.TH "TESTING/EIG/zhet21.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME TESTING/EIG/zhet21.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBzhet21\fP (itype, uplo, n, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, rwork, result)" .br .RI "\fBZHET21\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine zhet21 (integer itype, character uplo, integer n, integer kband, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, double precision, dimension( 2 ) result)" .PP \fBZHET21\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHET21 generally checks a decomposition of the form A = U S U**H where **H means conjugate transpose, A is hermitian, U is unitary, and S is diagonal (if KBAND=0) or (real) 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**H | / ( |A| n ulp ) and RESULT(2) = | I - U U**H | / ( n ulp ) If ITYPE=2, then: RESULT(1) = | A - V S V**H | / ( |A| n ulp ) If ITYPE=3, then: RESULT(1) = | I - U V**H | / ( 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)**H and each vector v(j) has its first j elements 0 and the remaining n-j elements stored in V(j+1:n,j)\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIITYPE\fP .PP .nf ITYPE is INTEGER Specifies the type of tests to be performed\&. 1: U expressed as a dense unitary matrix: RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and RESULT(2) = | I - U U**H | / ( n ulp ) 2: U expressed as a product V of Housholder transformations: RESULT(1) = | A - V S V**H | / ( |A| n ulp ) 3: U expressed both as a dense unitary matrix and as a product of Housholder transformations: RESULT(1) = | I - U V**H | / ( n ulp ) .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The size of the matrix\&. If it is zero, ZHET21 does nothing\&. It must be at least zero\&. .fi .PP .br \fIKBAND\fP .PP .nf 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\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA, N) The original (unfactored) matrix\&. It is assumed to be hermitian, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of A\&. It must be at least 1 and at least N\&. .fi .PP .br \fID\fP .PP .nf D is DOUBLE PRECISION array, dimension (N) The diagonal of the (symmetric tri-) diagonal matrix\&. .fi .PP .br \fIE\fP .PP .nf E is DOUBLE PRECISION 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\&. .fi .PP .br \fIU\fP .PP .nf U is COMPLEX*16 array, dimension (LDU, N) If ITYPE=1 or 3, this contains the unitary matrix in the decomposition, expressed as a dense matrix\&. If ITYPE=2, then it is not referenced\&. .fi .PP .br \fILDU\fP .PP .nf LDU is INTEGER The leading dimension of U\&. LDU must be at least N and at least 1\&. .fi .PP .br \fIV\fP .PP .nf V is COMPLEX*16 array, dimension (LDV, N) If ITYPE=2 or 3, the columns of this array contain the Householder vectors used to describe the unitary 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\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of V\&. LDV must be at least N and at least 1\&. .fi .PP .br \fITAU\fP .PP .nf TAU is COMPLEX*16 array, dimension (N) If ITYPE >= 2, then TAU(j) is the scalar factor of v(j) v(j)**H in the Householder transformation H(j) of the product U = H(1)\&.\&.\&.H(n-2) If ITYPE < 2, then TAU is not referenced\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N**2) .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION array, dimension (N) .fi .PP .br \fIRESULT\fP .PP .nf RESULT is 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 ITYPE=1\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB212\fP of file \fBzhet21\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.