LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  zgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
ZGBMV  
subroutine  zgemv (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
ZGEMV  
subroutine  zgerc (M, N, ALPHA, X, INCX, Y, INCY, A, LDA) 
ZGERC  
subroutine  zgeru (M, N, ALPHA, X, INCX, Y, INCY, A, LDA) 
ZGERU  
subroutine  zhbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
ZHBMV  
subroutine  zhemv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
ZHEMV  
subroutine  zher (UPLO, N, ALPHA, X, INCX, A, LDA) 
ZHER  
subroutine  zher2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA) 
ZHER2  
subroutine  zhpmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY) 
ZHPMV  
subroutine  zhpr (UPLO, N, ALPHA, X, INCX, AP) 
ZHPR  
subroutine  zhpr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP) 
ZHPR2  
subroutine  ztbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) 
ZTBMV  
subroutine  ztbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) 
ZTBSV  
subroutine  ztpmv (UPLO, TRANS, DIAG, N, AP, X, INCX) 
ZTPMV  
subroutine  ztpsv (UPLO, TRANS, DIAG, N, AP, X, INCX) 
ZTPSV  
subroutine  ztrmv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) 
ZTRMV  
subroutine  ztrsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) 
ZTRSV 
This is the group of complex16 LEVEL 2 BLAS routines.
subroutine zgbmv  (  character  TRANS, 
integer  M,  
integer  N,  
integer  KL,  
integer  KU,  
complex*16  ALPHA,  
complex*16, dimension(lda,*)  A,  
integer  LDA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16  BETA,  
complex*16, dimension(*)  Y,  
integer  INCY  
) 
ZGBMV
ZGBMV performs one of the matrixvector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or y := alpha*A**H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl subdiagonals and ku superdiagonals.
[in]  TRANS  TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. 
[in]  M  M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. 
[in]  N  N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. 
[in]  KL  KL is INTEGER On entry, KL specifies the number of subdiagonals of the matrix A. KL must satisfy 0 .le. KL. 
[in]  KU  KU is INTEGER On entry, KU specifies the number of superdiagonals of the matrix A. KU must satisfy 0 .le. KU. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first superdiagonal starting at position 2 in row ku, the first subdiagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N K = KU + 1  J DO 10, I = MAX( 1, J  KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( kl + ku + 1 ). 
[in]  X  X is COMPLEX*16 array of DIMENSION at least ( 1 + ( n  1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m  1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  BETA  BETA is COMPLEX*16 On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. 
[in,out]  Y  Y is COMPLEX*16 array of DIMENSION at least ( 1 + ( m  1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n  1 )*abs( INCY ) ) otherwise. Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 188 of file zgbmv.f.
subroutine zgemv  (  character  TRANS, 
integer  M,  
integer  N,  
complex*16  ALPHA,  
complex*16, dimension(lda,*)  A,  
integer  LDA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16  BETA,  
complex*16, dimension(*)  Y,  
integer  INCY  
) 
ZGEMV
ZGEMV performs one of the matrixvector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or y := alpha*A**H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.
[in]  TRANS  TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. 
[in]  M  M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. 
[in]  N  N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). 
[in]  X  X is COMPLEX*16 array of DIMENSION at least ( 1 + ( n  1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m  1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  BETA  BETA is COMPLEX*16 On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. 
[in,out]  Y  Y is COMPLEX*16 array of DIMENSION at least ( 1 + ( m  1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n  1 )*abs( INCY ) ) otherwise. Before entry with BETA nonzero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 159 of file zgemv.f.
subroutine zgerc  (  integer  M, 
integer  N,  
complex*16  ALPHA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16, dimension(*)  Y,  
integer  INCY,  
complex*16, dimension(lda,*)  A,  
integer  LDA  
) 
ZGERC
ZGERC performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.
[in]  M  M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. 
[in]  N  N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( m  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m element vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  Y  Y is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
[in,out]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 131 of file zgerc.f.
subroutine zgeru  (  integer  M, 
integer  N,  
complex*16  ALPHA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16, dimension(*)  Y,  
integer  INCY,  
complex*16, dimension(lda,*)  A,  
integer  LDA  
) 
ZGERU
ZGERU performs the rank 1 operation A := alpha*x*y**T + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.
