.TH "tbsv" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME tbsv \- tbsv: triangular matrix-vector solve .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBctbsv\fP (uplo, trans, diag, n, k, a, lda, x, incx)" .br .RI "\fBCTBSV\fP " .ti -1c .RI "subroutine \fBdtbsv\fP (uplo, trans, diag, n, k, a, lda, x, incx)" .br .RI "\fBDTBSV\fP " .ti -1c .RI "subroutine \fBstbsv\fP (uplo, trans, diag, n, k, a, lda, x, incx)" .br .RI "\fBSTBSV\fP " .ti -1c .RI "subroutine \fBztbsv\fP (uplo, trans, diag, n, k, a, lda, x, incx)" .br .RI "\fBZTBSV\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine ctbsv (character uplo, character trans, character diag, integer n, integer k, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx)" .PP \fBCTBSV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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 !> non-unit, upper or lower triangular band matrix, with ( k + 1 ) !> diagonals\&. !> !> No test for singularity or near-singularity is included in this !> routine\&. Such tests must be performed before calling this routine\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> 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\&. !> .fi .PP .br \fITRANS\fP .PP .nf !> 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\&. !> .fi .PP .br \fIDIAG\fP .PP .nf !> 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\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> On entry, N specifies the order of the matrix A\&. !> N must be at least zero\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> On entry with UPLO = 'U' or 'u', K specifies the number of !> super-diagonals of the matrix A\&. !> On entry with UPLO = 'L' or 'l', K specifies the number of !> sub-diagonals of the matrix A\&. !> K must satisfy 0 \&.le\&. K\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, 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 super-diagonal 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 sub-diagonal 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> 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 )\&. !> .fi .PP .br \fIX\fP .PP .nf !> X is COMPLEX array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) )\&. !> Before entry, the incremented array X must contain the n !> element right-hand side vector b\&. On exit, X is overwritten !> with the solution vector x\&. !> .fi .PP .br \fIINCX\fP .PP .nf !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X\&. INCX must not be zero\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> Level 2 Blas routine\&. !> !> -- Written on 22-October-1986\&. !> Jack Dongarra, Argonne National Lab\&. !> Jeremy Du Croz, Nag Central Office\&. !> Sven Hammarling, Nag Central Office\&. !> Richard Hanson, Sandia National Labs\&. !> .fi .PP .RE .PP .PP Definition at line \fB188\fP of file \fBctbsv\&.f\fP\&. .SS "subroutine dtbsv (character uplo, character trans, character diag, integer n, integer k, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx)" .PP \fBDTBSV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DTBSV solves one of the systems of equations !> !> A*x = b, or A**T*x = b, !> !> where b and x are n element vectors and A is an n by n unit, or !> non-unit, upper or lower triangular band matrix, with ( k + 1 ) !> diagonals\&. !> !> No test for singularity or near-singularity is included in this !> routine\&. Such tests must be performed before calling this routine\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> 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\&. !> .fi .PP .br \fITRANS\fP .PP .nf !> 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**T*x = b\&. !> .fi .PP .br \fIDIAG\fP .PP .nf !> 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\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> On entry, N specifies the order of the matrix A\&. !> N must be at least zero\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> On entry with UPLO = 'U' or 'u', K specifies the number of !> super-diagonals of the matrix A\&. !> On entry with UPLO = 'L' or 'l', K specifies the number of !> sub-diagonals of the matrix A\&. !> K must satisfy 0 \&.le\&. K\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, 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 super-diagonal 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 sub-diagonal 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> 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 )\&. !> .fi .PP .br \fIX\fP .PP .nf !> X is DOUBLE PRECISION array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) )\&. !> Before entry, the incremented array X must contain the n !> element right-hand side vector b\&. On exit, X is overwritten !> with the solution vector x\&. !> .fi .PP .br \fIINCX\fP .PP .nf !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X\&. INCX must not be zero\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> Level 2 Blas routine\&. !