sgehrd - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
SUBROUTINE SGEHRD( N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN, INFO) INTEGER N, ILO, IHI, LDA, LWORKIN, INFO REAL A(LDA,*), TAU(*), WORKIN(*)
SUBROUTINE SGEHRD_64( N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN, * INFO) INTEGER*8 N, ILO, IHI, LDA, LWORKIN, INFO REAL A(LDA,*), TAU(*), WORKIN(*)
SUBROUTINE GEHRD( [N], ILO, IHI, A, [LDA], TAU, [WORKIN], [LWORKIN], * [INFO]) INTEGER :: N, ILO, IHI, LDA, LWORKIN, INFO REAL, DIMENSION(:) :: TAU, WORKIN REAL, DIMENSION(:,:) :: A
SUBROUTINE GEHRD_64( [N], ILO, IHI, A, [LDA], TAU, [WORKIN], * [LWORKIN], [INFO]) INTEGER(8) :: N, ILO, IHI, LDA, LWORKIN, INFO REAL, DIMENSION(:) :: TAU, WORKIN REAL, DIMENSION(:,:) :: A
#include <sunperf.h>
void sgehrd(int n, int ilo, int ihi, float *a, int lda, float *tau, int *info);
void sgehrd_64(long n, long ilo, long ihi, float *a, long lda, float *tau, long *info);
sgehrd reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H .
WORKIN(1)
returns the optimal LWORKIN.
If LWORKIN = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORKIN array, returns this value as the first entry of the WORKIN array, and no error message related to LWORKIN is issued by XERBLA.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
The matrix Q is represented as a product of (ihi-ilo) elementary reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i)
has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i)
= 0, v(i+1)
= 1 and v(ihi+1:n)
= 0; v(i+2:ihi)
is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with n = 7, ilo = 2 and ihi = 6:
on entry, on exit,
( a a a a a a a ) ( a a h h h h a ) ( a a a a a a ) ( a h h h h a ) ( a a a a a a ) ( h h h h h h ) ( a a a a a a ) ( v2 h h h h h ) ( a a a a a a ) ( v2 v3 h h h h ) ( a a a a a a ) ( v2 v3 v4 h h h ) ( a ) ( a )
where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i).