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---
:name: cgghrd
:md5sum: 62029756327bc968ec07529087b0e19a
:category: :subroutine
:arguments:
- compq:
:type: char
:intent: input
- compz:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ilo:
:type: integer
:intent: input
- ihi:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: complex
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- q:
:type: complex
:intent: input/output
:dims:
- ldq
- n
- ldq:
:type: integer
:intent: input
- z:
:type: complex
:intent: input/output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CGGHRD reduces a pair of complex matrices (A,B) to generalized upper\n\
* Hessenberg form using unitary transformations, where A is a\n\
* general matrix and B is upper triangular. The form of the generalized\n\
* eigenvalue problem is\n\
* A*x = lambda*B*x,\n\
* and B is typically made upper triangular by computing its QR\n\
* factorization and moving the unitary matrix Q to the left side\n\
* of the equation.\n\
*\n\
* This subroutine simultaneously reduces A to a Hessenberg matrix H:\n\
* Q**H*A*Z = H\n\
* and transforms B to another upper triangular matrix T:\n\
* Q**H*B*Z = T\n\
* in order to reduce the problem to its standard form\n\
* H*y = lambda*T*y\n\
* where y = Z**H*x.\n\
*\n\
* The unitary matrices Q and Z are determined as products of Givens\n\
* rotations. They may either be formed explicitly, or they may be\n\
* postmultiplied into input matrices Q1 and Z1, so that\n\
* Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H\n\
* Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H\n\
* If Q1 is the unitary matrix from the QR factorization of B in the\n\
* original equation A*x = lambda*B*x, then CGGHRD reduces the original\n\
* problem to generalized Hessenberg form.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* COMPQ (input) CHARACTER*1\n\
* = 'N': do not compute Q;\n\
* = 'I': Q is initialized to the unit matrix, and the\n\
* unitary matrix Q is returned;\n\
* = 'V': Q must contain a unitary matrix Q1 on entry,\n\
* and the product Q1*Q is returned.\n\
*\n\
* COMPZ (input) CHARACTER*1\n\
* = 'N': do not compute Q;\n\
* = 'I': Q is initialized to the unit matrix, and the\n\
* unitary matrix Q is returned;\n\
* = 'V': Q must contain a unitary matrix Q1 on entry,\n\
* and the product Q1*Q is returned.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A and B. N >= 0.\n\
*\n\
* ILO (input) INTEGER\n\
* IHI (input) INTEGER\n\
* ILO and IHI mark the rows and columns of A which are to be\n\
* reduced. It is assumed that A is already upper triangular\n\
* in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are\n\
* normally set by a previous call to CGGBAL; otherwise they\n\
* should be set to 1 and N respectively.\n\
* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA, N)\n\
* On entry, the N-by-N general matrix to be reduced.\n\
* On exit, the upper triangle and the first subdiagonal of A\n\
* are overwritten with the upper Hessenberg matrix H, and the\n\
* rest is set to zero.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* B (input/output) COMPLEX array, dimension (LDB, N)\n\
* On entry, the N-by-N upper triangular matrix B.\n\
* On exit, the upper triangular matrix T = Q**H B Z. The\n\
* elements below the diagonal are set to zero.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* Q (input/output) COMPLEX array, dimension (LDQ, N)\n\
* On entry, if COMPQ = 'V', the unitary matrix Q1, typically\n\
* from the QR factorization of B.\n\
* On exit, if COMPQ='I', the unitary matrix Q, and if\n\
* COMPQ = 'V', the product Q1*Q.\n\
* Not referenced if COMPQ='N'.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q.\n\
* LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.\n\
*\n\
* Z (input/output) COMPLEX array, dimension (LDZ, N)\n\
* On entry, if COMPZ = 'V', the unitary matrix Z1.\n\
* On exit, if COMPZ='I', the unitary matrix Z, and if\n\
* COMPZ = 'V', the product Z1*Z.\n\
* Not referenced if COMPZ='N'.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z.\n\
* LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise.\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\
* This routine reduces A to Hessenberg and B to triangular form by\n\
* an unblocked reduction, as described in _Matrix_Computations_,\n\
* by Golub and van Loan (Johns Hopkins Press).\n\
*\n\
* =====================================================================\n\
*\n"
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