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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine dsyt22 | ( | integer | ITYPE, |
character | UPLO, | ||
integer | N, | ||
integer | M, | ||
integer | KBAND, | ||
double precision, dimension( lda, * ) | A, | ||
integer | LDA, | ||
double precision, dimension( * ) | D, | ||
double precision, dimension( * ) | E, | ||
double precision, dimension( ldu, * ) | U, | ||
integer | LDU, | ||
double precision, dimension( ldv, * ) | V, | ||
integer | LDV, | ||
double precision, dimension( * ) | TAU, | ||
double precision, dimension( * ) | WORK, | ||
double precision, dimension( 2 ) | RESULT | ||
) |
DSYT22
DSYT22 generally checks a decomposition of the form A U = U S where A is symmetric, the columns of U are orthonormal, 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 the 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) = | U' A U - S | / ( |A| m ulp ) *andC> RESULT(2) = | I - U'U | / ( m ulp )
ITYPE INTEGER Specifies the type of tests to be performed. 1: U expressed as a dense orthogonal matrix: RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) UPLO CHARACTER If UPLO='U', the upper triangle of A will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A will be used and the (strictly) upper triangle will not be referenced. Not modified. N INTEGER The size of the matrix. If it is zero, DSYT22 does nothing. It must be at least zero. Not modified. M INTEGER The number of columns of U. If it is zero, DSYT22 does nothing. It must be at least zero. Not modified. KBAND 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. Not modified. A DOUBLE PRECISION 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. Not modified. LDA INTEGER The leading dimension of A. It must be at least 1 and at least N. Not modified. D DOUBLE PRECISION array, dimension (N) The diagonal of the (symmetric tri-) diagonal matrix. Not modified. E DOUBLE PRECISION array, dimension (N) The off-diagonal of the (symmetric tri-) diagonal matrix. E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. Not referenced if KBAND=0. Not modified. U DOUBLE PRECISION 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. Not modified. LDU INTEGER The leading dimension of U. LDU must be at least N and at least 1. Not modified. V DOUBLE PRECISION array, dimension (LDV, N) If ITYPE=2 or 3, the lower triangle of this array contains the Householder vectors used to describe the orthogonal matrix in the decomposition. If ITYPE=1, then it is not referenced. Not modified. LDV INTEGER The leading dimension of V. LDV must be at least N and at least 1. Not modified. TAU DOUBLE PRECISION array, dimension (N) If ITYPE >= 2, then TAU(j) is the scalar factor of v(j) v(j)' in the Householder transformation H(j) of the product U = H(1)...H(n-2) If ITYPE < 2, then TAU is not referenced. Not modified. WORK DOUBLE PRECISION array, dimension (2*N**2) Workspace. Modified. RESULT DOUBLE PRECISION 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 LDU is at least N. Modified.
Definition at line 157 of file dsyt22.f.