.TH "single_blas_level2" 3 "Sun Nov 27 2022" "Version 3.11.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME single_blas_level2 \- real .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBsgbmv\fP (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)" .br .RI "\fBSGBMV\fP " .ti -1c .RI "subroutine \fBsgemv\fP (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)" .br .RI "\fBSGEMV\fP " .ti -1c .RI "subroutine \fBsger\fP (M, N, ALPHA, X, INCX, Y, INCY, A, LDA)" .br .RI "\fBSGER\fP " .ti -1c .RI "subroutine \fBssbmv\fP (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)" .br .RI "\fBSSBMV\fP " .ti -1c .RI "subroutine \fBsspmv\fP (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)" .br .RI "\fBSSPMV\fP " .ti -1c .RI "subroutine \fBsspr\fP (UPLO, N, ALPHA, X, INCX, AP)" .br .RI "\fBSSPR\fP " .ti -1c .RI "subroutine \fBsspr2\fP (UPLO, N, ALPHA, X, INCX, Y, INCY, AP)" .br .RI "\fBSSPR2\fP " .ti -1c .RI "subroutine \fBssymv\fP (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)" .br .RI "\fBSSYMV\fP " .ti -1c .RI "subroutine \fBssyr\fP (UPLO, N, ALPHA, X, INCX, A, LDA)" .br .RI "\fBSSYR\fP " .ti -1c .RI "subroutine \fBssyr2\fP (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)" .br .RI "\fBSSYR2\fP " .ti -1c .RI "subroutine \fBstbmv\fP (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)" .br .RI "\fBSTBMV\fP " .ti -1c .RI "subroutine \fBstbsv\fP (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)" .br .RI "\fBSTBSV\fP " .ti -1c .RI "subroutine \fBstpmv\fP (UPLO, TRANS, DIAG, N, AP, X, INCX)" .br .RI "\fBSTPMV\fP " .ti -1c .RI "subroutine \fBstpsv\fP (UPLO, TRANS, DIAG, N, AP, X, INCX)" .br .RI "\fBSTPSV\fP " .ti -1c .RI "subroutine \fBstrmv\fP (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)" .br .RI "\fBSTRMV\fP " .ti -1c .RI "subroutine \fBstrsv\fP (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)" .br .RI "\fBSTRSV\fP " .in -1c .SH "Detailed Description" .PP This is the group of real LEVEL 2 BLAS routines\&. .SH "Function Documentation" .PP .SS "subroutine sgbmv (character TRANS, integer M, integer N, integer KL, integer KU, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)" .PP \fBSGBMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGBMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*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 sub-diagonals and ku super-diagonals\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf 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**T*x + beta*y\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix A\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIKL\fP .PP .nf KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A\&. KL must satisfy 0 \&.le\&. KL\&. .fi .PP .br \fIKU\fP .PP .nf KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A\&. KU must satisfy 0 \&.le\&. KU\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, 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 super-diagonal starting at position 2 in row ku, the first sub-diagonal 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 .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 ( kl + ku + 1 )\&. .fi .PP .br \fIX\fP .PP .nf X is REAL array, 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\&. .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 .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then Y need not be set on input\&. .fi .PP .br \fIY\fP .PP .nf Y is REAL array, 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\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY 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\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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 .SS "subroutine sgemv (character TRANS, integer M, integer N, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)" .PP \fBSGEMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf 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**T*x + beta*y\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix A\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension ( LDA, N ) Before entry, the leading m by n part of the array A must contain the matrix of coefficients\&. .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 max( 1, m )\&. .fi .PP .br \fIX\fP .PP .nf X is REAL array, 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\&. .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 .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then Y need not be set on input\&. .fi .PP .br \fIY\fP .PP .nf Y is REAL array, 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 non-zero, the incremented array Y must contain the vector y\&. On exit, Y is overwritten by the updated vector y\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY 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\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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 .SS "subroutine sger (integer M, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) Y, integer INCY, real, dimension(lda,*) A, integer LDA)" .PP \fBSGER\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGER 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER On entry, M specifies the number of rows of the matrix A\&. M must be at least zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the number of columns of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIX\fP .PP .nf X is REAL array, dimension at least ( 1 + ( m - 1 )*abs( INCX ) )\&. Before entry, the incremented array X must contain the m element 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 .br \fIY\fP .PP .nf Y is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) )\&. Before entry, the incremented array Y must contain the n element vector y\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, 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\&. .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 max( 1, m )\&. .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 .SS "subroutine ssbmv (character UPLO, integer N, integer K, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)" .PP \fBSSBMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSBMV performs the matrix-vector 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 symmetric band matrix, with k super-diagonals\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .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, K specifies the number of super-diagonals of the matrix A\&. K must satisfy 0 \&.le\&. K\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .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 symmetric matrix, 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 the upper triangular part of a symmetric 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 symmetric matrix, 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 the lower triangular part of a symmetric 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 .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 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 .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIY\fP .PP .nf Y is REAL array, 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\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY 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\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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 .SS "subroutine sspmv (character UPLO, integer N, real ALPHA, real, dimension(*) AP, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)" .PP \fBSSPMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSPMV performs the matrix-vector 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 symmetric matrix, supplied in packed form\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .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 \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIAP\fP .PP .nf AP is REAL array, 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 symmetric 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 symmetric 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\&. .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 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 .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then Y need not be set on input\&. .fi .PP .br \fIY\fP .PP .nf Y is REAL array, 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\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY 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\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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 .SS "subroutine sspr (character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) AP)" .PP \fBSSPR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSPR performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .