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---
:name: zgbbrd
:md5sum: 8e300267613885efce454baefeee7dd6
:category: :subroutine
:arguments:
- vect:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- ncc:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- ab:
:type: doublecomplex
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: output
:dims:
- MIN(m,n)
- e:
:type: doublereal
:intent: output
:dims:
- MIN(m,n)-1
- q:
:type: doublecomplex
:intent: output
:dims:
- ldq
- m
- ldq:
:type: integer
:intent: input
- pt:
:type: doublecomplex
:intent: output
:dims:
- ldpt
- n
- ldpt:
:type: integer
:intent: input
- c:
:type: doublecomplex
:intent: input/output
:dims:
- ldc
- ncc
- ldc:
:type: integer
:intent: input
- work:
:type: doublecomplex
:intent: workspace
:dims:
- MAX(m,n)
- rwork:
:type: doublereal
:intent: workspace
:dims:
- MAX(m,n)
- info:
:type: integer
:intent: output
:substitutions:
m: ldab
ldq: "((lsame_(&vect,\"Q\")) || (lsame_(&vect,\"B\"))) ? MAX(1,m) : 1"
ldpt: "((lsame_(&vect,\"P\")) || (lsame_(&vect,\"B\"))) ? MAX(1,n) : 1"
:fortran_help: " SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZGBBRD reduces a complex general m-by-n band matrix A to real upper\n\
* bidiagonal form B by a unitary transformation: Q' * A * P = B.\n\
*\n\
* The routine computes B, and optionally forms Q or P', or computes\n\
* Q'*C for a given matrix C.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* VECT (input) CHARACTER*1\n\
* Specifies whether or not the matrices Q and P' are to be\n\
* formed.\n\
* = 'N': do not form Q or P';\n\
* = 'Q': form Q only;\n\
* = 'P': form P' only;\n\
* = 'B': form both.\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix A. N >= 0.\n\
*\n\
* NCC (input) INTEGER\n\
* The number of columns of the matrix C. NCC >= 0.\n\
*\n\
* KL (input) INTEGER\n\
* The number of subdiagonals of the matrix A. KL >= 0.\n\
*\n\
* KU (input) INTEGER\n\
* The number of superdiagonals of the matrix A. KU >= 0.\n\
*\n\
* AB (input/output) COMPLEX*16 array, dimension (LDAB,N)\n\
* On entry, the m-by-n band matrix A, stored in rows 1 to\n\
* KL+KU+1. The j-th column of A is stored in the j-th column of\n\
* the array AB as follows:\n\
* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).\n\
* On exit, A is overwritten by values generated during the\n\
* reduction.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array A. LDAB >= KL+KU+1.\n\
*\n\
* D (output) DOUBLE PRECISION array, dimension (min(M,N))\n\
* The diagonal elements of the bidiagonal matrix B.\n\
*\n\
* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1)\n\
* The superdiagonal elements of the bidiagonal matrix B.\n\
*\n\
* Q (output) COMPLEX*16 array, dimension (LDQ,M)\n\
* If VECT = 'Q' or 'B', the m-by-m unitary matrix Q.\n\
* If VECT = 'N' or 'P', the array Q is not referenced.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q.\n\
* LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.\n\
*\n\
* PT (output) COMPLEX*16 array, dimension (LDPT,N)\n\
* If VECT = 'P' or 'B', the n-by-n unitary matrix P'.\n\
* If VECT = 'N' or 'Q', the array PT is not referenced.\n\
*\n\
* LDPT (input) INTEGER\n\
* The leading dimension of the array PT.\n\
* LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.\n\
*\n\
* C (input/output) COMPLEX*16 array, dimension (LDC,NCC)\n\
* On entry, an m-by-ncc matrix C.\n\
* On exit, C is overwritten by Q'*C.\n\
* C is not referenced if NCC = 0.\n\
*\n\
* LDC (input) INTEGER\n\
* The leading dimension of the array C.\n\
* LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.\n\
*\n\
* WORK (workspace) COMPLEX*16 array, dimension (max(M,N))\n\
*\n\
* RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N))\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\
* =====================================================================\n\
*\n"
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