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clatrd.f(3) LAPACK clatrd.f(3)clatrd.fNAME-Functions/Subroutines subroutine clatrd (UPLO, N, NB, A, LDA, E, TAU, W, LDW) CLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an unitary similarity transformation.SYNOPSISFunction/Subroutine Documentation subroutine clatrd (characterUPLO, integerN, integerNB, complex, dimension( lda, * )A, integerLDA, real, dimension( * )E, complex, dimension( * )TAU, complex, dimension( ldw, * )W, integerLDW) CLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an unitary similarity transformation. Purpose: CLATRD reduces NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q**H * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A. If UPLO = 'U', CLATRD reduces the last NB rows and columns of a matrix, of which the upper triangle is supplied; if UPLO = 'L', CLATRD reduces the first NB rows and columns of a matrix, of which the lower triangle is supplied. This is an auxiliary routine called by CHETRD. Parameters: UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. NB NB is INTEGER The number of rows and columns to be reduced. A A is COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit: if UPLO = 'U', the last NB columns have been reduced to tridiagonal form, with the diagonal elements overwriting the diagonal elements of A; the elements above the diagonal with the array TAU, represent the unitary matrix Q as a product of elementary reflectors; if UPLO = 'L', the first NB columns have been reduced to tridiagonal form, with the diagonal elements overwriting the diagonal elements of A; the elements below the diagonal with the array TAU, represent the unitary matrix Q as a product of elementary reflectors. See Further Details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). E E is REAL array, dimension (N-1) If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal elements of the last NB columns of the reduced matrix; if UPLO = 'L', E(1:nb) contains the subdiagonal elements of the first NB columns of the reduced matrix. TAU TAU is COMPLEX array, dimension (N-1) The scalar factors of the elementary reflectors, stored in TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. See Further Details. W W is COMPLEX array, dimension (LDW,NB) The n-by-nb matrix W required to update the unreduced part of A. LDW LDW is INTEGER The leading dimension of the array W. LDW >= max(1,N). Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Further Details: If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n) H(n-1) . . . H(n-nb+1). Each H(i) has the form H(i) = I - tau * v * v**H where tau is a complex scalar, and v is a complex vector with v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), and tau in TAU(i-1). If UPLO = 'L', the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(nb). Each H(i) has the form H(i) = I - tau * v * v**H where tau is a complex scalar, and v is a complex vector with v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), and tau in TAU(i). The elements of the vectors v together form the n-by-nb matrix V which is needed, with W, to apply the transformation to the unreduced part of the matrix, using a Hermitian rank-2k update of the form: A := A - V*W**H - W*V**H. The contents of A on exit are illustrated by the following examples with n = 5 and nb = 2: if UPLO = 'U': if UPLO = 'L': ( a a a v4 v5 ) ( d ) ( a a v4 v5 ) ( 1 d ) ( a 1 v5 ) ( v1 1 a ) ( d 1 ) ( v1 v2 a a ) ( d ) ( v1 v2 a a a ) where d denotes a diagonal element of the reduced matrix, a denotes an element of the original matrix that is unchanged, and vi denotes an element of the vector defining H(i). Definition at line 200 of file clatrd.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 clatrd.f(3)

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