gelss - Man Page

subroutine cgelss (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, rwork, info)
CGELSS solves overdetermined or underdetermined systems for GE matrices
subroutine dgelss (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, info)
DGELSS solves overdetermined or underdetermined systems for GE matrices
subroutine sgelss (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, info)
SGELSS solves overdetermined or underdetermined systems for GE matrices
subroutine zgelss (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, rwork, info)
ZGELSS solves overdetermined or underdetermined systems for GE matrices

CGELSS solves overdetermined or underdetermined systems for GE matrices  

Purpose:

 CGELSS computes the minimum norm solution to a complex linear
 least squares problem:

 Minimize 2-norm(| b - A*x |).

 using the singular value decomposition (SVD) 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 effective rank of A is determined by treating as zero those
 singular values which are less than RCOND times the largest singular
 value.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A. N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X. NRHS >= 0.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the first min(m,n) rows of A are overwritten with
          its right singular vectors, stored rowwise.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,M).

B

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the M-by-NRHS right hand side matrix B.
          On exit, B is overwritten by the N-by-NRHS solution matrix X.
          If m >= n and RANK = n, the residual sum-of-squares for
          the solution in the i-th column is given by the sum of
          squares of the modulus of elements n+1:m in that column.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M,N).

S

          S is REAL array, dimension (min(M,N))
          The singular values of A in decreasing order.
          The condition number of A in the 2-norm = S(1)/S(min(m,n)).

RCOND

          RCOND is REAL
          RCOND is used to determine the effective rank of A.
          Singular values S(i) <= RCOND*S(1) are treated as zero.
          If RCOND < 0, machine precision is used instead.

RANK

          RANK is INTEGER
          The effective rank of A, i.e., the number of singular values
          which are greater than RCOND*S(1).

WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK. LWORK >= 1, and also:
          LWORK >=  2*min(M,N) + max(M,N,NRHS)
          For good performance, LWORK should generally be larger.

          If LWORK = -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 LWORK is issued by XERBLA.

RWORK

          RWORK is REAL array, dimension (5*min(M,N))

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  the algorithm for computing the SVD failed to converge;
                if INFO = i, i off-diagonal elements of an intermediate
                bidiagonal form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 176 of file cgelss.f.

DGELSS solves overdetermined or underdetermined systems for GE matrices  

Purpose:

 DGELSS computes the minimum norm solution to a real linear least
 squares problem:

 Minimize 2-norm(| b - A*x |).

 using the singular value decomposition (SVD) 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 effective rank of A is determined by treating as zero those
 singular values which are less than RCOND times the largest singular
 value.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A. N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X. NRHS >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the first min(m,n) rows of A are overwritten with
          its right singular vectors, stored rowwise.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

B

          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the M-by-NRHS right hand side matrix B.
          On exit, B is overwritten by the N-by-NRHS solution
          matrix X.  If m >= n and RANK = n, the residual
          sum-of-squares for the solution in the i-th column is given
          by the sum of squares of elements n+1:m in that column.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,max(M,N)).

S

          S is DOUBLE PRECISION array, dimension (min(M,N))
          The singular values of A in decreasing order.
          The condition number of A in the 2-norm = S(1)/S(min(m,n)).

RCOND

          RCOND is DOUBLE PRECISION
          RCOND is used to determine the effective rank of A.
          Singular values S(i) <= RCOND*S(1) are treated as zero.
          If RCOND < 0, machine precision is used instead.

RANK

          RANK is INTEGER
          The effective rank of A, i.e., the number of singular values
          which are greater than RCOND*S(1).

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK. LWORK >= 1, and also:
          LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS )
          For good performance, LWORK should generally be larger.

          If LWORK = -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 LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  the algorithm for computing the SVD failed to converge;
                if INFO = i, i off-diagonal elements of an intermediate
                bidiagonal form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 170 of file dgelss.f.

SGELSS solves overdetermined or underdetermined systems for GE matrices  

Purpose:

 SGELSS computes the minimum norm solution to a real linear least
 squares problem:

 Minimize 2-norm(| b - A*x |).

 using the singular value decomposition (SVD) 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 effective rank of A is determined by treating as zero those
 singular values which are less than RCOND times the largest singular
 value.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A. N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X. NRHS >= 0.

A

          A is REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the first min(m,n) rows of A are overwritten with
          its right singular vectors, stored rowwise.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

B

          B is REAL array, dimension (LDB,NRHS)
          On entry, the M-by-NRHS right hand side matrix B.
          On exit, B is overwritten by the N-by-NRHS solution
          matrix X.  If m >= n and RANK = n, the residual
          sum-of-squares for the solution in the i-th column is given
          by the sum of squares of elements n+1:m in that column.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,max(M,N)).

S

          S is REAL array, dimension (min(M,N))
          The singular values of A in decreasing order.
          The condition number of A in the 2-norm = S(1)/S(min(m,n)).

RCOND

          RCOND is REAL
          RCOND is used to determine the effective rank of A.
          Singular values S(i) <= RCOND*S(1) are treated as zero.
          If RCOND < 0, machine precision is used instead.

RANK

          RANK is INTEGER
          The effective rank of A, i.e., the number of singular values
          which are greater than RCOND*S(1).

WORK

          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK. LWORK >= 1, and also:
          LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS )
          For good performance, LWORK should generally be larger.

          If LWORK = -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 LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  the algorithm for computing the SVD failed to converge;
                if INFO = i, i off-diagonal elements of an intermediate
                bidiagonal form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 170 of file sgelss.f.

ZGELSS solves overdetermined or underdetermined systems for GE matrices  

Purpose:

 ZGELSS computes the minimum norm solution to a complex linear
 least squares problem:

 Minimize 2-norm(| b - A*x |).

 using the singular value decomposition (SVD) 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 effective rank of A is determined by treating as zero those
 singular values which are less than RCOND times the largest singular
 value.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A. N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X. NRHS >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the first min(m,n) rows of A are overwritten with
          its right singular vectors, stored rowwise.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,M).

B

          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the M-by-NRHS right hand side matrix B.
          On exit, B is overwritten by the N-by-NRHS solution matrix X.
          If m >= n and RANK = n, the residual sum-of-squares for
          the solution in the i-th column is given by the sum of
          squares of the modulus of elements n+1:m in that column.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M,N).

S

          S is DOUBLE PRECISION array, dimension (min(M,N))
          The singular values of A in decreasing order.
          The condition number of A in the 2-norm = S(1)/S(min(m,n)).

RCOND

          RCOND is DOUBLE PRECISION
          RCOND is used to determine the effective rank of A.
          Singular values S(i) <= RCOND*S(1) are treated as zero.
          If RCOND < 0, machine precision is used instead.

RANK

          RANK is INTEGER
          The effective rank of A, i.e., the number of singular values
          which are greater than RCOND*S(1).

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK. LWORK >= 1, and also:
          LWORK >=  2*min(M,N) + max(M,N,NRHS)
          For good performance, LWORK should generally be larger.

          If LWORK = -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 LWORK is issued by XERBLA.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (5*min(M,N))

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  the algorithm for computing the SVD failed to converge;
                if INFO = i, i off-diagonal elements of an intermediate
                bidiagonal form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 176 of file zgelss.f.