[in]  M  M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. 
[in]  N  N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( m  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m element vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  Y  Y is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
[in,out]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 131 of file zgeru.f.
subroutine zhbmv  (  character  UPLO, 
integer  N,  
integer  K,  
complex*16  ALPHA,  
complex*16, dimension(lda,*)  A,  
integer  LDA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16  BETA,  
complex*16, dimension(*)  Y,  
integer  INCY  
) 
ZHBMV
ZHBMV performs the matrixvector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian band matrix, with k superdiagonals.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows: UPLO = 'U' or 'u' The upper triangular part of A is being supplied. UPLO = 'L' or 'l' The lower triangular part of A is being supplied. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  K  K is INTEGER On entry, K specifies the number of superdiagonals of the matrix A. K must satisfy 0 .le. K. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first superdiagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer the upper triangular part of a hermitian band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1  J DO 10, I = MAX( 1, J  K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first subdiagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer the lower triangular part of a hermitian band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1  J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ). 
[in]  X  X is COMPLEX*16 array of DIMENSION at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  BETA  BETA is COMPLEX*16 On entry, BETA specifies the scalar beta. 
[in,out]  Y  Y is COMPLEX*16 array of DIMENSION at least ( 1 + ( n  1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 188 of file zhbmv.f.
subroutine zhemv  (  character  UPLO, 
integer  N,  
complex*16  ALPHA,  
complex*16, dimension(lda,*)  A,  
integer  LDA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16  BETA,  
complex*16, dimension(*)  Y,  
integer  INCY  
) 
ZHEMV
ZHEMV performs the matrixvector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian matrix.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). 
[in]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  BETA  BETA is COMPLEX*16 On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. 
[in,out]  Y  Y is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 155 of file zhemv.f.
subroutine zher  (  character  UPLO, 
integer  N,  
double precision  ALPHA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16, dimension(lda,*)  A,  
integer  LDA  
) 
ZHER
ZHER performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in,out]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 136 of file zher.f.
subroutine zher2  (  character  UPLO, 
integer  N,  
complex*16  ALPHA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16, dimension(*)  Y,  
integer  INCY,  
complex*16, dimension(lda,*)  A,  
integer  LDA  
) 
ZHER2
ZHER2 performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  Y  Y is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
[in,out]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 151 of file zher2.f.
subroutine zhpmv  (  character  UPLO, 
integer  N,  
complex*16  ALPHA,  
complex*16, dimension(*)  AP,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16  BETA,  
complex*16, dimension(*)  Y,  
integer  INCY  
) 
ZHPMV
ZHPMV performs the matrixvector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  AP  AP is COMPLEX*16 array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. 
[in]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  BETA  BETA is COMPLEX*16 On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. 
[in,out]  Y  Y is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 150 of file zhpmv.f.
subroutine zhpr  (  character  UPLO, 
integer  N,  
double precision  ALPHA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16, dimension(*)  AP  
) 
ZHPR
ZHPR performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix, supplied in packed form.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in,out]  AP  AP is COMPLEX*16 array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 131 of file zhpr.f.
subroutine zhpr2  (  character  UPLO, 
integer  N,  
complex*16  ALPHA,  
complex*16, dimension(*)  X,  
integer  INCX,  
complex*16, dimension(*)  Y,  
integer  INCY,  
complex*16, dimension(*)  AP  
) 
ZHPR2
ZHPR2 performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  ALPHA  ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  Y  Y is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
[in,out]  AP  AP is COMPLEX*16 array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 146 of file zhpr2.f.
subroutine ztbmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
integer  K,  
complex*16, dimension(lda,*)  A,  
integer  LDA,  
complex*16, dimension(*)  X,  
integer  INCX  
) 
ZTBMV
ZTBMV performs one of the matrixvector operations x := A*x, or x := A**T*x, or x := A**H*x, where x is an n element vector and A is an n by n unit, or nonunit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. 
[in]  TRANS  TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A**T*x. TRANS = 'C' or 'c' x := A**H*x. 
