dgels
dgels - solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A
SUBROUTINE DGELS( TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK,
* INFO)
CHARACTER * 1 TRANSA
INTEGER M, N, NRHS, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)
SUBROUTINE DGELS_64( TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK,
* LDWORK, INFO)
CHARACTER * 1 TRANSA
INTEGER*8 M, N, NRHS, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)
SUBROUTINE GELS( [TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB],
* [WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER :: M, N, NRHS, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE GELS_64( [TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB],
* [WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: M, N, NRHS, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B
#include <sunperf.h>
void dgels(char transa, int m, int n, int nrhs, double *a, int lda, double *b, int ldb, int *info);
void dgels_64(char transa, long m, long n, long nrhs, double *a, long lda, double *b, long ldb, long *info);
dgels solves overdetermined or underdetermined real linear systems
involving an M-by-N matrix A, or its transpose, using a QR or LQ
factorization of A. It is assumed that A has full rank.
The following options are provided:
1. If TRANS = 'N' and m >= n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A*X ||.
2. If TRANS = 'N' and m < n: find the minimum norm solution of
an underdetermined system A * X = B.
3. If TRANS = 'T' and m >= n: find the minimum norm solution of
an undetermined system A**T * X = B.
4. If TRANS = 'T' and m < n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A**T * X ||.
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.
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* TRANSA (input)
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* M (input)
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The number of rows of the matrix A. M >= 0.
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* N (input)
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The number of columns of the matrix A. N >= 0.
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* NRHS (input)
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The number of right hand sides, i.e., the number of
columns of the matrices B and X. NRHS >=0.
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* A (input/output)
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On entry, the M-by-N matrix A.
On exit,
if M >= N, A is overwritten by details of its QR
factorization as returned by SGEQRF;
if M < N, A is overwritten by details of its LQ
factorization as returned by SGELQF.
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* LDA (input)
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The leading dimension of the array A. LDA >= max(1,M).
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* B (input/output)
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On entry, the matrix B of right hand side vectors, stored
columnwise; B is M-by-NRHS if TRANSA = 'N', or N-by-NRHS
if TRANSA = 'T'.
On exit, B is overwritten by the solution vectors, stored
columnwise:
if TRANSA = 'N' and m >= n, rows 1 to n of B contain the least
squares solution vectors; the residual sum of squares for the
solution in each column is given by the sum of squares of
elements N+1 to M in that column;
if TRANSA = 'N' and m < n, rows 1 to N of B contain the
minimum norm solution vectors;
if TRANSA = 'T' and m >= n, rows 1 to M of B contain the
minimum norm solution vectors;
if TRANSA = 'T' and m < n, rows 1 to M of B contain the
least squares solution vectors; the residual sum of squares
for the solution in each column is given by the sum of
squares of elements M+1 to N in that column.
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* LDB (input)
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The leading dimension of the array B. LDB >= MAX(1,M,N).
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* WORK (workspace)
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On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
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* LDWORK (input)
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The dimension of the array WORK.
LDWORK >= max( 1, MN + max( MN, NRHS ) ).
For optimal performance,
LDWORK >= max( 1, MN + max( MN, NRHS )*NB ).
where MN = min(M,N) and NB is the optimum block size.
If LDWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LDWORK is issued by XERBLA.
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* INFO (output)
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