tptri(3) Library Functions Manual tptri(3) NAME tptri - tptri: triangular inverse SYNOPSIS Functions subroutine ctptri (uplo, diag, n, ap, info) CTPTRI subroutine dtptri (uplo, diag, n, ap, info) DTPTRI subroutine stptri (uplo, diag, n, ap, info) STPTRI subroutine ztptri (uplo, diag, n, ap, info) ZTPTRI Detailed Description Function Documentation subroutine ctptri (character uplo, character diag, integer n, complex, dimension( * ) ap, integer info) CTPTRI Purpose: CTPTRI computes the inverse of a complex upper or lower triangular matrix A stored in packed format. Parameters UPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. AP AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangular matrix A, stored columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the (triangular) inverse of the original matrix, in the same packed storage format. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: A triangular matrix A can be transferred to packed storage using one of the following program segments: UPLO = 'U': UPLO = 'L': JC = 1 JC = 1 DO 2 J = 1, N DO 2 J = 1, N DO 1 I = 1, J DO 1 I = J, N AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) 1 CONTINUE 1 CONTINUE JC = JC + J JC = JC + N - J + 1 2 CONTINUE 2 CONTINUE Definition at line 116 of file ctptri.f. subroutine dtptri (character uplo, character diag, integer n, double precision, dimension( * ) ap, integer info) DTPTRI Purpose: DTPTRI computes the inverse of a real upper or lower triangular matrix A stored in packed format. Parameters UPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. AP AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the upper or lower triangular matrix A, stored columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the (triangular) inverse of the original matrix, in the same packed storage format. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: A triangular matrix A can be transferred to packed storage using one of the following program segments: UPLO = 'U': UPLO = 'L': JC = 1 JC = 1 DO 2 J = 1, N DO 2 J = 1, N DO 1 I = 1, J DO 1 I = J, N AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) 1 CONTINUE 1 CONTINUE JC = JC + J JC = JC + N - J + 1 2 CONTINUE 2 CONTINUE Definition at line 116 of file dtptri.f. subroutine stptri (character uplo, character diag, integer n, real, dimension( * ) ap, integer info) STPTRI Purpose: STPTRI computes the inverse of a real upper or lower triangular matrix A stored in packed format. Parameters UPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. AP AP is REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangular matrix A, stored columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the (triangular) inverse of the original matrix, in the same packed storage format. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: A triangular matrix A can be transferred to packed storage using one of the following program segments: UPLO = 'U': UPLO = 'L': JC = 1 JC = 1 DO 2 J = 1, N DO 2 J = 1, N DO 1 I = 1, J DO 1 I = J, N AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) 1 CONTINUE 1 CONTINUE JC = JC + J JC = JC + N - J + 1 2 CONTINUE 2 CONTINUE Definition at line 116 of file stptri.f. subroutine ztptri (character uplo, character diag, integer n, complex*16, dimension( * ) ap, integer info) ZTPTRI Purpose: ZTPTRI computes the inverse of a complex upper or lower triangular matrix A stored in packed format. Parameters UPLO UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N N is INTEGER The order of the matrix A. N >= 0. AP AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangular matrix A, stored columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the (triangular) inverse of the original matrix, in the same packed storage format. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: A triangular matrix A can be transferred to packed storage using one of the following program segments: UPLO = 'U': UPLO = 'L': JC = 1 JC = 1 DO 2 J = 1, N DO 2 J = 1, N DO 1 I = 1, J DO 1 I = J, N AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) 1 CONTINUE 1 CONTINUE JC = JC + J JC = JC + N - J + 1 2 CONTINUE 2 CONTINUE Definition at line 116 of file ztptri.f. 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