[in]  DIAG  DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  K  K is INTEGER On entry with UPLO = 'U' or 'u', K specifies the number of superdiagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of subdiagonals of the matrix A. K must satisfy 0 .le. K. 
[in]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first superdiagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer an upper triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1  J DO 10, I = MAX( 1, J  K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first subdiagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1  J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, but are assumed to be unity. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ). 
[in]  X  X is (input/output) COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 187 of file ztbmv.f.
subroutine ztbsv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
integer  K,  
complex*16, dimension(lda,*)  A,  
integer  LDA,  
complex*16, dimension(*)  X,  
integer  INCX  
) 
ZTBSV
ZTBSV solves one of the systems of equations A*x = b, or A**T*x = b, or A**H*x = b, where b and x are n element vectors and A is an n by n unit, or nonunit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. No test for singularity or nearsingularity is included in this routine. Such tests must be performed before calling this routine.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. 
[in]  TRANS  TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**H*x = b. 
[in]  DIAG  DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  K  K is INTEGER On entry with UPLO = 'U' or 'u', K specifies the number of superdiagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of subdiagonals of the matrix A. K must satisfy 0 .le. K. 
[in]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first superdiagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer an upper triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1  J DO 10, I = MAX( 1, J  K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first subdiagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1  J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, but are assumed to be unity. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ). 
[in,out]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element righthand side vector b. On exit, X is overwritten with the solution vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 190 of file ztbsv.f.
subroutine ztpmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
complex*16, dimension(*)  AP,  
complex*16, dimension(*)  X,  
integer  INCX  
) 
ZTPMV
ZTPMV performs one of the matrixvector operations x := A*x, or x := A**T*x, or x := A**H*x, where x is an n element vector and A is an n by n unit, or nonunit, upper or lower triangular matrix, supplied in packed form.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. 
[in]  TRANS  TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A**T*x. TRANS = 'C' or 'c' x := A**H*x. 
[in]  DIAG  DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  AP  AP is COMPLEX*16 array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. 
[in]  X  X is (input/output) COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 143 of file ztpmv.f.
subroutine ztpsv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
complex*16, dimension(*)  AP,  
complex*16, dimension(*)  X,  
integer  INCX  
) 
ZTPSV
ZTPSV solves one of the systems of equations A*x = b, or A**T*x = b, or A**H*x = b, where b and x are n element vectors and A is an n by n unit, or nonunit, upper or lower triangular matrix, supplied in packed form. No test for singularity or nearsingularity is included in this routine. Such tests must be performed before calling this routine.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. 
[in]  TRANS  TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**H*x = b. 
[in]  DIAG  DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  AP  AP is COMPLEX*16 array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. 
[in,out]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element righthand side vector b. On exit, X is overwritten with the solution vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 145 of file ztpsv.f.
subroutine ztrmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
complex*16, dimension(lda,*)  A,  
integer  LDA,  
complex*16, dimension(*)  X,  
integer  INCX  
) 
ZTRMV
ZTRMV performs one of the matrixvector operations x := A*x, or x := A**T*x, or x := A**H*x, where x is an n element vector and A is an n by n unit, or nonunit, upper or lower triangular matrix.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. 
[in]  TRANS  TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A**T*x. TRANS = 'C' or 'c' x := A**H*x. 
[in]  DIAG  DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). 
[in]  X  X is (input/output) COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 148 of file ztrmv.f.
subroutine ztrsv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
complex*16, dimension(lda,*)  A,  
integer  LDA,  
complex*16, dimension(*)  X,  
integer  INCX  
) 
ZTRSV
ZTRSV solves one of the systems of equations A*x = b, or A**T*x = b, or A**H*x = b, where b and x are n element vectors and A is an n by n unit, or nonunit, upper or lower triangular matrix. No test for singularity or nearsingularity is included in this routine. Such tests must be performed before calling this routine.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. 
[in]  TRANS  TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**H*x = b. 
[in]  DIAG  DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  A  A is COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). 
[in,out]  X  X is COMPLEX*16 array of dimension at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element righthand side vector b. On exit, X is overwritten with the solution vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
Level 2 Blas routine.  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 150 of file ztrsv.f.