegal value. FURTHER DETAILS 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.) 7 Nov 2015 sgghrd(3P)