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 \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .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 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 .br \fIAP\fP .PP .nf AP is REAL array, 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 symmetric 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 symmetric 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\&. .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 .SS "subroutine sspr2 (character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) Y, integer INCY, real, dimension(*) AP)" .PP \fBSSPR2\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSPR2 performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .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 \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .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 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 .br \fIY\fP .PP .nf Y is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) )\&. Before entry, the incremented array Y must contain the n element vector y\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .br \fIAP\fP .PP .nf AP is REAL array, 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 symmetric 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 symmetric 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\&. .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 .SS "subroutine ssymv (character UPLO, integer N, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY)" .PP \fBSSYMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSYMV performs the matrix-vector 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 symmetric matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .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 \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, 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 symmetric 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 symmetric matrix and the strictly upper triangular part of A is not referenced\&. .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 max( 1, n )\&. .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 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 .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. When BETA is supplied as zero then Y need not be set on input\&. .fi .PP .br \fIY\fP .PP .nf Y is REAL array, 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\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY 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\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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 .SS "subroutine ssyr (character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(lda,*) A, integer LDA)" .PP \fBSSYR\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSYR performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .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 \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .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 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 .br \fIA\fP .PP .nf A is REAL array, 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 symmetric 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 symmetric 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\&. .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 max( 1, n )\&. .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 .SS "subroutine ssyr2 (character UPLO, integer N, real ALPHA, real, dimension(*) X, integer INCX, real, dimension(*) Y, integer INCY, real, dimension(lda,*) A, integer LDA)" .PP \fBSSYR2\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSYR2 performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .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 \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .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 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 .br \fIY\fP .PP .nf Y is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) )\&. Before entry, the incremented array Y must contain the n element vector y\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, 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 symmetric 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 symmetric 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\&. .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 max( 1, n )\&. .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 .SS "subroutine stbmv (character UPLO, character TRANS, character DIAG, integer N, integer K, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX)" .PP \fBSTBMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf STBMV performs one of the matrix-vector operations x := A*x, or x := A**T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals\&. .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 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**T*x\&. .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 vector x\&. On exit, X is overwritten with the transformed 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\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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 .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 .SS "subroutine stpmv (character UPLO, character TRANS, character DIAG, integer N, real, dimension(*) AP, real, dimension(*) X, integer INCX)" .PP \fBSTPMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf STPMV performs one of the matrix-vector operations x := A*x, or x := A**T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form\&. .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 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**T*x\&. .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 \fIAP\fP .PP .nf AP is REAL array, 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\&. .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 vector x\&. On exit, X is overwritten with the transformed 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\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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 .SS "subroutine stpsv (character UPLO, character TRANS, character DIAG, integer N, real, dimension(*) AP, real, dimension(*) X, integer INCX)" .PP \fBSTPSV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf STPSV 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 matrix, supplied in packed form\&. 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 \fIAP\fP .PP .nf AP is REAL array, 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\&. .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 .SS "subroutine strmv (character UPLO, character TRANS, character DIAG, integer N, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX)" .PP \fBSTRMV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf STRMV performs one of the matrix-vector operations x := A*x, or x := A**T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix\&. .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 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**T*x\&. .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 \fIA\fP .PP .nf A is REAL array, 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\&. .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 max( 1, n )\&. .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 vector x\&. On exit, X is overwritten with the transformed 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\&. The vector and matrix arguments are not referenced when N = 0, or M = 0 -- 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 .SS "subroutine strsv (character UPLO, character TRANS, character DIAG, integer N, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX)" .PP \fBSTRSV\fP .PP \fBPurpose:\fP .RS 4 .PP .nf STRSV 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 matrix\&. 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 \fIA\fP .PP .nf A is REAL array, 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\&. .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 max( 1, n )\&. .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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.