LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  cgesc2 (N, A, LDA, RHS, IPIV, JPIV, SCALE) 
CGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.  
subroutine  cgetc2 (N, A, LDA, IPIV, JPIV, INFO) 
CGETC2 computes the LU factorization with complete pivoting of the general nbyn matrix.  
REAL function  clange (NORM, M, N, A, LDA, WORK) 
CLANGE returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of a general rectangular matrix.  
subroutine  claqge (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED) 
CLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.  
subroutine  ctgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO) 
CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation. 
This is the group of complex auxiliary functions for GE matrices
subroutine cgesc2  (  integer  N, 
complex, dimension( lda, * )  A,  
integer  LDA,  
complex, dimension( * )  RHS,  
integer, dimension( * )  IPIV,  
integer, dimension( * )  JPIV,  
real  SCALE  
) 
CGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.
Download CGESC2 + dependencies [TGZ] [ZIP] [TXT]CGESC2 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 CGETC2.
[in]  N  N is INTEGER The number of columns of the matrix A. 
[in]  A  A is COMPLEX array, dimension (LDA, N) On entry, the LU part of the factorization of the nbyn matrix A computed by CGETC2: 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 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 REAL 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 cgesc2.f.
subroutine cgetc2  (  integer  N, 
complex, dimension( lda, * )  A,  
integer  LDA,  
integer, dimension( * )  IPIV,  
integer, dimension( * )  JPIV,  
integer  INFO  
) 
CGETC2 computes the LU factorization with complete pivoting of the general nbyn matrix.
Download CGETC2 + dependencies [TGZ] [ZIP] [TXT]CGETC2 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 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 cgetc2.f.
REAL function clange  (  character  NORM, 
integer  M,  
integer  N,  
complex, dimension( lda, * )  A,  
integer  LDA,  
real, dimension( * )  WORK  
) 
CLANGE returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of a general rectangular matrix.
Download CLANGE + dependencies [TGZ] [ZIP] [TXT]CLANGE 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.
CLANGE = ( 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 CLANGE as described above. 
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. When M = 0, CLANGE is set to zero. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= 0. When N = 0, CLANGE is set to zero. 
[in]  A  A is COMPLEX 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 REAL array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. 
Definition at line 116 of file clange.f.
subroutine claqge  (  integer  M, 
integer  N,  
complex, dimension( lda, * )  A,  
integer  LDA,  
real, dimension( * )  R,  
real, dimension( * )  C,  
real  ROWCND,  
real  COLCND,  
real  AMAX,  
character  EQUED  
) 
CLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
Download CLAQGE + dependencies [TGZ] [ZIP] [TXT]CLAQGE 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 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 REAL array, dimension (M) The row scale factors for A. 
[in]  C  C is REAL array, dimension (N) The column scale factors for A. 
[in]  ROWCND  ROWCND is REAL Ratio of the smallest R(i) to the largest R(i). 
[in]  COLCND  COLCND is REAL Ratio of the smallest C(i) to the largest C(i). 
[in]  AMAX  AMAX is REAL 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 claqge.f.
subroutine ctgex2  (  logical  WANTQ, 
logical  WANTZ,  
integer  N,  
complex, dimension( lda, * )  A,  
integer  LDA,  
complex, dimension( ldb, * )  B,  
integer  LDB,  
complex, dimension( ldq, * )  Q,  
integer  LDQ,  
complex, dimension( ldz, * )  Z,  
integer  LDZ,  
integer  J1,  
integer  INFO  
) 
CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.
Download CTGEX2 + dependencies [TGZ] [ZIP] [TXT]CTGEX2 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 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 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 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 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 ctgex2.f.