--- 
:name: zhetrd
:md5sum: 8ff61910f96d3aa218cab2a83ffadca4
:category: :subroutine
:arguments: 
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: doublecomplex
    :intent: input/output
    :dims: 
    - lda
    - n
- lda: 
    :type: integer
    :intent: input
- d: 
    :type: doublereal
    :intent: output
    :dims: 
    - n
- e: 
    :type: doublereal
    :intent: output
    :dims: 
    - n-1
- tau: 
    :type: doublecomplex
    :intent: output
    :dims: 
    - n-1
- work: 
    :type: doublecomplex
    :intent: output
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
- info: 
    :type: integer
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  ZHETRD reduces a complex Hermitian matrix A to real symmetric\n\
  *  tridiagonal form T by a unitary similarity transformation:\n\
  *  Q**H * A * Q = T.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *          = 'U':  Upper triangle of A is stored;\n\
  *          = 'L':  Lower triangle of A is stored.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix A.  N >= 0.\n\
  *\n\
  *  A       (input/output) COMPLEX*16 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) DOUBLE PRECISION array, dimension (N)\n\
  *          The diagonal elements of the tridiagonal matrix T:\n\
  *          D(i) = A(i,i).\n\
  *\n\
  *  E       (output) DOUBLE PRECISION 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*16 array, dimension (N-1)\n\
  *          The scalar factors of the elementary reflectors (see Further\n\
  *          Details).\n\
  *\n\
  *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))\n\
  *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
  *\n\
  *  LWORK   (input) INTEGER\n\
  *          The dimension of the array WORK.  LWORK >= 1.\n\
  *          For optimum performance LWORK >= N*NB, where NB is the\n\
  *          optimal blocksize.\n\
  *\n\
  *          If LWORK = -1, then a workspace query is assumed; the routine\n\
  *          only calculates the optimal size of the WORK array, returns\n\
  *          this value as the first entry of the WORK array, and no error\n\
  *          message related to LWORK is issued by XERBLA.\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"
