--- name: "gtcon" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/gtcon" --- # gtcon(3) gtcon: condition number estimate ## NAME gtcon - gtcon: condition number estimate ## SYNOPSIS ### Functions subroutine **cgtcon** (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)\ **CGTCON** subroutine **dgtcon** (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)\ **DGTCON** subroutine **sgtcon** (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)\ **SGTCON** subroutine **zgtcon** (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)\ **ZGTCON** ## Detailed Description ## Function Documentation ### subroutine cgtcon (character norm, integer n, complex, dimension( \* ) dl, complex, dimension( \* ) d, complex, dimension( \* ) du, complex, dimension( \* ) du2, integer, dimension( \* ) ipiv, real anorm, real rcond, complex, dimension( \* ) work, integer info) **CGTCON** **Purpose:** ``` !> !> CGTCON estimates the reciprocal of the condition number of a complex !> tridiagonal matrix A using the LU factorization as computed by !> CGTTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> ``` **Parameters** *NORM* ``` !> NORM is CHARACTER*1 !> Specifies whether the 1-norm condition number or the !> infinity-norm condition number is required: !> = '1' or 'O': 1-norm; !> = 'I': Infinity-norm. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *DL* ``` !> DL is COMPLEX array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by CGTTRF. !> ``` *D* ``` !> D is COMPLEX array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !> ``` *DU* ``` !> DU is COMPLEX array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !> ``` *DU2* ``` !> DU2 is COMPLEX array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !> ``` *ANORM* ``` !> ANORM is REAL !> If NORM = '1' or 'O', the 1-norm of the original matrix A. !> If NORM = 'I', the infinity-norm of the original matrix A. !> ``` *RCOND* ``` !> RCOND is REAL !> The reciprocal of the condition number of the matrix A, !> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an !> estimate of the 1-norm of inv(A) computed in this routine. !> ``` *WORK* ``` !> WORK is COMPLEX array, dimension (2*N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **139** of file **cgtcon.f**. ### subroutine dgtcon (character norm, integer n, double precision, dimension( \* ) dl, double precision, dimension( \* ) d, double precision, dimension( \* ) du, double precision, dimension( \* ) du2, integer, dimension( \* ) ipiv, double precision anorm, double precision rcond, double precision, dimension( \* ) work, integer, dimension( \* ) iwork, integer info) **DGTCON** **Purpose:** ``` !> !> DGTCON estimates the reciprocal of the condition number of a real !> tridiagonal matrix A using the LU factorization as computed by !> DGTTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> ``` **Parameters** *NORM* ``` !> NORM is CHARACTER*1 !> Specifies whether the 1-norm condition number or the !> infinity-norm condition number is required: !> = '1' or 'O': 1-norm; !> = 'I': Infinity-norm. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *DL* ``` !> DL is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by DGTTRF. !> ``` *D* ``` !> D is DOUBLE PRECISION array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !> ``` *DU* ``` !> DU is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !> ``` *DU2* ``` !> DU2 is DOUBLE PRECISION array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !> ``` *ANORM* ``` !> ANORM is DOUBLE PRECISION !> If NORM = '1' or 'O', the 1-norm of the original matrix A. !> If NORM = 'I', the infinity-norm of the original matrix A. !> ``` *RCOND* ``` !> RCOND is DOUBLE PRECISION !> The reciprocal of the condition number of the matrix A, !> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an !> estimate of the 1-norm of inv(A) computed in this routine. !> ``` *WORK* ``` !> WORK is DOUBLE PRECISION array, dimension (2*N) !> ``` *IWORK* ``` !> IWORK is INTEGER array, dimension (N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **144** of file **dgtcon.f**. ### subroutine sgtcon (character norm, integer n, real, dimension( \* ) dl, real, dimension( \* ) d, real, dimension( \* ) du, real, dimension( \* ) du2, integer, dimension( \* ) ipiv, real anorm, real rcond, real, dimension( \* ) work, integer, dimension( \* ) iwork, integer info) **SGTCON** **Purpose:** ``` !> !> SGTCON estimates the reciprocal of the condition number of a real !> tridiagonal matrix A using the LU factorization as computed by !> SGTTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> ``` **Parameters** *NORM* ``` !> NORM is CHARACTER*1 !> Specifies whether the 1-norm condition number or the !> infinity-norm condition number is required: !> = '1' or 'O': 1-norm; !> = 'I': Infinity-norm. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *DL* ``` !> DL is REAL array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by SGTTRF. !> ``` *D* ``` !> D is REAL array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !> ``` *DU* ``` !> DU is REAL array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !> ``` *DU2* ``` !> DU2 is REAL array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !> ``` *ANORM* ``` !> ANORM is REAL !> If NORM = '1' or 'O', the 1-norm of the original matrix A. !> If NORM = 'I', the infinity-norm of the original matrix A. !> ``` *RCOND* ``` !> RCOND is REAL !> The reciprocal of the condition number of the matrix A, !> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an !> estimate of the 1-norm of inv(A) computed in this routine. !> ``` *WORK* ``` !> WORK is REAL array, dimension (2*N) !> ``` *IWORK* ``` !> IWORK is INTEGER array, dimension (N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **144** of file **sgtcon.f**. ### subroutine zgtcon (character norm, integer n, complex\*16, dimension( \* ) dl, complex\*16, dimension( \* ) d, complex\*16, dimension( \* ) du, complex\*16, dimension( \* ) du2, integer, dimension( \* ) ipiv, double precision anorm, double precision rcond, complex\*16, dimension( \* ) work, integer info) **ZGTCON** **Purpose:** ``` !> !> ZGTCON estimates the reciprocal of the condition number of a complex !> tridiagonal matrix A using the LU factorization as computed by !> ZGTTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> ``` **Parameters** *NORM* ``` !> NORM is CHARACTER*1 !> Specifies whether the 1-norm condition number or the !> infinity-norm condition number is required: !> = '1' or 'O': 1-norm; !> = 'I': Infinity-norm. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *DL* ``` !> DL is COMPLEX*16 array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by ZGTTRF. !> ``` *D* ``` !> D is COMPLEX*16 array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !> ``` *DU* ``` !> DU is COMPLEX*16 array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !> ``` *DU2* ``` !> DU2 is COMPLEX*16 array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !> ``` *ANORM* ``` !> ANORM is DOUBLE PRECISION !> If NORM = '1' or 'O', the 1-norm of the original matrix A. !> If NORM = 'I', the infinity-norm of the original matrix A. !> ``` *RCOND* ``` !> RCOND is DOUBLE PRECISION !> The reciprocal of the condition number of the matrix A, !> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an !> estimate of the 1-norm of inv(A) computed in this routine. !> ``` *WORK* ``` !> WORK is COMPLEX*16 array, dimension (2*N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **139** of file **zgtcon.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.