SUBROUTINE ZGELSX( M, N, NRHS, A, LDA, B, LDB, JPIVOT, RCOND, IRANK, * WORK, WORK2, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER M, N, NRHS, LDA, LDB, IRANK, INFO INTEGER JPIVOT(*) DOUBLE PRECISION RCOND DOUBLE PRECISION WORK2(*) SUBROUTINE ZGELSX_64( M, N, NRHS, A, LDA, B, LDB, JPIVOT, RCOND, * IRANK, WORK, WORK2, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 M, N, NRHS, LDA, LDB, IRANK, INFO INTEGER*8 JPIVOT(*) DOUBLE PRECISION RCOND DOUBLE PRECISION WORK2(*)
SUBROUTINE GELSX( [M], [N], [NRHS], A, [LDA], B, [LDB], JPIVOT, * RCOND, IRANK, [WORK], [WORK2], [INFO]) COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: M, N, NRHS, LDA, LDB, IRANK, INFO INTEGER, DIMENSION(:) :: JPIVOT REAL(8) :: RCOND REAL(8), DIMENSION(:) :: WORK2 SUBROUTINE GELSX_64( [M], [N], [NRHS], A, [LDA], B, [LDB], JPIVOT, * RCOND, IRANK, [WORK], [WORK2], [INFO]) COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: M, N, NRHS, LDA, LDB, IRANK, INFO INTEGER(8), DIMENSION(:) :: JPIVOT REAL(8) :: RCOND REAL(8), DIMENSION(:) :: WORK2
void zgelsx(int m, int n, int nrhs, doublecomplex *a, int lda, doublecomplex *b, int ldb, int *jpivot, double rcond, int *irank, int *info);
void zgelsx_64(long m, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb, long *jpivot, double rcond, long *irank, long *info);
CGELSX computes the minimum-norm solution to a complex linear least squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X.
The routine first computes a QR factorization with column pivoting: A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND. The order of R11, RANK, is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated by unitary transformations from the right, arriving at the complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z [ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ] [ 0 ]
where Q1 consists of the first RANK columns of Q.