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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine ssyt21 | ( | integer | itype, |
| character | uplo, | ||
| integer | n, | ||
| integer | kband, | ||
| real, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| real, dimension( * ) | d, | ||
| real, dimension( * ) | e, | ||
| real, dimension( ldu, * ) | u, | ||
| integer | ldu, | ||
| real, dimension( ldv, * ) | v, | ||
| integer | ldv, | ||
| real, dimension( * ) | tau, | ||
| real, dimension( * ) | work, | ||
| real, dimension( 2 ) | result | ||
| ) |
SSYT21
SSYT21 generally checks a decomposition of the form
A = U S U**T
where **T means transpose, A is symmetric, U is orthogonal, and S is
diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
If ITYPE=1, then U is represented as a dense matrix; otherwise U is
expressed as a product of Householder transformations, whose vectors
are stored in the array "V" and whose scaling constants are in "TAU".
We shall use the letter "V" to refer to the product of Householder
transformations (which should be equal to U).
Specifically, if ITYPE=1, then:
RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
RESULT(2) = | I - U U**T | / ( n ulp )
If ITYPE=2, then:
RESULT(1) = | A - V S V**T | / ( |A| n ulp )
If ITYPE=3, then:
RESULT(1) = | I - V U**T | / ( n ulp )
For ITYPE > 1, the transformation U is expressed as a product
V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)**T and each
vector v(j) has its first j elements 0 and the remaining n-j elements
stored in V(j+1:n,j). | [in] | ITYPE | ITYPE is INTEGER
Specifies the type of tests to be performed.
1: U expressed as a dense orthogonal matrix:
RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
RESULT(2) = | I - U U**T | / ( n ulp )
2: U expressed as a product V of Housholder transformations:
RESULT(1) = | A - V S V**T | / ( |A| n ulp )
3: U expressed both as a dense orthogonal matrix and
as a product of Housholder transformations:
RESULT(1) = | I - V 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, SSYT21 does nothing.
It must be at least zero. |
| [in] | KBAND | KBAND is INTEGER
The bandwidth of the matrix. 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 N. |
| [in] | D | D is REAL array, dimension (N)
The diagonal of the (symmetric tri-) diagonal matrix. |
| [in] | E | E is REAL array, dimension (N-1)
The off-diagonal of the (symmetric tri-) diagonal matrix.
E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
(3,2) element, etc.
Not referenced if KBAND=0. |
| [in] | U | U is REAL array, dimension (LDU, N)
If ITYPE=1 or 3, this contains the orthogonal matrix in
the decomposition, expressed as a dense matrix. If ITYPE=2,
then it is not referenced. |
| [in] | LDU | LDU is INTEGER
The leading dimension of U. LDU must be at least N and
at least 1. |
| [in] | V | V is REAL array, dimension (LDV, N)
If ITYPE=2 or 3, the columns of this array contain the
Householder vectors used to describe the orthogonal matrix
in the decomposition. If UPLO='L', then the vectors are in
the lower triangle, if UPLO='U', then in the upper
triangle.
*NOTE* If ITYPE=2 or 3, V is modified and restored. The
subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')
is set to one, and later reset to its original value, during
the course of the calculation.
If ITYPE=1, then it is neither referenced nor modified. |
| [in] | LDV | LDV is INTEGER
The leading dimension of V. LDV must be at least N and
at least 1. |
| [in] | TAU | TAU is REAL array, dimension (N)
If ITYPE >= 2, then TAU(j) is the scalar factor of
v(j) v(j)**T in the Householder transformation H(j) of
the product U = H(1)...H(n-2)
If ITYPE < 2, then TAU is not referenced. |
| [out] | WORK | WORK is REAL array, dimension (2*N**2) |
| [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.
RESULT(1) is always modified. RESULT(2) is modified only
if ITYPE=1. |
Definition at line 205 of file ssyt21.f.
1.9.7