LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  zgesc2 (N, A, LDA, RHS, IPIV, JPIV, SCALE) 
ZGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.  
subroutine  zgetc2 (N, A, LDA, IPIV, JPIV, INFO) 
ZGETC2 computes the LU factorization with complete pivoting of the general nbyn matrix.  
DOUBLE PRECISION function  zlange (NORM, M, N, A, LDA, WORK) 
ZLANGE returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of a general rectangular matrix.  
subroutine  zlaqge (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED) 
ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.  
subroutine  ztgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO) 
ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation. 
This is the group of complex16 auxiliary functions for GE matrices
subroutine zgesc2  (  integer  N, 
complex*16, dimension( lda, * )  A,  
integer  LDA,  
complex*16, dimension( * )  RHS,  
integer, dimension( * )  IPIV,  
integer, dimension( * )  JPIV,  
double precision  SCALE  
) 
ZGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.
Download ZGESC2 + dependencies [TGZ] [ZIP] [TXT]ZGESC2 solves a system of linear equations A * X = scale* RHS with a general NbyN matrix A using the LU factorization with complete pivoting computed by ZGETC2.
[in]  N  N is INTEGER The number of columns of the matrix A. 
[in]  A  A is COMPLEX*16 array, dimension (LDA, N) On entry, the LU part of the factorization of the nbyn matrix A computed by ZGETC2: A = P * L * U * Q 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1, N). 
[in,out]  RHS  RHS is COMPLEX*16 array, dimension N. On entry, the right hand side vector b. On exit, the solution vector X. 
[in]  IPIV  IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i). 
[in]  JPIV  JPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j). 
[out]  SCALE  SCALE is DOUBLE PRECISION On exit, SCALE contains the scale factor. SCALE is chosen 0 <= SCALE <= 1 to prevent owerflow in the solution. 
Definition at line 116 of file zgesc2.f.
subroutine zgetc2  (  integer  N, 
complex*16, dimension( lda, * )  A,  
integer  LDA,  
integer, dimension( * )  IPIV,  
integer, dimension( * )  JPIV,  
integer  INFO  
) 
ZGETC2 computes the LU factorization with complete pivoting of the general nbyn matrix.
Download ZGETC2 + dependencies [TGZ] [ZIP] [TXT]ZGETC2 computes an LU factorization, using complete pivoting, of the nbyn matrix A. The factorization has the form A = P * L * U * Q, where P and Q are permutation matrices, L is lower triangular with unit diagonal elements and U is upper triangular. This is a level 1 BLAS version of the algorithm.
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in,out]  A  A is COMPLEX*16 array, dimension (LDA, N) On entry, the nbyn matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U*Q; the unit diagonal elements of L are not stored. If U(k, k) appears to be less than SMIN, U(k, k) is given the value of SMIN, giving a nonsingular perturbed system. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1, N). 
[out]  IPIV  IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i). 
[out]  JPIV  JPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j). 
[out]  INFO  INFO is INTEGER = 0: successful exit > 0: if INFO = k, U(k, k) is likely to produce overflow if one tries to solve for x in Ax = b. So U is perturbed to avoid the overflow. 
Definition at line 112 of file zgetc2.f.
DOUBLE PRECISION function zlange  (  character  NORM, 
integer  M,  
integer  N,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( * )  WORK  
) 
ZLANGE returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of a general rectangular matrix.
Download ZLANGE + dependencies [TGZ] [ZIP] [TXT]ZLANGE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A.
ZLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm' ( ( norm1(A), NORM = '1', 'O' or 'o' ( ( normI(A), NORM = 'I' or 'i' ( ( normF(A), NORM = 'F', 'f', 'E' or 'e' where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
[in]  NORM  NORM is CHARACTER*1 Specifies the value to be returned in ZLANGE as described above. 
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. When M = 0, ZLANGE is set to zero. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= 0. When N = 0, ZLANGE is set to zero. 
[in]  A  A is COMPLEX*16 array, dimension (LDA,N) The m by n matrix A. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(M,1). 
[out]  WORK  WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. 
Definition at line 116 of file zlange.f.
subroutine zlaqge  (  integer  M, 
integer  N,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( * )  R,  
double precision, dimension( * )  C,  
double precision  ROWCND,  
double precision  COLCND,  
double precision  AMAX,  
character  EQUED  
) 
ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
Download ZLAQGE + dependencies [TGZ] [ZIP] [TXT]ZLAQGE equilibrates a general M by N matrix A using the row and column scaling factors in the vectors R and C.
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= 0. 
[in,out]  A  A is COMPLEX*16 array, dimension (LDA,N) On entry, the M by N matrix A. On exit, the equilibrated matrix. See EQUED for the form of the equilibrated matrix. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(M,1). 
[in]  R  R is DOUBLE PRECISION array, dimension (M) The row scale factors for A. 
[in]  C  C is DOUBLE PRECISION array, dimension (N) The column scale factors for A. 
[in]  ROWCND  ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i). 
[in]  COLCND  COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i). 
[in]  AMAX  AMAX is DOUBLE PRECISION Absolute value of largest matrix entry. 
[out]  EQUED  EQUED is CHARACTER*1 Specifies the form of equilibration that was done. = 'N': No equilibration = 'R': Row equilibration, i.e., A has been premultiplied by diag(R). = 'C': Column equilibration, i.e., A has been postmultiplied by diag(C). = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C). 
THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors. If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done. LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
Definition at line 143 of file zlaqge.f.
subroutine ztgex2  (  logical  WANTQ, 
logical  WANTZ,  
integer  N,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
complex*16, dimension( ldb, * )  B,  
integer  LDB,  
complex*16, dimension( ldq, * )  Q,  
integer  LDQ,  
complex*16, dimension( ldz, * )  Z,  
integer  LDZ,  
integer  J1,  
integer  INFO  
) 
ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.
Download ZTGEX2 + dependencies [TGZ] [ZIP] [TXT]ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22) in an upper triangular matrix pair (A, B) by an unitary equivalence transformation. (A, B) must be in generalized Schur canonical form, that is, A and B are both upper triangular. Optionally, the matrices Q and Z of generalized Schur vectors are updated. Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
[in]  WANTQ  WANTQ is LOGICAL .TRUE. : update the left transformation matrix Q; .FALSE.: do not update Q. 
[in]  WANTZ  WANTZ is LOGICAL .TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z. 
[in]  N  N is INTEGER The order of the matrices A and B. N >= 0. 
[in,out]  A  A is COMPLEX*16 arrays, dimensions (LDA,N) On entry, the matrix A in the pair (A, B). On exit, the updated matrix A. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[in,out]  B  B is COMPLEX*16 arrays, dimensions (LDB,N) On entry, the matrix B in the pair (A, B). On exit, the updated matrix B. 
[in]  LDB  LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[in,out]  Q  Q is COMPLEX*16 array, dimension (LDZ,N) If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, the updated matrix Q. Not referenced if WANTQ = .FALSE.. 
[in]  LDQ  LDQ is INTEGER The leading dimension of the array Q. LDQ >= 1; If WANTQ = .TRUE., LDQ >= N. 
[in,out]  Z  Z is COMPLEX*16 array, dimension (LDZ,N) If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit, the updated matrix Z. Not referenced if WANTZ = .FALSE.. 
[in]  LDZ  LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1; If WANTZ = .TRUE., LDZ >= N. 
[in]  J1  J1 is INTEGER The index to the first block (A11, B11). 
[out]  INFO  INFO is INTEGER =0: Successful exit. =1: The transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill conditioned. 
Definition at line 190 of file ztgex2.f.