> !> -- Written on 22-October-1986\&. !> Jack Dongarra, Argonne National Lab\&. !> Jeremy Du Croz, Nag Central Office\&. !> Sven Hammarling, Nag Central Office\&. !> Richard Hanson, Sandia National Labs\&. !> .fi .PP .RE .PP .PP Definition at line \fB188\fP of file \fBdtbsv\&.f\fP\&. .SS "subroutine stbsv (character uplo, character trans, character diag, integer n, integer k, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx)" .PP \fBSTBSV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> STBSV solves one of the systems of equations !> !> A*x = b, or A**T*x = b, !> !> where b and x are n element vectors and A is an n by n unit, or !> non-unit, upper or lower triangular band matrix, with ( k + 1 ) !> diagonals\&. !> !> No test for singularity or near-singularity is included in this !> routine\&. Such tests must be performed before calling this routine\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> 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\&. !> .fi .PP .br \fITRANS\fP .PP .nf !> 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**T*x = b\&. !> .fi .PP .br \fIDIAG\fP .PP .nf !> 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\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> On entry, N specifies the order of the matrix A\&. !> N must be at least zero\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> On entry with UPLO = 'U' or 'u', K specifies the number of !> super-diagonals of the matrix A\&. !> On entry with UPLO = 'L' or 'l', K specifies the number of !> sub-diagonals of the matrix A\&. !> K must satisfy 0 \&.le\&. K\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, 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 super-diagonal 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 sub-diagonal 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> 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 )\&. !> .fi .PP .br \fIX\fP .PP .nf !> X is REAL array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) )\&. !> Before entry, the incremented array X must contain the n !> element right-hand side vector b\&. On exit, X is overwritten !> with the solution vector x\&. !> .fi .PP .br \fIINCX\fP .PP .nf !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X\&. INCX must not be zero\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> Level 2 Blas routine\&. !> !> -- Written on 22-October-1986\&. !> Jack Dongarra, Argonne National Lab\&. !> Jeremy Du Croz, Nag Central Office\&. !> Sven Hammarling, Nag Central Office\&. !> Richard Hanson, Sandia National Labs\&. !> .fi .PP .RE .PP .PP Definition at line \fB188\fP of file \fBstbsv\&.f\fP\&. .SS "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)" .PP \fBZTBSV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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 !> non-unit, upper or lower triangular band matrix, with ( k + 1 ) !> diagonals\&. !> !> No test for singularity or near-singularity is included in this !> routine\&. Such tests must be performed before calling this routine\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> 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\&. !> .fi .PP .br \fITRANS\fP .PP .nf !> 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\&. !> .fi .PP .br \fIDIAG\fP .PP .nf !> 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\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> On entry, N specifies the order of the matrix A\&. !> N must be at least zero\&. !> .fi .PP .br \fIK\fP .PP .nf !> K is INTEGER !> On entry with UPLO = 'U' or 'u', K specifies the number of !> super-diagonals of the matrix A\&. !> On entry with UPLO = 'L' or 'l', K specifies the number of !> sub-diagonals of the matrix A\&. !> K must satisfy 0 \&.le\&. K\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, 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 super-diagonal 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 sub-diagonal 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> 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 )\&. !> .fi .PP .br \fIX\fP .PP .nf !> X is COMPLEX*16 array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) )\&. !> Before entry, the incremented array X must contain the n !> element right-hand side vector b\&. On exit, X is overwritten !> with the solution vector x\&. !> .fi .PP .br \fIINCX\fP .PP .nf !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X\&. INCX must not be zero\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> Level 2 Blas routine\&. !> !> -- Written on 22-October-1986\&. !> Jack Dongarra, Argonne National Lab\&. !> Jeremy Du Croz, Nag Central Office\&. !> Sven Hammarling, Nag Central Office\&. !> Richard Hanson, Sandia National Labs\&. !> .fi .PP .RE .PP .PP Definition at line \fB188\fP of file \fBztbsv\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.