LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
subroutine  cgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
CGBMV  
subroutine  cgemv (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
CGEMV  
subroutine  cgerc (M, N, ALPHA, X, INCX, Y, INCY, A, LDA) 
CGERC  
subroutine  cgeru (M, N, ALPHA, X, INCX, Y, INCY, A, LDA) 
CGERU  
subroutine  chbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
CHBMV  
subroutine  chemv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
CHEMV  
subroutine  cher (UPLO, N, ALPHA, X, INCX, A, LDA) 
CHER  
subroutine  cher2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA) 
CHER2  
subroutine  chpmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY) 
CHPMV  
subroutine  chpr (UPLO, N, ALPHA, X, INCX, AP) 
CHPR  
subroutine  chpr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP) 
CHPR2  
subroutine  ctbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) 
CTBMV  
subroutine  ctbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) 
CTBSV  
subroutine  ctpmv (UPLO, TRANS, DIAG, N, AP, X, INCX) 
CTPMV  
subroutine  ctpsv (UPLO, TRANS, DIAG, N, AP, X, INCX) 
CTPSV  
subroutine  ctrmv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) 
CTRMV  
subroutine  ctrsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) 
CTRSV 
This is the group of complex LEVEL 2 BLAS routines.
subroutine cgbmv  (  character  TRANS, 
integer  M,  
integer  N,  
integer  KL,  
integer  KU,  
complex  ALPHA,  
complex, dimension(lda,*)  A,  
integer  LDA,  
complex, dimension(*)  X,  
integer  INCX,  
complex  BETA,  
complex, dimension(*)  Y,  
integer  INCY  
) 
CGBMV
CGBMV 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 On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is COMPLEX 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 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 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 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 cgbmv.f.
subroutine cgemv  (  character  TRANS, 
integer  M,  
integer  N,  
complex  ALPHA,  
complex, dimension(lda,*)  A,  
integer  LDA,  
complex, dimension(*)  X,  
integer  INCX,  
complex  BETA,  
complex, dimension(*)  Y,  
integer  INCY  
) 
CGEMV
CGEMV 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 On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is COMPLEX 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 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 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 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 cgemv.f.
subroutine cgerc  (  integer  M, 
integer  N,  
complex  ALPHA,  
complex, dimension(*)  X,  
integer  INCX,  
complex, dimension(*)  Y,  
integer  INCY,  
complex, dimension(lda,*)  A,  
integer  LDA  
) 
CGERC
CGERC 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 On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX 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 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 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 cgerc.f.
subroutine cgeru  (  integer  M, 
integer  N,  
complex  ALPHA,  
complex, dimension(*)  X,  
integer  INCX,  
complex, dimension(*)  Y,  
integer  INCY,  
complex, dimension(lda,*)  A,  
integer  LDA  
) 
CGERU
CGERU 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 On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX 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 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 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 cgeru.f.
subroutine chbmv  (  character  UPLO, 
integer  N,  
integer  K,  
complex  ALPHA,  
complex, dimension(lda,*)  A,  
integer  LDA,  
complex, dimension(*)  X,  
integer  INCX,  
complex  BETA,  
complex, dimension(*)  Y,  
integer  INCY  
) 
CHBMV
CHBMV 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 On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is COMPLEX 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 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 On entry, BETA specifies the scalar beta. 
[in,out]  Y  Y is COMPLEX 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 chbmv.f.
subroutine chemv  (  character  UPLO, 
integer  N,  
complex  ALPHA,  
complex, dimension(lda,*)  A,  
integer  LDA,  
complex, dimension(*)  X,  
integer  INCX,  
complex  BETA,  
complex, dimension(*)  Y,  
integer  INCY  
) 
CHEMV
CHEMV 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 On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is COMPLEX 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 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 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 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 chemv.f.
subroutine cher  (  character  UPLO, 
integer  N,  
real  ALPHA,  
complex, dimension(*)  X,  
integer  INCX,  
complex, dimension(lda,*)  A,  
integer  LDA  
) 
CHER
CHER 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 REAL On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX 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 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 cher.f.
subroutine cher2  (  character  UPLO, 
integer  N,  
complex  ALPHA,  
complex, dimension(*)  X,  
integer  INCX,  
complex, dimension(*)  Y,  
integer  INCY,  
complex, dimension(lda,*)  A,  
integer  LDA  
) 
CHER2
CHER2 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 On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX 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 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 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 cher2.f.
subroutine chpmv  (  character  UPLO, 
integer  N,  
complex  ALPHA,  
complex, dimension(*)  AP,  
complex, dimension(*)  X,  
integer  INCX,  
complex  BETA,  
complex, dimension(*)  Y,  
integer  INCY  
) 
CHPMV
CHPMV 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 On entry, ALPHA specifies the scalar alpha. 
[in]  AP  AP is COMPLEX 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 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 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 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 chpmv.f.
subroutine chpr  (  character  UPLO, 
integer  N,  
real  ALPHA,  
complex, dimension(*)  X,  
integer  INCX,  
complex, dimension(*)  AP  
) 
CHPR
CHPR 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 REAL On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX 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 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 chpr.f.
subroutine chpr2  (  character  UPLO, 
integer  N,  
complex  ALPHA,  
complex, dimension(*)  X,  
integer  INCX,  
complex, dimension(*)  Y,  
integer  INCY,  
complex, dimension(*)  AP  
) 
CHPR2
CHPR2 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 On entry, ALPHA specifies the scalar alpha. 
[in]  X  X is COMPLEX 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 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 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 chpr2.f.
subroutine ctbmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
integer  K,  
complex, dimension(lda,*)  A,  
integer  LDA,  
complex, dimension(*)  X,  
integer  INCX  
) 
CTBMV
CTBMV 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 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 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 ctbmv.f.
subroutine ctbsv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
integer  K,  
complex, dimension(lda,*)  A,  
integer  LDA,  
complex, dimension(*)  X,  
integer  INCX  
) 
CTBSV
CTBSV 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 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 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 ctbsv.f.
subroutine ctpmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
complex, dimension(*)  AP,  
complex, dimension(*)  X,  
integer  INCX  
) 
CTPMV
CTPMV 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 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 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 ctpmv.f.
subroutine ctpsv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
complex, dimension(*)  AP,  
complex, dimension(*)  X,  
integer  INCX  
) 
CTPSV
CTPSV 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 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 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 ctpsv.f.
subroutine ctrmv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
complex, dimension(lda,*)  A,  
integer  LDA,  
complex, dimension(*)  X,  
integer  INCX  
) 
CTRMV
CTRMV 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 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 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 ctrmv.f.
subroutine ctrsv  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
complex, dimension(lda,*)  A,  
integer  LDA,  
complex, dimension(*)  X,  
integer  INCX  
) 
CTRSV
CTRSV 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 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 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 ctrsv.f.