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LAPACK
3.7.0
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' where ' 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' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( 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. |
Definition at line 148 of file ssbt21.f.