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---
:name: chetd2
:md5sum: 71b4642e8124d75edc818a52bbfcacc7
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- d:
:type: real
:intent: output
:dims:
- n
- e:
:type: real
:intent: output
:dims:
- n-1
- tau:
:type: complex
:intent: output
:dims:
- n-1
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CHETD2( UPLO, N, A, LDA, D, E, TAU, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CHETD2 reduces a complex Hermitian matrix A to real symmetric\n\
* tridiagonal form T by a unitary similarity transformation:\n\
* Q' * A * Q = T.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* Specifies whether the upper or lower triangular part of the\n\
* Hermitian matrix A is stored:\n\
* = 'U': Upper triangular\n\
* = 'L': Lower triangular\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA,N)\n\
* On entry, the Hermitian matrix A. If UPLO = 'U', the leading\n\
* n-by-n upper triangular part of A contains the upper\n\
* triangular part of the matrix A, and the strictly lower\n\
* triangular part of A is not referenced. If UPLO = 'L', the\n\
* leading n-by-n lower triangular part of A contains the lower\n\
* triangular part of the matrix A, and the strictly upper\n\
* triangular part of A is not referenced.\n\
* On exit, if UPLO = 'U', the diagonal and first superdiagonal\n\
* of A are overwritten by the corresponding elements of the\n\
* tridiagonal matrix T, and the elements above the first\n\
* superdiagonal, with the array TAU, represent the unitary\n\
* matrix Q as a product of elementary reflectors; if UPLO\n\
* = 'L', the diagonal and first subdiagonal of A are over-\n\
* written by the corresponding elements of the tridiagonal\n\
* matrix T, and the elements below the first subdiagonal, with\n\
* the array TAU, represent the unitary matrix Q as a product\n\
* of elementary reflectors. See Further Details.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* D (output) REAL array, dimension (N)\n\
* The diagonal elements of the tridiagonal matrix T:\n\
* D(i) = A(i,i).\n\
*\n\
* E (output) REAL array, dimension (N-1)\n\
* The off-diagonal elements of the tridiagonal matrix T:\n\
* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.\n\
*\n\
* TAU (output) COMPLEX array, dimension (N-1)\n\
* The scalar factors of the elementary reflectors (see Further\n\
* Details).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* If UPLO = 'U', the matrix Q is represented as a product of elementary\n\
* reflectors\n\
*\n\
* Q = H(n-1) . . . H(2) H(1).\n\
*\n\
* Each H(i) has the form\n\
*\n\
* H(i) = I - tau * v * v'\n\
*\n\
* where tau is a complex scalar, and v is a complex vector with\n\
* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in\n\
* A(1:i-1,i+1), and tau in TAU(i).\n\
*\n\
* If UPLO = 'L', the matrix Q is represented as a product of elementary\n\
* reflectors\n\
*\n\
* Q = H(1) H(2) . . . H(n-1).\n\
*\n\
* Each H(i) has the form\n\
*\n\
* H(i) = I - tau * v * v'\n\
*\n\
* where tau is a complex scalar, and v is a complex vector with\n\
* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),\n\
* and tau in TAU(i).\n\
*\n\
* The contents of A on exit are illustrated by the following examples\n\
* with n = 5:\n\
*\n\
* if UPLO = 'U': if UPLO = 'L':\n\
*\n\
* ( d e v2 v3 v4 ) ( d )\n\
* ( d e v3 v4 ) ( e d )\n\
* ( d e v4 ) ( v1 e d )\n\
* ( d e ) ( v1 v2 e d )\n\
* ( d ) ( v1 v2 v3 e d )\n\
*\n\
* where d and e denote diagonal and off-diagonal elements of T, and vi\n\
* denotes an element of the vector defining H(i).\n\
*\n\
* =====================================================================\n\
*\n"
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