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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine ssbt21 | ( | character | UPLO, |
| integer | N, | ||
| integer | KA, | ||
| integer | KS, | ||
| real, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| real, dimension( * ) | D, | ||
| real, dimension( * ) | E, | ||
| real, dimension( ldu, * ) | U, | ||
| integer | LDU, | ||
| real, dimension( * ) | WORK, | ||
| real, dimension( 2 ) | RESULT | ||
| ) |
SSBT21
SSBT21 generally checks a decomposition of the form
A = U S U**T
where **T means transpose, A is symmetric banded, U is
orthogonal, and S is diagonal (if KS=0) or symmetric
tridiagonal (if KS=1).
Specifically:
RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
RESULT(2) = | I - U U**T | / ( n ulp ) | [in] | UPLO | UPLO is CHARACTER
If UPLO='U', the upper triangle of A and V will be used and
the (strictly) lower triangle will not be referenced.
If UPLO='L', the lower triangle of A and V will be used and
the (strictly) upper triangle will not be referenced. |
| [in] | N | N is INTEGER
The size of the matrix. If it is zero, SSBT21 does nothing.
It must be at least zero. |
| [in] | KA | KA is INTEGER
The bandwidth of the matrix A. It must be at least zero. If
it is larger than N-1, then max( 0, N-1 ) will be used. |
| [in] | KS | KS is INTEGER
The bandwidth of the matrix S. It may only be zero or one.
If zero, then S is diagonal, and E is not referenced. If
one, then S is symmetric tri-diagonal. |
| [in] | A | A is REAL array, dimension (LDA, N)
The original (unfactored) matrix. It is assumed to be
symmetric, and only the upper (UPLO='U') or only the lower
(UPLO='L') will be referenced. |
| [in] | LDA | LDA is INTEGER
The leading dimension of A. It must be at least 1
and at least min( KA, N-1 ). |
| [in] | D | D is REAL array, dimension (N)
The diagonal of the (symmetric tri-) diagonal matrix S. |
| [in] | E | E is REAL array, dimension (N-1)
The off-diagonal of the (symmetric tri-) diagonal matrix S.
E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
(3,2) element, etc.
Not referenced if KS=0. |
| [in] | U | U is REAL array, dimension (LDU, N)
The orthogonal matrix in the decomposition, expressed as a
dense matrix (i.e., not as a product of Householder
transformations, Givens transformations, etc.) |
| [in] | LDU | LDU is INTEGER
The leading dimension of U. LDU must be at least N and
at least 1. |
| [out] | WORK | WORK is REAL array, dimension (N**2+N) |
| [out] | RESULT | RESULT is REAL array, dimension (2)
The values computed by the two tests described above. The
values are currently limited to 1/ulp, to avoid overflow. |
1.9.4